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    Source code for qiskit.providers.backend

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +
    +# pylint: disable=invalid-name
    +
    +"""Backend abstract interface for providers."""
    +
    +
    +from abc import ABC
    +from abc import abstractmethod
    +import datetime
    +from typing import List, Union, Iterable, Tuple
    +
    +from qiskit.providers.provider import Provider
    +from qiskit.providers.models.backendstatus import BackendStatus
    +from qiskit.circuit.gate import Instruction
    +
    +
    +class Backend:
    +    """Base common type for all versioned Backend abstract classes.
    +
    +    Note this class should not be inherited from directly, it is intended
    +    to be used for type checking. When implementing a provider you should use
    +    the versioned abstract classes as the parent class and not this class
    +    directly.
    +    """
    +
    +    version = 0
    +
    +
    +class BackendV1(Backend, ABC):
    +    """Abstract class for Backends
    +
    +    This abstract class is to be used for all Backend objects created by a
    +    provider. There are several classes of information contained in a Backend.
    +    The first are the attributes of the class itself. These should be used to
    +    defined the immutable characteristics of the backend. The ``options``
    +    attribute of the backend is used to contain the dynamic user configurable
    +    options of the backend. It should be used more for runtime options
    +    that configure how the backend is used. For example, something like a
    +    ``shots`` field for a backend that runs experiments which would contain an
    +    int for how many shots to execute. The ``properties`` attribute is
    +    optionally defined :class:`~qiskit.providers.models.BackendProperties`
    +    object and is used to return measured properties, or properties
    +    of a backend that may change over time. The simplest example of this would
    +    be a version string, which will change as a backend is updated, but also
    +    could be something like noise parameters for backends that run experiments.
    +
    +    This first version of the Backend abstract class is written to be mostly
    +    backwards compatible with the legacy providers interface. This includes reusing
    +    the model objects :class:`~qiskit.providers.models.BackendProperties` and
    +    :class:`~qiskit.providers.models.BackendConfiguration`. This was done to
    +    ease the transition for users and provider maintainers to the new versioned providers.
    +    Expect, future versions of this abstract class to change the data model and
    +    interface.
    +
    +    Subclasses of this should override the public method :meth:`run` and the internal
    +    :meth:`_default_options`:
    +
    +    .. automethod:: _default_options
    +    """
    +
    +    version = 1
    +
    +    def __init__(self, configuration, provider=None, **fields):
    +        """Initialize a backend class
    +
    +        Args:
    +            configuration (BackendConfiguration): A backend configuration
    +                object for the backend object.
    +            provider (qiskit.providers.Provider): Optionally, the provider
    +                object that this Backend comes from.
    +            fields: kwargs for the values to use to override the default
    +                options.
    +        Raises:
    +            AttributeError: if input field not a valid options
    +
    +        ..
    +            This next bit is necessary just because autosummary generally won't summarise private
    +            methods; changing that behaviour would have annoying knock-on effects through all the
    +            rest of the documentation, so instead we just hard-code the automethod directive.
    +
    +        In addition to the public abstract methods, subclasses should also implement the following
    +        private methods:
    +
    +        .. automethod:: _default_options
    +           :noindex:
    +        """
    +        self._configuration = configuration
    +        self._options = self._default_options()
    +        self._provider = provider
    +        if fields:
    +            for field in fields:
    +                if field not in self._options.data:
    +                    raise AttributeError("Options field %s is not valid for this backend" % field)
    +            self._options.update_config(**fields)
    +
    +    @classmethod
    +    @abstractmethod
    +    def _default_options(cls):
    +        """Return the default options
    +
    +        This method will return a :class:`qiskit.providers.Options`
    +        subclass object that will be used for the default options. These
    +        should be the default parameters to use for the options of the
    +        backend.
    +
    +        Returns:
    +            qiskit.providers.Options: A options object with
    +                default values set
    +        """
    +
    +    def set_options(self, **fields):
    +        """Set the options fields for the backend
    +
    +        This method is used to update the options of a backend. If
    +        you need to change any of the options prior to running just
    +        pass in the kwarg with the new value for the options.
    +
    +        Args:
    +            fields: The fields to update the options
    +
    +        Raises:
    +            AttributeError: If the field passed in is not part of the
    +                options
    +        """
    +        for field in fields:
    +            if not hasattr(self._options, field):
    +                raise AttributeError("Options field %s is not valid for this backend" % field)
    +        self._options.update_options(**fields)
    +
    +    def configuration(self):
    +        """Return the backend configuration.
    +
    +        Returns:
    +            BackendConfiguration: the configuration for the backend.
    +        """
    +        return self._configuration
    +
    +    def properties(self):
    +        """Return the backend properties.
    +
    +        Returns:
    +            BackendProperties: the configuration for the backend. If the backend
    +            does not support properties, it returns ``None``.
    +        """
    +        return None
    +
    +    def provider(self):
    +        """Return the backend Provider.
    +
    +        Returns:
    +            Provider: the Provider responsible for the backend.
    +        """
    +        return self._provider
    +
    +    def status(self):
    +        """Return the backend status.
    +
    +        Returns:
    +            BackendStatus: the status of the backend.
    +        """
    +        return BackendStatus(
    +            backend_name=self.name(),
    +            backend_version="1",
    +            operational=True,
    +            pending_jobs=0,
    +            status_msg="",
    +        )
    +
    +    def name(self):
    +        """Return the backend name.
    +
    +        Returns:
    +            str: the name of the backend.
    +        """
    +        return self._configuration.backend_name
    +
    +    def __str__(self):
    +        return self.name()
    +
    +    def __repr__(self):
    +        """Official string representation of a Backend.
    +
    +        Note that, by Qiskit convention, it is consciously *not* a fully valid
    +        Python expression. Subclasses should provide 'a string of the form
    +        <...some useful description...>'. [0]
    +
    +        [0] https://docs.python.org/3/reference/datamodel.html#object.__repr__
    +        """
    +        return f"<{self.__class__.__name__}('{self.name()}')>"
    +
    +    @property
    +    def options(self):
    +        """Return the options for the backend
    +
    +        The options of a backend are the dynamic parameters defining
    +        how the backend is used. These are used to control the :meth:`run`
    +        method.
    +        """
    +        return self._options
    +
    +    @abstractmethod
    +    def run(self, run_input, **options):
    +        """Run on the backend.
    +
    +        This method returns a :class:`~qiskit.providers.Job` object
    +        that runs circuits. Depending on the backend this may be either an async
    +        or sync call. It is at the discretion of the provider to decide whether
    +        running should block until the execution is finished or not: the Job
    +        class can handle either situation.
    +
    +        Args:
    +            run_input (QuantumCircuit or Schedule or list): An individual or a
    +                list of :class:`~qiskit.circuit.QuantumCircuit` or
    +                :class:`~qiskit.pulse.Schedule` objects to run on the backend.
    +                For legacy providers migrating to the new versioned providers,
    +                provider interface a :class:`~qiskit.qobj.QasmQobj` or
    +                :class:`~qiskit.qobj.PulseQobj` objects should probably be
    +                supported too (but deprecated) for backwards compatibility. Be
    +                sure to update the docstrings of subclasses implementing this
    +                method to document that. New provider implementations should not
    +                do this though as :mod:`qiskit.qobj` will be deprecated and
    +                removed along with the legacy providers interface.
    +            options: Any kwarg options to pass to the backend for running the
    +                config. If a key is also present in the options
    +                attribute/object then the expectation is that the value
    +                specified will be used instead of what's set in the options
    +                object.
    +        Returns:
    +            Job: The job object for the run
    +        """
    +        pass
    +
    +
    +class QubitProperties:
    +    """A representation of the properties of a qubit on a backend.
    +
    +    This class provides the optional properties that a backend can provide for
    +    a qubit. These represent the set of qubit properties that Qiskit can
    +    currently work with if present. However if your backend provides additional
    +    properties of qubits you should subclass this to add additional custom
    +    attributes for those custom/additional properties provided by the backend.
    +    """
    +
    +    __slots__ = ("t1", "t2", "frequency")
    +
    +    def __init__(self, t1=None, t2=None, frequency=None):
    +        """Create a new :class:`QubitProperties` object.
    +
    +        Args:
    +            t1: The T1 time for a qubit in seconds
    +            t2: The T2 time for a qubit in seconds
    +            frequency: The frequency of a qubit in Hz
    +        """
    +        self.t1 = t1
    +        self.t2 = t2
    +        self.frequency = frequency
    +
    +    def __repr__(self):
    +        return f"QubitProperties(t1={self.t1}, t2={self.t2}, " f"frequency={self.frequency})"
    +
    +
    +class BackendV2(Backend, ABC):
    +    """Abstract class for Backends
    +
    +    This abstract class is to be used for all Backend objects created by a
    +    provider. This version differs from earlier abstract Backend classes in
    +    that the configuration attribute no longer exists. Instead, attributes
    +    exposing equivalent required immutable properties of the backend device
    +    are added. For example ``backend.configuration().n_qubits`` is accessible
    +    from ``backend.num_qubits`` now.
    +
    +    The ``options`` attribute of the backend is used to contain the dynamic
    +    user configurable options of the backend. It should be used more for
    +    runtime options that configure how the backend is used. For example,
    +    something like a ``shots`` field for a backend that runs experiments which
    +    would contain an int for how many shots to execute.
    +
    +    If migrating a provider from :class:`~qiskit.providers.BackendV1`
    +    one thing to keep in mind is for
    +    backwards compatibility you might need to add a configuration method that
    +    will build a :class:`~qiskit.providers.models.BackendConfiguration` object
    +    and :class:`~qiskit.providers.models.BackendProperties` from the attributes
    +    defined in this class for backwards compatibility.
    +
    +    A backend object can optionally contain methods named
    +    ``get_translation_stage_plugin`` and ``get_scheduling_stage_plugin``. If these
    +    methods are present on a backend object and this object is used for
    +    :func:`~.transpile` or :func:`~.generate_preset_pass_manager` the
    +    transpilation process will default to using the output from those methods
    +    as the scheduling stage and the translation compilation stage. This
    +    enables a backend which has custom requirements for compilation to specify a
    +    stage plugin for these stages to enable custom transformation of
    +    the circuit to ensure it is runnable on the backend. These hooks are enabled
    +    by default and should only be used to enable extra compilation steps
    +    if they are **required** to ensure a circuit is executable on the backend or
    +    have the expected level of performance. These methods are passed no input
    +    arguments and are expected to return a ``str`` representing the method name
    +    which should be a stage plugin (see: :mod:`qiskit.transpiler.preset_passmanagers.plugin`
    +    for more details on plugins). The typical expected use case is for a backend
    +    provider to implement a stage plugin for ``translation`` or ``scheduling``
    +    that contains the custom compilation passes and then for the hook methods on
    +    the backend object to return the plugin name so that :func:`~.transpile` will
    +    use it by default when targetting the backend.
    +
    +    Subclasses of this should override the public method :meth:`run` and the internal
    +    :meth:`_default_options`:
    +
    +    .. automethod:: _default_options
    +    """
    +
    +    version = 2
    +
    +    def __init__(
    +        self,
    +        provider: Provider = None,
    +        name: str = None,
    +        description: str = None,
    +        online_date: datetime.datetime = None,
    +        backend_version: str = None,
    +        **fields,
    +    ):
    +        """Initialize a BackendV2 based backend
    +
    +        Args:
    +            provider: An optional backwards reference to the
    +                :class:`~qiskit.providers.Provider` object that the backend
    +                is from
    +            name: An optional name for the backend
    +            description: An optional description of the backend
    +            online_date: An optional datetime the backend was brought online
    +            backend_version: An optional backend version string. This differs
    +                from the :attr:`~qiskit.providers.BackendV2.version` attribute
    +                as :attr:`~qiskit.providers.BackendV2.version` is for the
    +                abstract :attr:`~qiskit.providers.Backend` abstract interface
    +                version of the object while ``backend_version`` is for
    +                versioning the backend itself.
    +            fields: kwargs for the values to use to override the default
    +                options.
    +
    +        Raises:
    +            AttributeError: If a field is specified that's outside the backend's
    +                options
    +        """
    +
    +        self._options = self._default_options()
    +        self._provider = provider
    +        if fields:
    +            for field in fields:
    +                if field not in self._options.data:
    +                    raise AttributeError("Options field %s is not valid for this backend" % field)
    +            self._options.update_config(**fields)
    +        self.name = name
    +        """Name of the backend."""
    +        self.description = description
    +        """Optional human-readable description."""
    +        self.online_date = online_date
    +        """Date that the backend came online."""
    +        self.backend_version = backend_version
    +        """Version of the backend being provided.  This is not the same as
    +        :attr:`.BackendV2.version`, which is the version of the :class:`~.providers.Backend`
    +        abstract interface."""
    +        self._coupling_map = None
    +
    +    @property
    +    def instructions(self) -> List[Tuple[Instruction, Tuple[int]]]:
    +        """A list of Instruction tuples on the backend of the form ``(instruction, (qubits)``"""
    +        return self.target.instructions
    +
    +    @property
    +    def operations(self) -> List[Instruction]:
    +        """A list of :class:`~qiskit.circuit.Instruction` instances that the backend supports."""
    +        return list(self.target.operations)
    +
    +    @property
    +    def operation_names(self) -> List[str]:
    +        """A list of instruction names that the backend supports."""
    +        return list(self.target.operation_names)
    +
    +    @property
    +    @abstractmethod
    +    def target(self):
    +        """A :class:`qiskit.transpiler.Target` object for the backend.
    +
    +        :rtype: Target
    +        """
    +        pass
    +
    +    @property
    +    def num_qubits(self) -> int:
    +        """Return the number of qubits the backend has."""
    +        return self.target.num_qubits
    +
    +    @property
    +    def coupling_map(self):
    +        """Return the :class:`~qiskit.transpiler.CouplingMap` object"""
    +        if self._coupling_map is None:
    +            self._coupling_map = self.target.build_coupling_map()
    +        return self._coupling_map
    +
    +    @property
    +    def instruction_durations(self):
    +        """Return the :class:`~qiskit.transpiler.InstructionDurations` object."""
    +        return self.target.durations()
    +
    +    @property
    +    @abstractmethod
    +    def max_circuits(self):
    +        """The maximum number of circuits (or Pulse schedules) that can be
    +        run in a single job.
    +
    +        If there is no limit this will return None
    +        """
    +        pass
    +
    +    @classmethod
    +    @abstractmethod
    +    def _default_options(cls):
    +        """Return the default options
    +
    +        This method will return a :class:`qiskit.providers.Options`
    +        subclass object that will be used for the default options. These
    +        should be the default parameters to use for the options of the
    +        backend.
    +
    +        Returns:
    +            qiskit.providers.Options: A options object with
    +                default values set
    +        """
    +        pass
    +
    +    @property
    +    def dt(self) -> Union[float, None]:
    +        """Return the system time resolution of input signals
    +
    +        This is required to be implemented if the backend supports Pulse
    +        scheduling.
    +
    +        Returns:
    +            The input signal timestep in seconds. If the backend doesn't define ``dt``, ``None`` will
    +            be returned.
    +        """
    +        return self.target.dt
    +
    +    @property
    +    def dtm(self) -> float:
    +        """Return the system time resolution of output signals
    +
    +        Returns:
    +            The output signal timestep in seconds.
    +
    +        Raises:
    +            NotImplementedError: if the backend doesn't support querying the
    +                output signal timestep
    +        """
    +        raise NotImplementedError
    +
    +    @property
    +    def meas_map(self) -> List[List[int]]:
    +        """Return the grouping of measurements which are multiplexed
    +
    +        This is required to be implemented if the backend supports Pulse
    +        scheduling.
    +
    +        Returns:
    +            The grouping of measurements which are multiplexed
    +
    +        Raises:
    +            NotImplementedError: if the backend doesn't support querying the
    +                measurement mapping
    +        """
    +        raise NotImplementedError
    +
    +    @property
    +    def instruction_schedule_map(self):
    +        """Return the :class:`~qiskit.pulse.InstructionScheduleMap` for the
    +        instructions defined in this backend's target."""
    +        return self.target.instruction_schedule_map()
    +
    +    def qubit_properties(
    +        self, qubit: Union[int, List[int]]
    +    ) -> Union[QubitProperties, List[QubitProperties]]:
    +        """Return QubitProperties for a given qubit.
    +
    +        If there are no defined or the backend doesn't support querying these
    +        details this method does not need to be implemented.
    +
    +        Args:
    +            qubit: The qubit to get the
    +                :class:`.QubitProperties` object for. This can
    +                be a single integer for 1 qubit or a list of qubits and a list
    +                of :class:`.QubitProperties` objects will be
    +                returned in the same order
    +        Returns:
    +            The :class:`~.QubitProperties` object for the
    +            specified qubit. If a list of qubits is provided a list will be
    +            returned. If properties are missing for a qubit this can be
    +            ``None``.
    +
    +        Raises:
    +            NotImplementedError: if the backend doesn't support querying the
    +                qubit properties
    +        """
    +        # Since the target didn't always have a qubit properties attribute
    +        # to ensure the behavior here is backwards compatible with earlier
    +        # BacekendV2 implementations where this would raise a NotImplemented
    +        # error.
    +        if self.target.qubit_properties is None:
    +            raise NotImplementedError
    +        if isinstance(qubit, int):
    +            return self.target.qubit_properties[qubit]
    +        return [self.target.qubit_properties[q] for q in qubit]
    +
    +    def drive_channel(self, qubit: int):
    +        """Return the drive channel for the given qubit.
    +
    +        This is required to be implemented if the backend supports Pulse
    +        scheduling.
    +
    +        Returns:
    +            DriveChannel: The Qubit drive channel
    +
    +        Raises:
    +            NotImplementedError: if the backend doesn't support querying the
    +                measurement mapping
    +        """
    +        raise NotImplementedError
    +
    +    def measure_channel(self, qubit: int):
    +        """Return the measure stimulus channel for the given qubit.
    +
    +        This is required to be implemented if the backend supports Pulse
    +        scheduling.
    +
    +        Returns:
    +            MeasureChannel: The Qubit measurement stimulus line
    +
    +        Raises:
    +            NotImplementedError: if the backend doesn't support querying the
    +                measurement mapping
    +        """
    +        raise NotImplementedError
    +
    +    def acquire_channel(self, qubit: int):
    +        """Return the acquisition channel for the given qubit.
    +
    +        This is required to be implemented if the backend supports Pulse
    +        scheduling.
    +
    +        Returns:
    +            AcquireChannel: The Qubit measurement acquisition line.
    +
    +        Raises:
    +            NotImplementedError: if the backend doesn't support querying the
    +                measurement mapping
    +        """
    +        raise NotImplementedError
    +
    +    def control_channel(self, qubits: Iterable[int]):
    +        """Return the secondary drive channel for the given qubit
    +
    +        This is typically utilized for controlling multiqubit interactions.
    +        This channel is derived from other channels.
    +
    +        This is required to be implemented if the backend supports Pulse
    +        scheduling.
    +
    +        Args:
    +            qubits: Tuple or list of qubits of the form
    +                ``(control_qubit, target_qubit)``.
    +
    +        Returns:
    +            List[ControlChannel]: The multi qubit control line.
    +
    +        Raises:
    +            NotImplementedError: if the backend doesn't support querying the
    +                measurement mapping
    +        """
    +        raise NotImplementedError
    +
    +    def set_options(self, **fields):
    +        """Set the options fields for the backend
    +
    +        This method is used to update the options of a backend. If
    +        you need to change any of the options prior to running just
    +        pass in the kwarg with the new value for the options.
    +
    +        Args:
    +            fields: The fields to update the options
    +
    +        Raises:
    +            AttributeError: If the field passed in is not part of the
    +                options
    +        """
    +        for field in fields:
    +            if not hasattr(self._options, field):
    +                raise AttributeError("Options field %s is not valid for this backend" % field)
    +        self._options.update_options(**fields)
    +
    +    @property
    +    def options(self):
    +        """Return the options for the backend
    +
    +        The options of a backend are the dynamic parameters defining
    +        how the backend is used. These are used to control the :meth:`run`
    +        method.
    +        """
    +        return self._options
    +
    +    @property
    +    def provider(self):
    +        """Return the backend Provider.
    +
    +        Returns:
    +            Provider: the Provider responsible for the backend.
    +        """
    +        return self._provider
    +
    +    @abstractmethod
    +    def run(self, run_input, **options):
    +        """Run on the backend.
    +
    +        This method returns a :class:`~qiskit.providers.Job` object
    +        that runs circuits. Depending on the backend this may be either an async
    +        or sync call. It is at the discretion of the provider to decide whether
    +        running should block until the execution is finished or not: the Job
    +        class can handle either situation.
    +
    +        Args:
    +            run_input (QuantumCircuit or Schedule or ScheduleBlock or list): An
    +                individual or a list of :class:`.QuantumCircuit`,
    +                :class:`~qiskit.pulse.ScheduleBlock`, or :class:`~qiskit.pulse.Schedule` objects to
    +                run on the backend.
    +            options: Any kwarg options to pass to the backend for running the
    +                config. If a key is also present in the options
    +                attribute/object then the expectation is that the value
    +                specified will be used instead of what's set in the options
    +                object.
    +
    +        Returns:
    +            Job: The job object for the run
    +        """
    +        pass
    +
    +
    +
    +
    + +
    +
    + + Made with Sphinx and @pradyunsg's + + Furo +
    + Last updated on 2024/03/18
    +
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/array/array.html b/stable/0.4/_modules/qiskit_dynamics/array/array.html new file mode 100644 index 000000000..2054dba2b --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/array/array.html @@ -0,0 +1,647 @@ + + + + + + + + qiskit_dynamics.array.array - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    +

    Source code for qiskit_dynamics.array.array

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +
    +"""Array Class"""
    +
    +import copy
    +from functools import wraps
    +from types import BuiltinMethodType, MethodType
    +from typing import Any, Optional, Union, Tuple, Set
    +from numbers import Number
    +
    +import numpy
    +from numpy.lib.mixins import NDArrayOperatorsMixin
    +
    +from qiskit_dynamics.dispatch.dispatch import Dispatch, asarray
    +
    +__all__ = ["Array"]
    +
    +
    +
    +[docs] +class Array(NDArrayOperatorsMixin): + """Qiskit array class. + + This class provides a Numpy compatible wrapper to supported Python array libraries. Supported + backends are ``"numpy"`` and ``"jax"``. + """ + + def __init__( + self, + data: Any, + dtype: Optional[Any] = None, + order: Optional[str] = None, + backend: Optional[str] = None, + ): + """Initialize an :class:`Array` container. + + Args: + data: An ``array_like`` input. This can be an object of any type supported by the + registered :math:`asarray` method for the specified backend. + dtype: Optional. The dtype of the returned array. This value must be supported by the + specified array backend. + order: Optional. The array order. This value must be supported by the specified array + backend. + backend: A registered array backend name. If ``None`` the default array backend will + be used. + + Raises: + ValueError: If input cannot be converted to an :class:`Array`. + """ + + # Check if we can override setattr and + # set _data and _backend directly + if ( + isinstance(data, numpy.ndarray) + and _is_numpy_backend(backend) + and _is_equivalent_numpy_array(data, dtype, order) + ): + self.__dict__["_data"] = data + self.__dict__["_backend"] = "numpy" + return + + if hasattr(data, "__qiskit_array__"): + array = data.__qiskit_array__(dtype=dtype, backend=backend) + if not isinstance(array, Array): + raise ValueError("object __qiskit_array__ method is not producing an Array") + self._data = array._data + self._backend = array._backend + if dtype or order or (backend and backend != self._backend): + if backend is None: + backend = self._backend + else: + self._backend = backend + self._data = asarray(self._data, dtype=dtype, order=order, backend=backend) + return + + # Standard init + self._data = asarray(data, dtype=dtype, order=order, backend=backend) + self._backend = backend if backend else Dispatch.backend(self._data, subclass=True) + + @property + def data(self): + """The wrapped array data object.""" + return self._data + + @data.setter + def data(self, value): + self._data[:] = value + + @property + def backend(self): + """The backend of the wrapped array class.""" + return self._backend + + @backend.setter + def backend(self, value: str): + Dispatch.validate_backend(value) + self._data = asarray(self._data, backend=value) + self._backend = value + +
    +[docs] + @classmethod + def set_default_backend(cls, backend: Union[str, None]): + """Set the default array backend.""" + if backend is not None: + Dispatch.validate_backend(backend) + Dispatch.DEFAULT_BACKEND = backend
    + + +
    +[docs] + @classmethod + def default_backend(cls) -> str: + """Return the default array backend.""" + return Dispatch.DEFAULT_BACKEND
    + + +
    +[docs] + @classmethod + def available_backends(cls) -> Set[str]: + """Return a tuple of available array backends.""" + return Dispatch.REGISTERED_BACKENDS
    + + + def __repr__(self): + prefix = "Array(" + if self._backend == Dispatch.DEFAULT_BACKEND: + suffix = ")" + else: + suffix = f"backend='{self._backend}')" + return Dispatch.repr(self.backend)(self._data, prefix=prefix, suffix=suffix) + + def __copy__(self): + """Return a shallow copy referencing the same wrapped data array""" + return Array(self._data, backend=self.backend) + + def __deepcopy__(self, memo=None): + """Return a deep copy with a copy of the wrapped data array""" + return Array(copy.deepcopy(self._data), backend=self.backend) + + def __iter__(self): + return iter(self._data) + + def __getstate__(self): + return {"_data": self._data, "_backend": self._backend} + + def __setstate__(self, state): + self._backend = state["_backend"] + self._data = state["_data"] + + def __getitem__(self, key: str) -> Any: + """Return value from wrapped array.""" + return self._data[key] + + def __setitem__(self, key: str, value: Any): + """Return value of wrapped array.""" + self._data[key] = value + + def __setattr__(self, name: str, value: Any): + """Set attribute of wrapped array.""" + if name in ("_data", "data", "_backend", "backend"): + super().__setattr__(name, value) + else: + setattr(self._data, name, value) + + def __getattr__(self, name: str) -> Any: + """Get attribute of wrapped array and convert to an :class:`Array`.""" + # Call attribute on inner array object + attr = getattr(self._data, name) + + # If attribute is a function wrap the return values + if isinstance(attr, (MethodType, BuiltinMethodType)): + + @wraps(attr) + def wrapped_method(*args, **kwargs): + return self._wrap(attr(*args, **kwargs)) + + return wrapped_method + + # If return object is a backend array wrap result + return self._wrap(attr) + + def __qiskit_array__(self, dtype=None, backend=None): + if (backend and backend != self.backend) or (dtype and dtype != self.data.dtype): + return Array(self.data, dtype=dtype, backend=backend) + return self + + def __array__(self, dtype=None) -> numpy.ndarray: + if isinstance(self._data, numpy.ndarray) and (dtype is None or dtype == self._data.dtype): + return self._data + return numpy.asarray(self._data, dtype=dtype) + + def __len__(self) -> int: + return len(self._data) + + def __str__(self) -> str: + return str(self._data) + + def __bool__(self) -> bool: + return bool(self._data) + + def __int__(self): + """Convert size 1 array to an int.""" + if numpy.size(self) != 1: + raise TypeError("only size-1 Arrays can be converted to Python scalars.") + return int(self._data) + + def __float__(self): + """Convert size 1 array to a float.""" + if numpy.size(self) != 1: + raise TypeError("only size-1 Arrays can be converted to Python scalars.") + return float(self._data) + + def __complex__(self): + """Convert size 1 array to a complex.""" + if numpy.size(self) != 1: + raise TypeError("only size-1 Arrays can be converted to Python scalars.") + return complex(self._data) + + @staticmethod + def _wrap(obj: Union[Any, Tuple[Any]], backend: Optional[str] = None) -> Union[Any, Tuple[Any]]: + """Wrap return array backend objects as :class:`Array` objects.""" + if isinstance(obj, tuple): + return tuple( + Array(x, backend=backend) if isinstance(x, Dispatch.REGISTERED_TYPES) else x + for x in obj + ) + if isinstance(obj, Dispatch.REGISTERED_TYPES): + return Array(obj, backend=backend) + return obj + + @classmethod + def _unwrap(cls, obj): + """Unwrap an Array or list of :class:`Array` objects.""" + if isinstance(obj, Array): + return obj._data + if isinstance(obj, tuple): + return tuple(cls._unwrap(i) for i in obj) + if isinstance(obj, list): + return list(cls._unwrap(i) for i in obj) + return obj + + def __array_ufunc__(self, ufunc, method, *inputs, **kwargs): + """Dispatcher for NumPy ufuncs to support the wrapped array backend.""" + out = kwargs.get("out", tuple()) + + for i in inputs + out: + # Only support operations with instances of REGISTERED_TYPES. + # Use ArrayLike instead of type(self) for isinstance to + # allow subclasses that don't override __array_ufunc__ to + # handle ArrayLike objects. + if not isinstance(i, Dispatch.REGISTERED_TYPES + (Array, Number)): + return NotImplemented + + # Defer to the implementation of the ufunc on unwrapped values. + inputs = self._unwrap(inputs) + if out: + kwargs["out"] = self._unwrap(out) + + # Get implementation for backend + backend = self.backend + dispatch_func = Dispatch.array_ufunc(backend, ufunc, method) + if dispatch_func == NotImplemented: + return NotImplemented + result = dispatch_func(*inputs, **kwargs) + + # Not sure what this case from NumPy docs is? + if method == "at": + return None + + # Wrap array results back into Array objects + return self._wrap(result, backend=self.backend) + + def __array_function__(self, func, types, args, kwargs): + """Dispatcher for NumPy array function to support the wrapped :class:`Array` backend.""" + if not all(issubclass(t, (Array,) + Dispatch.REGISTERED_TYPES) for t in types): + return NotImplemented + + # Unwrap function Array arguments + args = self._unwrap(args) + out = kwargs.get("out", tuple()) + if out: + kwargs["out"] = self._unwrap(out) + + # Get implementation for backend + backend = self.backend + dispatch_func = Dispatch.array_function(backend, func) + if dispatch_func == NotImplemented: + return NotImplemented + result = dispatch_func(*args, **kwargs) + return self._wrap(result, backend=self.backend)
    + + + +def _is_numpy_backend(backend: Optional[str] = None): + return backend == "numpy" or (not backend and Dispatch.DEFAULT_BACKEND == "numpy") + + +def _is_equivalent_numpy_array(data: Any, dtype: Optional[Any] = None, order: Optional[str] = None): + return (not dtype or dtype == data.dtype) and ( + not order + or (order == "C" and data.flags["C_CONTIGUOUS"]) + or (order == "F" and data.flags["F_CONTIGUOUS"]) + ) +
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/array/wrap.html b/stable/0.4/_modules/qiskit_dynamics/array/wrap.html new file mode 100644 index 000000000..57b854643 --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/array/wrap.html @@ -0,0 +1,550 @@ + + + + + + + + qiskit_dynamics.array.wrap - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    Source code for qiskit_dynamics.array.wrap

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2017, 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +
    +"""Functions for working with :class:`Array` dispatch."""
    +
    +import functools
    +from types import FunctionType
    +from typing import Callable
    +
    +from .array import Array
    +
    +
    +
    +[docs] +def wrap( + func: Callable, wrap_return: bool = True, wrap_args: bool = True, decorator: bool = False +) -> Callable: + r"""Wrap an array backend function to work with :class:`Array`\s. + + Args: + func: A function to wrap. + wrap_return: If ``True`` convert results that are registered array backend types into + :class:`Array` objects. + wrap_args: If ``True`` also wrap function type args and kwargs of the wrapped function. + decorator: If ``True`` the wrapped decorator function ``func`` will also wrap the + decorated functions. + + Returns: + Callable: The wrapped function. + """ + if decorator: + return _wrap_decorator(func, wrap_return=wrap_return, wrap_args=wrap_args) + else: + return _wrap_function(func, wrap_return=wrap_return, wrap_args=wrap_args)
    + + + +def _wrap_array_function(func: Callable) -> Callable: + r"""Wrap a function to handle :class:`Array`\-like inputs and returns.""" + + @functools.wraps(func) + def wrapped_function(*args, **kwargs): + # Unwrap inputs + args = tuple( + x.__qiskit_array__().data if hasattr(x, "__qiskit_array__") else x for x in args + ) + kwargs = dict( + (key, val.__qiskit_array__().data) if hasattr(val, "__qiskit_array__") else (key, val) + for key, val in kwargs.items() + ) + + # Evaluate function with unwrapped inputs + result = func(*args, **kwargs) + + # Unwrap result + if isinstance(result, tuple): + result = tuple( + x.__qiskit_array__().data if hasattr(x, "__qiskit_array__") else x for x in result + ) + elif hasattr(result, "__qiskit_array__"): + result = result.__qiskit_array__().data + return result + + return wrapped_function + + +def _wrap_args(args): + """Return wrapped args.""" + return tuple(_wrap_array_function(x) if isinstance(x, FunctionType) else x for x in args) + + +def _wrap_kwargs(kwargs): + """Return wrapped kwargs.""" + return dict( + (key, _wrap_array_function(val)) if isinstance(val, FunctionType) else (key, val) + for key, val in kwargs.items() + ) + + +def _wrap_function(func: Callable, wrap_return: bool = True, wrap_args: bool = True) -> Callable: + r"""Wrap an array backend function to work with :class:`Array`\s. + + Args: + func: A function to wrap. + wrap_return: If ``True`` convert results that are registered array backend types into + :class:`Array` objects. + wrap_args: If ``True`` also wrap function type args and kwargs of the wrapped function. + + Returns: + Callable: The wrapped function. + """ + # pylint: disable = function-redefined + if wrap_return and wrap_args: + + @functools.wraps(func) + def wrapped_func(*args, **kwargs): + args = _wrap_args(args) + kwargs = _wrap_kwargs(kwargs) + result = _wrap_array_function(func)(*args, **kwargs) + return Array._wrap(result) + + return wrapped_func + + elif wrap_return and not wrap_args: + + @functools.wraps(func) + def wrapped_func(*args, **kwargs): + result = _wrap_array_function(func)(*args, **kwargs) + return Array._wrap(result) + + return wrapped_func + + elif not wrap_return and wrap_args: + + @functools.wraps(func) + def wrapped_func(*args, **kwargs): + args = _wrap_args(args) + kwargs = _wrap_kwargs(kwargs) + return _wrap_array_function(func)(*args, **kwargs) + + return wrapped_func + + else: + + @functools.wraps(func) + def wrapped_func(*args, **kwargs): + return _wrap_array_function(func)(*args, **kwargs) + + return wrapped_func + + +def _wrap_decorator(func: Callable, wrap_return: bool = True, wrap_args: bool = True) -> Callable: + r"""Wrap a function decorator to work with :class:`Array`\s. + + Args: + func: A function to wrap. + wrap_return: If ``True`` convert results that are registered array backend types into + :class:`Array` objects. + wrap_args: If ``True`` also wrap function type args and kwargs of the wrapped function. + + Returns: + Callable: The wrapped function. + """ + # pylint: disable = function-redefined + if wrap_return and wrap_args: + + @functools.wraps(func) + def wrapped_func(*args, **kwargs): + args = _wrap_args(args) + kwargs = _wrap_kwargs(kwargs) + decorated = _wrap_array_function(func)(*args, **kwargs) + + @functools.wraps(args[0]) + def wrapped_decorated(*f_args, **f_kwargs): + f_args = _wrap_args(f_args) + f_kwargs = _wrap_kwargs(f_kwargs) + result = _wrap_function(decorated)(*f_args, **f_kwargs) + return Array._wrap(result) + + return wrapped_decorated + + return wrapped_func + + if wrap_return and not wrap_args: + + @functools.wraps(func) + def wrapped_func(*args, **kwargs): + decorated = _wrap_array_function(func)(*args, **kwargs) + + @functools.wraps(args[0]) + def wrapped_decorated(*f_args, **f_kwargs): + result = _wrap_function(decorated)(*f_args, **f_kwargs) + return Array._wrap(result) + + return wrapped_decorated + + return wrapped_func + + if not wrap_return and wrap_args: + + @functools.wraps(func) + def wrapped_func(*args, **kwargs): + args = _wrap_args(args) + kwargs = _wrap_kwargs(kwargs) + decorated = _wrap_array_function(func)(*args, **kwargs) + + @functools.wraps(args[0]) + def wrapped_decorated(*f_args, **f_kwargs): + f_args = _wrap_args(f_args) + f_kwargs = _wrap_kwargs(f_kwargs) + return _wrap_function(decorated)(*f_args, **f_kwargs) + + return wrapped_decorated + + return wrapped_func + + else: + + @functools.wraps(func) + def wrapped_func(*args, **kwargs): + decorated = _wrap_array_function(func)(*args, **kwargs) + + @functools.wraps(args[0]) + def wrapped_decorated(*f_args, **f_kwargs): + return _wrap_function(decorated)(*f_args, **f_kwargs) + + return wrapped_decorated + + return wrapped_func +
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/backend/backend_string_parser/hamiltonian_string_parser.html b/stable/0.4/_modules/qiskit_dynamics/backend/backend_string_parser/hamiltonian_string_parser.html new file mode 100644 index 000000000..cb8c2fcd1 --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/backend/backend_string_parser/hamiltonian_string_parser.html @@ -0,0 +1,645 @@ + + + + + + + + qiskit_dynamics.backend.backend_string_parser.hamiltonian_string_parser - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    Source code for qiskit_dynamics.backend.backend_string_parser.hamiltonian_string_parser

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2022.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Functionality for importing qiskit.pulse model string representation.
    +
    +This file is meant for internal use and may be changed at any point.
    +"""
    +
    +from typing import Tuple, List, Optional
    +from collections import OrderedDict
    +
    +# required for calls to exec
    +# pylint: disable=unused-import
    +import numpy as np
    +
    +from qiskit import QiskitError
    +
    +from .regex_parser import _regex_parser
    +
    +
    +# valid channel characters
    +CHANNEL_CHARS = ["U", "D", "M", "A", "u", "d", "m", "a"]
    +
    +
    +
    +[docs] +def parse_backend_hamiltonian_dict( + hamiltonian_dict: dict, subsystem_list: Optional[List[int]] = None +) -> Tuple[np.ndarray, np.ndarray, List[str], dict]: + r"""Convert Pulse backend Hamiltonian dictionary into concrete array format + with an ordered list of corresponding channels. + + The Pulse backend Hamiltonian dictionary, ``hamiltonian_dict``, must have the + following keys: + + * ``'h_str'``: List of Hamiltonian terms in string format (see below). + * ``'qub'``: Dictionary giving subsystem dimensions. Keys are subsystem labels, + values are their dimensions. + * ``'vars'``: Dictionary whose keys are the variables appearing in the terms in + the ``h_str`` list, and values being the numerical values of the variables. + + The optional argument ``subsystem_list`` specifies a subset of subsystems to keep when parsing. + If ``None``, all subsystems are kept. If ``subsystem_list`` is specified, then terms + including subsystems not in the list will be ignored. + + Entries in the list ``hamiltonian_dict['h_str']`` must be formatted as a product of + constants (either numerical constants or variables in ``hamiltonian_dict['vars'].keys()``) + with operators. Operators are indicated with a capital letters followed by an integer + indicating the subsystem the operator acts on. Accepted operator strings are: + + * ``'X'``: If the target subsystem is two dimensional, the + Pauli :math:`X` operator, and if greater than two dimensional, returns + :math:`a + a^\dagger`, where :math:`a` and :math:`a^\dagger` are the + annihiliation and creation operators, respectively. + * ``'Y'``: If the target subsystem is two dimensional, the + Pauli :math:`Y` operator, and if greater than two dimensional, returns + :math:`-i(a - a^\dagger)`, where :math:`a` and :math:`a^\dagger` are the + annihiliation and creation operators, respectively. + * ``'Z'``: If the target subsystem is two dimensional, the + Pauli :math:`Z` operator, and if greater than two dimensional, returns + :math:`I - 2 * N`, where :math:`N` is the number operator. + * ``'a'``, ``'A'``, or ``'Sm'``: If two dimensional, the sigma minus operator, and if greater, + generalizes to the operator. + * ``'C'``, or ``'Sp'``: If two dimensional, sigma plus operator, and if greater, + generalizes to the creation operator. + * ``'N'``, or ``'O'``: The number operator. + * ``'I'``: The identity operator. + + In addition to the above, a term in ``hamiltonian_dict['h_str']`` can be associated with + a channel by ending it with a string of the form ``'||Sxx'``, where ``S`` is a valid channel + label, and ``'xx'`` is an integer. Accepted channel labels are: + + * ``'D'`` or ``'d'`` for drive channels. + * ``'U'`` or ``'u'`` for control channels. + * ``'M'`` or ``'m'`` for measurement channels. + * ``'A'`` or ``'a'`` for acquire channels. + + Finally, summations of terms of the above form can be indicated in + ``hamiltonian_dict['h_str']`` via strings with syntax ``'_SUM[i, lb, ub, aa||S{i}]'``, + where: + + * ``i`` is the summation variable. + * ``lb`` and ``ub`` are the summation endpoints (inclusive). + * ``aa`` is a valid operator string, possibly including the string ``{i}`` to indicate + operators acting on subsystem ``i``. + * ``S{i}`` is the specification of a channel indexed by ``i``. + + + For example, the following ``hamiltonian_dict`` specifies a single + transmon with 4 levels: + + .. code-block:: python + + hamiltonian_dict = { + "h_str": ["v*np.pi*O0", "alpha*np.pi*O0*O0", "r*np.pi*X0||D0"], + "qub": {"0": 4}, + "vars": {"v": 2.1, "alpha": -0.33, "r": 0.02}, + } + + The following example specifies a two transmon system, with single system terms specified + using the summation format: + + .. code-block:: python + + hamiltonian_dict = { + "h_str": [ + "_SUM[i,0,1,wq{i}/2*(I{i}-Z{i})]", + "_SUM[i,0,1,delta{i}/2*O{i}*O{i}]", + "_SUM[i,0,1,-delta{i}/2*O{i}]", + "_SUM[i,0,1,omegad{i}*X{i}||D{i}]", + "jq0q1*Sp0*Sm1", + "jq0q1*Sm0*Sp1", + "omegad1*X0||U0", + "omegad0*X1||U1" + ], + "qub": {"0": 4, "1": 4}, + "vars": { + "delta0": -2.111793476400394, + "delta1": -2.0894421352015744, + "jq0q1": 0.010495754104003914, + "omegad0": 0.9715458990879812, + "omegad1": 0.9803812537440838, + "wq0": 32.517894442809514, + "wq1": 33.0948996120196, + }, + } + + Args: + hamiltonian_dict: Pulse backend Hamiltonian dictionary. + subsystem_list: List of subsystems to include in the model. If ``None`` all are kept. + + Returns: + Tuple: Model converted into concrete arrays - the static Hamiltonian, + a list of Hamiltonians corresponding to different channels, a list of + channel labels corresponding to the list of time-dependent Hamiltonians, + and a dictionary with subsystem dimensions whose keys are the subsystem labels. + """ + + # raise errors for invalid hamiltonian_dict + _hamiltonian_pre_parse_exceptions(hamiltonian_dict) + + # get variables + variables = OrderedDict() + if "vars" in hamiltonian_dict: + variables = OrderedDict(hamiltonian_dict["vars"]) + + # Get qubit subspace dimensions + if subsystem_list is None: + subsystem_list = [int(qubit) for qubit in hamiltonian_dict["qub"]] + else: + # if user supplied, make a copy and sort it + subsystem_list = sorted(subsystem_list) + + # force keys in hamiltonian['qub'] to be ints + qub_dict = {int(key): val for key, val in hamiltonian_dict["qub"].items()} + + subsystem_dims_dict = {int(qubit): qub_dict[int(qubit)] for qubit in subsystem_list} + + # Parse the Hamiltonian + system = _regex_parser( + operator_str=hamiltonian_dict["h_str"], + subsystem_dims_dict=subsystem_dims_dict, + subsystem_list=subsystem_list, + ) + + # Extract which channels are associated with which Hamiltonian terms. + # Assumes one channel appearing in each term appearing at the end. + channels = [] + for _, ham_str in system: + chan_idx = None + + for c in CHANNEL_CHARS: + # if c in ham_str, and all characters after are digits, treat + # as channel + if c in ham_str: + if all(a.isdigit() for a in ham_str[ham_str.index(c) + 1 :]): + chan_idx = ham_str.index(c) + break + + if chan_idx is None: + channels.append(None) + else: + channels.append(ham_str[chan_idx:]) + + # evaluate coefficients + local_vars = {chan: 1.0 for chan in set(channels) if chan is not None} + local_vars.update(variables) + + evaluated_ops = [] + for op, coeff in system: + # pylint: disable=exec-used + exec(f"evaluated_coeff = {coeff}", globals(), local_vars) + evaluated_ops.append(local_vars["evaluated_coeff"] * op) + + # merge terms based on channel + static_hamiltonian = None + hamiltonian_operators = [] + reduced_channels = [] + + for channel, op in zip(channels, evaluated_ops): + # if None, add it to the static hamiltonian + if channel is None: + if static_hamiltonian is None: + static_hamiltonian = op + else: + static_hamiltonian += op + else: + channel = channel.lower() + if channel in reduced_channels: + hamiltonian_operators[reduced_channels.index(channel)] += op + else: + hamiltonian_operators.append(op) + reduced_channels.append(channel) + + # sort channels/operators according to channel ordering + if len(reduced_channels) > 0: + reduced_channels, hamiltonian_operators = zip( + *sorted(zip(reduced_channels, hamiltonian_operators)) + ) + + return ( + static_hamiltonian, + list(hamiltonian_operators), + list(reduced_channels), + subsystem_dims_dict, + )
    + + + +def _hamiltonian_pre_parse_exceptions(hamiltonian_dict: dict): + """Raises exceptions for improperly formatted or unsupported elements of + hamiltonian dict specification. + + Parameters: + hamiltonian_dict: Dictionary specification of hamiltonian. + Returns: + Raises: + QiskitError: If some part of the Hamiltonian dictionary is unsupported or invalid. + """ + + ham_str = hamiltonian_dict.get("h_str", []) + if ham_str in ([], [""]): + raise QiskitError("Hamiltonian dict requires a non-empty 'h_str' entry.") + + if hamiltonian_dict.get("qub", {}) == {}: + raise QiskitError( + "Hamiltonian dict requires non-empty 'qub' entry with subsystem dimensions." + ) + + if hamiltonian_dict.get("osc", {}) != {}: + raise QiskitError("Oscillator-type systems are not supported.") + + # verify that if terms in h_str have the divider ||, then the channels are in the valid format + for term in hamiltonian_dict["h_str"]: + malformed_text = f"""Term '{term}' does not conform to required string format. + Channels may only be specified in the format + 'aa||Cxx', where 'aa' specifies an operator, + C is a valid channel character, + and 'xx' is a string of digits.""" + + # if two vertical bars used together, check if channels in correct format + if term.count("|") == 2 and term.count("||") == 1: + # get the string reserved for channel + channel_str = term[term.index("||") + 2 :] + + # if channel string is empty + if len(channel_str) == 0: + raise QiskitError(malformed_text) + + # if first entry in channel string isn't a valid channel character + if channel_str[0] not in CHANNEL_CHARS: + raise QiskitError(malformed_text) + + # Verify either that: all remaining characters are digits, or, + # if term starts with _SUM[ and ends with ], all remaining characters + # are either digits, or starts and ends with {} + if term[-1] == "]" and len(term) > 5 and term[:5] == "_SUM[": + # drop the closing ] + channel_str = channel_str[:-1] + + # if channel string doesn't contain anything other than channel character + if len(channel_str) == 1: + raise QiskitError(malformed_text) + + # if starts with opening bracket, verify that it ends with closing bracket + if channel_str[1] == "{": + if not channel_str[-1] == "}": + raise QiskitError(malformed_text) + # otherwise verify that the remainder of terms only contains digits + elif any(not c.isdigit() for c in channel_str[1:]): + raise QiskitError(malformed_text) + else: + # if channel string doesn't contain anything other than channel character + if len(channel_str) == 1: + raise QiskitError(malformed_text) + + if any(not c.isdigit() for c in channel_str[1:]): + raise QiskitError(malformed_text) + + # if bars present but not in correct format, raise error + elif term.count("|") != 0: + raise QiskitError(malformed_text) +
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    Source code for qiskit_dynamics.backend.dynamics_backend

    +# -*- coding: utf-8 -*-
    +
    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2022.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Pulse-enabled simulator backend.
    +"""
    +
    +import datetime
    +import uuid
    +import warnings
    +
    +from typing import List, Optional, Union, Dict, Tuple
    +import copy
    +import numpy as np
    +from scipy.integrate._ivp.ivp import OdeResult  # pylint: disable=unused-import
    +
    +from qiskit import pulse
    +from qiskit.qobj.utils import MeasLevel, MeasReturnType
    +from qiskit.qobj.common import QobjHeader
    +from qiskit.transpiler import Target, InstructionProperties
    +from qiskit.circuit.library import Measure
    +from qiskit.pulse import Schedule, ScheduleBlock
    +from qiskit.pulse.transforms.canonicalization import block_to_schedule
    +from qiskit.providers.options import Options
    +from qiskit.providers.backend import BackendV1, BackendV2
    +from qiskit.providers.models.pulsedefaults import PulseDefaults
    +from qiskit.providers.models.backendconfiguration import PulseBackendConfiguration
    +from qiskit.result import Result
    +from qiskit.result.models import ExperimentResult, ExperimentResultData
    +
    +from qiskit import QiskitError, QuantumCircuit
    +from qiskit import schedule as build_schedule
    +from qiskit.quantum_info import Statevector, DensityMatrix
    +
    +from qiskit_dynamics import RotatingFrame
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.solvers.solver_classes import Solver
    +
    +from .dynamics_job import DynamicsJob
    +from .backend_utils import (
    +    _get_dressed_state_decomposition,
    +    _get_lab_frame_static_hamiltonian,
    +    _get_memory_slot_probabilities,
    +    _sample_probability_dict,
    +    _get_counts_from_samples,
    +    _get_iq_data,
    +)
    +from .backend_string_parser import parse_backend_hamiltonian_dict
    +
    +
    +
    +[docs] +class DynamicsBackend(BackendV2): + r"""Pulse-level simulator backend. + + This class provides a :class:`~qiskit.providers.backend.BackendV2` interface wrapper around a + :class:`.Solver` instance setup to simulate pulse schedules. The backend can be configured to + take advantage of standard transpilation infrastructure to describe pulse-level simulations in + terms of :class:`~qiskit.circuit.QuantumCircuit`\s. Results are returned as + :class:`~qiskit.result.Result` instances. + + A minimal :class:`.DynamicsBackend` requires specifying only a :class:`.Solver` instance and a + list of subsystem dimensions, indicating the subsystem decomposition of the model in + :class:`.Solver`. For example, the following code builds a :class:`.DynamicsBackend` around a + :class:`.Solver` and indicates that the system specified by the :class:`.Solver` decomposes as + two ``3`` dimensional subsystems. + + .. code-block:: python + + backend = DynamicsBackend( + solver=solver, subsystem_dims=[3, 3] + ) + + Without further configuration, the above ``backend`` can be used to simulate either + :class:`~qiskit.pulse.Schedule` or :class:`~qiskit.pulse.ScheduleBlock` instances. + + Pulse-level simulations defined in terms of :class:`~qiskit.circuit.QuantumCircuit` instances + can also be performed if each gate in the circuit has a corresponding pulse-level definition, + either as an attached calibration, or as an instruction contained in ``backend.target``. + + Additionally, a :class:`.DynamicsBackend` can be instantiated from an existing backend using the + :meth:`.DynamicsBackend.from_backend` method, utilizing the additional ``subsystem_list`` + argument to specify which qubits to include in the model: + + .. code-block:: python + + backend = DynamicsBackend.from_backend(backend, subsystem_list=[0, 1]) + + + **Supported options** + + The behaviour of the backend can be configured via the following options. These can either be + passed as optional keyword arguments at construction, set with the + :meth:`.DynamicsBackend.set_options` method after construction, or passed as runtime arguments + to :meth:`.DynamicsBackend.run`. + + * ``shots``: Number of shots per experiment. Defaults to ``1024``. + * ``solver``: The Qiskit Dynamics :class:`.Solver` instance used for simulation. + * ``solver_options``: Dictionary containing optional kwargs for passing to :meth:`Solver.solve`, + indicating solver methods and options. Defaults to the empty dictionary ``{}``. + * ``subsystem_dims``: Dimensions of subsystems making up the system in ``solver``. Defaults to + ``[solver.model.dim]``. + * ``meas_map``: Measurement map. Defaults to ``[[idx] for idx in range(len(subsystem_dims))]``. + * ``control_channel_map``: A dictionary mapping control channel labels to indices, to be used + for control channel index lookup in the :meth:`DynamicsBackend.control_channel` method. + * ``initial_state``: Initial state for simulation, either the string ``"ground_state"``, + indicating that the ground state for the system Hamiltonian should be used, or an arbitrary + ``Statevector`` or ``DensityMatrix``. Defaults to ``"ground_state"``. + * ``normalize_states``: Boolean indicating whether to normalize states before computing outcome + probabilities, and normalize probablities before sampling. Defaults to ``True``. Setting to + ``False`` can result in errors if the solution tolerance results in probabilities with + significant numerical deviation from a proper probability distribution. + * ``meas_level``: Form of measurement output. Supported values are ``1`` and ``2``. ``1`` + returns IQ points and ``2`` returns counts. Defaults to ``meas_level == 2``. + * ``meas_return``: Level of measurement data to return. For ``meas_level = 1`` ``"single"`` + returns output from every shot. ``"avg"`` returns average over shots of measurement output. + Defaults to ``"avg"``. + * ``iq_centers``: Centers for IQ distribution when using ``meas_level==1`` results. Must have + type ``List[List[List[float, float]]]`` formatted as ``iq_centers[subsystem][level] = [I, + Q]``. If ``None``, the ``iq_centers`` are dynamically generated to be equally spaced points on + a unit circle with ground-state at ``(1, 0)``. The default is ``None``. + * ``iq_width``: Standard deviation of IQ distribution around the centers for ``meas_level==1``. + Must be a positive float. Defaults to ``0.2``. + * ``max_outcome_level``: For ``meas_level == 2``, the maximum outcome for each subsystem. Values + will be rounded down to be no larger than ``max_outcome_level``. Must be a positive integer or + ``None``. If ``None``, no rounding occurs. Defaults to ``1``. + * ``memory``: Boolean indicating whether to return a list of explicit measurement outcomes for + every experimental shot. Defaults to ``True``. + * ``seed_simulator``: Seed to use in random sampling. Defaults to ``None``. + * ``experiment_result_function``: Function for computing the ``ExperimentResult`` for each + simulated experiment. This option defaults to :func:`default_experiment_result_function`, and + any other function set to this option must have the same signature. Note that the default + utilizes various other options that control results computation, and hence changing it will + impact the meaning of other options. + * ``configuration``: A :class:`PulseBackendConfiguration` instance or ``None``. This option + defaults to ``None``, and is not required for the functioning of this class, but is provided + for compatibility. A set configuration will be returned by + :meth:`DynamicsBackend.configuration()`. + * ``defaults``: A :class:`PulseDefaults` instance or ``None``. This option defaults to ``None``, + and is not required for the functioning of this class, but is provided for compatibility. A + set defaults will be returned by :meth:`DynamicsBackend.defaults()`. + """ + + def __init__( + self, + solver: Solver, + target: Optional[Target] = None, + **options, + ): + """Instantiate with a :class:`.Solver` instance and additional options. + + Args: + solver: Solver instance configured for pulse simulation. + target: Target object. + options: Additional configuration options for the simulator. + + Raises: + QiskitError: If any instantiation arguments fail validation checks. + """ + + super().__init__( + name="DynamicsBackend", + description="Pulse enabled simulator backend.", + backend_version="0.1", + ) + + # Dressed states of solver, will be calculated when solver option is set + self._dressed_evals = None + self._dressed_states = None + self._dressed_states_adjoint = None + + # add subsystem_dims to options so set_options validation works + if "subsystem_dims" not in options: + options["subsystem_dims"] = [solver.model.dim] + + # Set simulator options + self.set_options(solver=solver, **options) + + if self.options.meas_map is None: + meas_map = [[idx] for idx in range(len(self.options.subsystem_dims))] + self.set_options(meas_map=meas_map) + + # self._target = target or Target() doesn't work as bool(target) can be False + if target is None: + target = Target() + else: + target = copy.copy(target) + + # add default simulator measure instructions + measure_properties = {} + instruction_schedule_map = target.instruction_schedule_map() + for qubit in range(len(self.options.subsystem_dims)): + if not instruction_schedule_map.has(instruction="measure", qubits=qubit): + with pulse.build() as meas_sched: + pulse.acquire( + duration=1, qubit_or_channel=qubit, register=pulse.MemorySlot(qubit) + ) + + measure_properties[(qubit,)] = InstructionProperties(calibration=meas_sched) + + if bool(measure_properties): + target.add_instruction(Measure(), measure_properties) + + target.dt = solver._dt + target.num_qubits = len(self.options.subsystem_dims) + + self._target = target + + def _default_options(self): + return Options( + shots=1024, + solver=None, + solver_options={}, + subsystem_dims=None, + meas_map=None, + control_channel_map=None, + normalize_states=True, + initial_state="ground_state", + meas_level=MeasLevel.CLASSIFIED, + meas_return=MeasReturnType.AVERAGE, + iq_centers=None, + iq_width=0.2, + max_outcome_level=1, + memory=True, + seed_simulator=None, + experiment_result_function=default_experiment_result_function, + configuration=None, + defaults=None, + ) + +
    +[docs] + def set_options(self, **fields): + """Set options for DynamicsBackend.""" + + validate_subsystem_dims = False + validate_iq_centers = False + + for key, value in fields.items(): + if not hasattr(self._options, key): + raise AttributeError(f"Invalid option {key}") + + # validation checks + if key == "initial_state": + if value != "ground_state" and not isinstance(value, (Statevector, DensityMatrix)): + raise QiskitError( + 'initial_state must be either "ground_state", or a Statevector or ' + "DensityMatrix instance." + ) + elif key == "meas_level" and value not in [1, 2]: + raise QiskitError("Only meas_level 1 and 2 are supported by DynamicsBackend.") + elif key == "meas_return" and value not in ["single", "avg"]: + raise QiskitError("meas_return must be either 'single' or 'avg'.") + elif key == "max_outcome_level": + if (value is not None) and (not isinstance(value, int) or (value <= 0)): + raise QiskitError("max_outcome_level must be a positive integer or None.") + elif key == "experiment_result_function" and not callable(value): + raise QiskitError("experiment_result_function must be callable.") + elif key == "configuration" and not isinstance(value, PulseBackendConfiguration): + raise QiskitError( + "configuration option must be an instance of PulseBackendConfiguration." + ) + elif key == "defaults" and not isinstance(value, PulseDefaults): + raise QiskitError("defaults option must be an instance of PulseDefaults.") + elif key == "iq_width" and (not isinstance(value, float) or (value <= 0)): + raise QiskitError("iq_width must be a positive float.") + elif key == "iq_centers": + if (value is not None) and not all( + (isinstance(level, List) and len(level) == 2) + for sub_system in value + for level in sub_system + ): + raise QiskitError( + "The iq_centers option must be either None or of type " + "List[List[List[int, int]]], where the innermost list is the (I, Q) pair." + ) + validate_iq_centers = True + elif key == "subsystem_dims": + validate_subsystem_dims = True + validate_iq_centers = True + elif key == "solver": + validate_subsystem_dims = True + elif key == "control_channel_map": + if value is not None: + if not isinstance(value, dict): + raise QiskitError( + "The control_channel_map option must either be None or a dictionary." + ) + if not all(isinstance(x, int) for x in value.values()): + raise QiskitError("The control_channel_map values must be of type int.") + + # special setting routines + if key == "solver": + self._set_solver(value) + else: + self._options.update_options(**{key: value}) + + # perform additional consistency validations if certain options were modified + if ( + validate_subsystem_dims + and np.prod(self._options.subsystem_dims) != self._options.solver.model.dim + ): + raise QiskitError( + "DynamicsBackend options subsystem_dims and solver.model.dim are inconsistent." + ) + + if validate_iq_centers and (self._options.iq_centers is not None): + if [ + len(sub_system) for sub_system in self._options.iq_centers + ] != self._options.subsystem_dims: + raise QiskitError( + """iq_centers option is not consistent with subsystem_dims. Must be None + or of type List[List[List[int, int]]], where the outermost list is of length equal + to the number of subsystems, and each inner list of length equal to the + corresponding subsystem dimension.""" + )
    + + + def _set_solver(self, solver): + """Configure simulator based on provided solver.""" + if solver._dt is None: + raise QiskitError( + "Solver passed to DynamicsBackend is not configured for Pulse simulation." + ) + + self._options.update_options(solver=solver) + # Get dressed states + static_hamiltonian = _get_lab_frame_static_hamiltonian(solver.model) + dressed_evals, dressed_states = _get_dressed_state_decomposition(static_hamiltonian) + self._dressed_evals = dressed_evals + self._dressed_states = dressed_states + self._dressed_states_adjoint = self._dressed_states.conj().transpose() + + # pylint: disable=arguments-differ +
    +[docs] + def run( + self, + run_input: List[Union[QuantumCircuit, Schedule, ScheduleBlock]], + validate: Optional[bool] = True, + **options, + ) -> DynamicsJob: + """Run a list of simulations. + + Args: + run_input: A list of simulations, specified by ``QuantumCircuit``, ``Schedule``, or + ``ScheduleBlock`` instances. + validate: Whether or not to run validation checks on the input. + **options: Additional run options to temporarily override current backend options. + + Returns: + DynamicsJob object containing results and status. + + Raises: + QiskitError: If invalid options are set. + """ + + if validate: + _validate_run_input(run_input) + + # Configure run options for simulation + if options: + backend = copy.deepcopy(self) + backend.set_options(**options) + else: + backend = self + + schedules, num_memory_slots_list = _to_schedule_list(run_input, backend=backend) + + # get the acquires sample times and subsystem measurement information + ( + t_span, + measurement_subsystems_list, + memory_slot_indices_list, + ) = _get_acquire_instruction_timings( + schedules, backend.options.subsystem_dims, backend.options.solver._dt + ) + + # Build and submit job + job_id = str(uuid.uuid4()) + dynamics_job = DynamicsJob( + backend=backend, + job_id=job_id, + fn=backend._run, + fn_kwargs={ + "t_span": t_span, + "schedules": schedules, + "measurement_subsystems_list": measurement_subsystems_list, + "memory_slot_indices_list": memory_slot_indices_list, + "num_memory_slots_list": num_memory_slots_list, + }, + ) + dynamics_job.submit() + + return dynamics_job
    + + + def _run( + self, + job_id, + t_span, + schedules, + measurement_subsystems_list, + memory_slot_indices_list, + num_memory_slots_list, + ) -> Result: + """Simulate a list of schedules.""" + + # simulate all schedules + y0 = self.options.initial_state + if y0 == "ground_state": + y0 = Statevector(self._dressed_states[:, 0]) + + solver_results = self.options.solver.solve( + t_span=t_span, y0=y0, signals=schedules, **self.options.solver_options + ) + + # compute results for each experiment + experiment_names = [schedule.name for schedule in schedules] + experiment_metadatas = [schedule.metadata for schedule in schedules] + rng = np.random.default_rng(self.options.seed_simulator) + experiment_results = [] + for ( + experiment_name, + solver_result, + measurement_subsystems, + memory_slot_indices, + num_memory_slots, + experiment_metadata, + ) in zip( + experiment_names, + solver_results, + measurement_subsystems_list, + memory_slot_indices_list, + num_memory_slots_list, + experiment_metadatas, + ): + experiment_results.append( + self.options.experiment_result_function( + experiment_name, + solver_result, + measurement_subsystems, + memory_slot_indices, + num_memory_slots, + self, + seed=rng.integers(low=0, high=9223372036854775807), + metadata=experiment_metadata, + ) + ) + + # Construct full result object + return Result( + backend_name=self.name, + backend_version=self.backend_version, + qobj_id="", + job_id=job_id, + success=True, + results=experiment_results, + date=datetime.datetime.now().isoformat(), + ) + + @property + def max_circuits(self): + return None + + @property + def target(self) -> Target: + return self._target + + @property + def meas_map(self) -> List[List[int]]: + return self.options.meas_map + + def _get_qubit_channel( + self, qubit: int, ChannelClass: pulse.channels.Channel, method_name: str + ): + """Construct a channel instance for a given qubit.""" + if qubit < len(self.options.subsystem_dims): + return ChannelClass(qubit) + + raise QiskitError(f"{method_name} requested for qubit {qubit}, which is out of bounds.") + +
    +[docs] + def drive_channel(self, qubit: int) -> pulse.DriveChannel: + """Return the drive channel for a given qubit.""" + return self._get_qubit_channel(qubit, pulse.DriveChannel, "drive_channel")
    + + +
    +[docs] + def measure_channel(self, qubit: int) -> pulse.MeasureChannel: + """Return the measure channel for a given qubit.""" + return self._get_qubit_channel(qubit, pulse.MeasureChannel, "measure_channel")
    + + +
    +[docs] + def acquire_channel(self, qubit: int) -> pulse.AcquireChannel: + """Return the measure channel for a given qubit.""" + return self._get_qubit_channel(qubit, pulse.AcquireChannel, "acquire_channel")
    + + +
    +[docs] + def control_channel( + self, qubits: Union[Tuple[int, int], List[Tuple[int, int]]] + ) -> List[pulse.ControlChannel]: + """Return the control channel with a given label specified by qubits. + + This method requires the ``control_channel_map`` option is set, and otherwise will raise + a ``NotImplementedError``. + + Args: + qubits: The label for the control channel, or a list of labels. + Returns: + A list containing the control channels specified by qubits. + Raises: + NotImplementedError: If the control_channel_map option is not set for this backend. + QiskitError: If a requested channel is not in the control_channel_map. + """ + if self.options.control_channel_map is None: + raise NotImplementedError + + if not isinstance(qubits, list): + qubits = [qubits] + + control_channels = [] + for x in qubits: + if x not in self.options.control_channel_map: + raise QiskitError(f"Key {x} not in control_channel_map.") + control_channels.append(pulse.ControlChannel(self.options.control_channel_map[x])) + + return control_channels
    + + +
    +[docs] + def configuration(self) -> PulseBackendConfiguration: + """Get the backend configuration.""" + return self.options.configuration
    + + +
    +[docs] + def defaults(self) -> PulseDefaults: + """Get the backend defaults.""" + return self.options.defaults
    + + +
    +[docs] + @classmethod + def from_backend( + cls, + backend: BackendV1, + subsystem_list: Optional[List[int]] = None, + rotating_frame: Optional[Union[Array, RotatingFrame, str]] = "auto", + evaluation_mode: str = "dense", + rwa_cutoff_freq: Optional[float] = None, + **options, + ) -> "DynamicsBackend": + """Construct a DynamicsBackend instance from an existing Backend instance. + + .. warning:: + + Due to inevitable model inaccuracies, gates calibrated on a real backend will not have + the same performance on the :class:`.DynamicsBackend` instance returned by this method. + As such, gates and calibrations are not be copied into the constructed + :class:`.DynamicsBackend`. + + The ``backend`` must contain sufficient information in the ``target``, ``configuration``, + and/or ``defaults`` attributes to be able to run simulations. The following table indicates + which parameters are required, along with their primary and secondary sources: + + .. list-table:: Backend parameter locations + :widths: 10 25 25 + :header-rows: 1 + + * - Parameter + - Primary source + - Secondary source + * - ``hamiltonian`` dictionary. + - ``configuration.hamiltonian`` + - N/A + * - Control channel frequency specification. + - ``configuration.u_channel_lo`` + - N/A + * - Number of qubits in the backend model. + - ``target.num_qubits`` + - ``configuration.n_qubits`` + * - Pulse schedule sample size ``dt``. + - ``target.dt`` + - ``configuration.dt`` + * - Drive channel frequencies. + - ``target.qubit_properties`` + - ``defaults.qubit_freq_est`` + * - Measurement channel frequencies, if measurement channels explicitly appear in the + model. + - ``defaults.meas_freq_est`` + - N/A + + .. note:: + + The ``target``, ``configuration``, and ``defaults`` attributes of the original backend + are not copied into the constructed :class:`DynamicsBackend` instance, only the required + data stored within these attributes will be extracted. If necessary, these attributes + can be set and configured by the user. + + The optional argument ``subsystem_list`` specifies which subset of qubits to model in the + constructed :class:`DynamicsBackend`. All other qubits are dropped from the model. + + Configuration of the underlying :class:`.Solver` is controlled via the ``rotating_frame``, + ``evaluation_mode``, and ``rwa_cutoff_freq`` options. In contrast to :class:`.Solver` + initialization, ``rotating_frame`` defaults to the string ``"auto"``, which allows this + method to choose the rotating frame based on ``evaluation_mode``: + + * If a dense evaluation mode is chosen, the rotating frame will be set to the + ``static_hamiltonian`` indicated by the Hamiltonian in ``backend.configuration()``. + * If a sparse evaluation mode is chosen, the rotating frame will be set to the diagonal of + ``static_hamiltonian``. + + Otherwise the ``rotating_frame``, ``evaluation_mode``, and ``rwa_cutoff_freq`` are passed + directly to the :class:`.Solver` initialization. + + Args: + backend: The ``Backend`` instance to build the :class:`.DynamicsBackend` from. + Note that while the type hint indicates that `backend` should be a + :class:`~qiskit.providers.backend.BackendV1` instance, this method also works for + :class:`~qiskit.providers.backend.BackendV2` instances that have been set up with + sufficiently populated ``configuration`` and ``defaults`` for backwards + compatibility. + subsystem_list: The list of qubits in the backend to include in the model. + rotating_frame: Rotating frame argument for the internal :class:`.Solver`. Defaults to + ``"auto"``, allowing this method to pick a rotating frame. + evaluation_mode: Evaluation mode argument for the internal :class:`.Solver`. + rwa_cutoff_freq: Rotating wave approximation argument for the internal :class:`.Solver`. + **options: Additional options to be applied in construction of the + :class:`.DynamicsBackend`. + + Returns: + DynamicsBackend + + Raises: + QiskitError: If any required parameters are missing from the passed backend. + """ + + # get available target, config, and defaults objects + backend_target = getattr(backend, "target", None) + + if not hasattr(backend, "configuration"): + raise QiskitError( + "DynamicsBackend.from_backend requires that the backend argument has a " + "configuration method." + ) + backend_config = backend.configuration() + + backend_defaults = None + if hasattr(backend, "defaults"): + backend_defaults = backend.defaults() + + # get and parse Hamiltonian string dictionary + if backend_target is not None: + backend_num_qubits = backend_target.num_qubits + else: + backend_num_qubits = backend_config.n_qubits + + if subsystem_list is not None: + subsystem_list = sorted(subsystem_list) + if subsystem_list[-1] >= backend_num_qubits: + raise QiskitError( + f"subsystem_list contained {subsystem_list[-1]}, which is out of bounds for " + f"backend with {backend_num_qubits} qubits." + ) + else: + subsystem_list = list(range(backend_num_qubits)) + + if backend_config.hamiltonian is None: + raise QiskitError( + "DynamicsBackend.from_backend requires that backend.configuration() has a " + "hamiltonian." + ) + + ( + static_hamiltonian, + hamiltonian_operators, + hamiltonian_channels, + subsystem_dims_dict, + ) = parse_backend_hamiltonian_dict(backend_config.hamiltonian, subsystem_list) + subsystem_dims = [subsystem_dims_dict.get(idx, 1) for idx in range(backend_num_qubits)] + + # construct model frequencies dictionary from backend + channel_freqs = _get_backend_channel_freqs( + backend_target=backend_target, + backend_config=backend_config, + backend_defaults=backend_defaults, + channels=hamiltonian_channels, + ) + + # Add control_channel_map from backend (only if not specified before by user) + if "control_channel_map" not in options: + if hasattr(backend, "control_channels"): + control_channel_map_backend = { + qubits: backend.control_channels[qubits][0].index + for qubits in backend.control_channels + } + + elif hasattr(backend.configuration(), "control_channels"): + control_channel_map_backend = { + qubits: backend.configuration().control_channels[qubits][0].index + for qubits in backend.configuration().control_channels + } + + else: + control_channel_map_backend = {} + + # Reduce control_channel_map based on which channels are in the model + if bool(control_channel_map_backend): + control_channel_map = {} + for label, idx in control_channel_map_backend.items(): + if f"u{idx}" in hamiltonian_channels: + control_channel_map[label] = idx + options["control_channel_map"] = control_channel_map + + # build the solver + if rotating_frame == "auto": + if "dense" in evaluation_mode: + rotating_frame = static_hamiltonian + else: + rotating_frame = np.diag(static_hamiltonian) + + # get time step size + if backend_target is not None and backend_target.dt is not None: + dt = backend_target.dt + else: + # config is guaranteed to have a dt + dt = backend_config.dt + + solver = Solver( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=hamiltonian_operators, + hamiltonian_channels=hamiltonian_channels, + channel_carrier_freqs=channel_freqs, + dt=dt, + rotating_frame=rotating_frame, + evaluation_mode=evaluation_mode, + rwa_cutoff_freq=rwa_cutoff_freq, + ) + + return cls( + solver=solver, + target=Target(dt=dt), + subsystem_dims=subsystem_dims, + **options, + )
    +
    + + + +
    +[docs] +def default_experiment_result_function( + experiment_name: str, + solver_result: OdeResult, + measurement_subsystems: List[int], + memory_slot_indices: List[int], + num_memory_slots: Union[None, int], + backend: DynamicsBackend, + seed: Optional[int] = None, + metadata: Optional[Dict] = None, +) -> ExperimentResult: + """Default routine for generating ExperimentResult object. + + To generate the results for a given experiment, this method takes the following steps: + + * The final state is transformed out of the rotating frame and into the lab frame using + ``backend.options.solver``. + * If ``backend.options.normalize_states==True``, the final state is normalized. + * Measurement results are computed, in the dressed basis, based on both the measurement-related + options in ``backend.options`` and the measurement specification extracted from the specific + experiment. + + Args: + experiment_name: Name of experiment. + solver_result: Result object from :class:`Solver.solve`. + measurement_subsystems: Labels of subsystems in the model being measured. + memory_slot_indices: Indices of memory slots to store the results in for each subsystem. + num_memory_slots: Total number of memory slots in the returned output. If ``None``, + ``max(memory_slot_indices)`` will be used. + backend: The backend instance that ran the simulation. Various options and properties + are utilized. + seed: Seed for any random number generation involved (e.g. when computing outcome samples). + metadata: Metadata to add to the header of the + :class:`~qiskit.result.models.ExperimentResult` object. + + Returns: + :class:`~qiskit.result.models.ExperimentResult` object containing results. + + Raises: + QiskitError: If a specified option is unsupported. + """ + + yf = solver_result.y[-1] + tf = solver_result.t[-1] + + # Take state out of frame, put in dressed basis, and normalize + if isinstance(yf, Statevector): + yf = np.array(backend.options.solver.model.rotating_frame.state_out_of_frame(t=tf, y=yf)) + yf = backend._dressed_states_adjoint @ yf + yf = Statevector(yf, dims=backend.options.subsystem_dims) + + if backend.options.normalize_states: + yf = yf / np.linalg.norm(yf.data) + elif isinstance(yf, DensityMatrix): + yf = np.array( + backend.options.solver.model.rotating_frame.operator_out_of_frame(t=tf, operator=yf) + ) + yf = backend._dressed_states_adjoint @ yf @ backend._dressed_states + yf = DensityMatrix(yf, dims=backend.options.subsystem_dims) + + if backend.options.normalize_states: + yf = yf / np.diag(yf.data).sum() + + if backend.options.meas_level == MeasLevel.CLASSIFIED: + memory_slot_probabilities = _get_memory_slot_probabilities( + probability_dict=yf.probabilities_dict(qargs=measurement_subsystems), + memory_slot_indices=memory_slot_indices, + num_memory_slots=num_memory_slots, + max_outcome_value=backend.options.max_outcome_level, + ) + + # sample + memory_samples = _sample_probability_dict( + memory_slot_probabilities, + shots=backend.options.shots, + normalize_probabilities=backend.options.normalize_states, + seed=seed, + ) + counts = _get_counts_from_samples(memory_samples) + + # construct results object + exp_data = ExperimentResultData( + counts=counts, memory=memory_samples if backend.options.memory else None + ) + return ExperimentResult( + shots=backend.options.shots, + success=True, + data=exp_data, + meas_level=MeasLevel.CLASSIFIED, + seed=seed, + header=QobjHeader(name=experiment_name, metadata=metadata), + ) + elif backend.options.meas_level == MeasLevel.KERNELED: + iq_centers = backend.options.iq_centers + if iq_centers is None: + # Default iq_centers + iq_centers = [] + for sub_dim in backend.options.subsystem_dims: + theta = 2 * np.pi / sub_dim + iq_centers.append( + [(np.cos(idx * theta), np.sin(idx * theta)) for idx in range(sub_dim)] + ) + + # generate IQ + measurement_data = _get_iq_data( + yf, + measurement_subsystems=measurement_subsystems, + iq_centers=iq_centers, + iq_width=backend.options.iq_width, + shots=backend.options.shots, + memory_slot_indices=memory_slot_indices, + num_memory_slots=num_memory_slots, + seed=seed, + ) + + if backend.options.meas_return == MeasReturnType.AVERAGE: + measurement_data = np.average(measurement_data, axis=0) + + # construct results object + exp_data = ExperimentResultData(memory=measurement_data) + return ExperimentResult( + shots=backend.options.shots, + success=True, + data=exp_data, + meas_level=MeasLevel.KERNELED, + seed=seed, + header=QobjHeader(name=experiment_name, metadata=metadata), + ) + + else: + raise QiskitError(f"meas_level=={backend.options.meas_level} not implemented.")
    + + + +def _validate_run_input(run_input, accept_list=True): + """Raise errors if the run_input is not one of QuantumCircuit, Schedule, ScheduleBlock, or + a list of these. + """ + if isinstance(run_input, list) and accept_list: + # if list apply recursively, but no longer accept lists + for x in run_input: + _validate_run_input(x, accept_list=False) + elif not isinstance(run_input, (QuantumCircuit, Schedule, ScheduleBlock)): + raise QiskitError(f"Input type {type(run_input)} not supported by DynamicsBackend.run.") + + +def _get_acquire_instruction_timings( + schedules: List[Schedule], subsystem_dims: List[int], dt: float +) -> Tuple[List[List[float]], List[List[int]], List[List[int]]]: + """Get the required data from the acquire commands in each schedule. + + Additionally validates that each schedule has Acquire instructions occurring at one time, at + least one memory slot is being listed, and all measured subsystem indices are less than + ``len(subsystem_dims)``. Additionally, a warning is raised if a 'trivial' subsystem is measured, + i.e. one with dimension 1. + + Args: + schedules: A list of schedules. + subsystem_dims: List of subsystem dimensions. + dt: The sample size. + Returns: + A tuple of lists containing, for each schedule: the list of integration intervals required + for each schedule (in absolute time, from 0.0 to the beginning of the acquire instructions), + a list of the subsystems being measured, and a list of the memory slots indices in which to + store the results of each subsystem measurement. + Raises: + QiskitError: If a schedule contains no measurement, if a schedule contains measurements at + different times, or if a measurement has an invalid subsystem label. + """ + t_span_list = [] + measurement_subsystems_list = [] + memory_slot_indices_list = [] + for schedule in schedules: + schedule_acquires = [] + schedule_acquire_times = [] + for start_time, inst in schedule.instructions: + # only track acquires saving in a memory slot + if isinstance(inst, pulse.Acquire) and inst.mem_slot is not None: + schedule_acquires.append(inst) + schedule_acquire_times.append(start_time) + + # validate + if len(schedule_acquire_times) == 0: + raise QiskitError( + "At least one measurement saving a a result in a MemorySlot " + "must be present in each schedule." + ) + + for acquire_time in schedule_acquire_times[1:]: + if acquire_time != schedule_acquire_times[0]: + raise QiskitError("DynamicsBackend.run only supports measurements at one time.") + + # use dt to convert acquire start time from sample index to the integration interval + t_span_list.append([0.0, dt * schedule_acquire_times[0]]) + measurement_subsystems = [] + memory_slot_indices = [] + for inst in schedule_acquires: + if not inst.channel.index < len(subsystem_dims): + raise QiskitError( + f"Attempted to measure out of bounds subsystem {inst.channel.index}." + ) + + if subsystem_dims[inst.channel.index] == 1: + warnings.warn(f"Measuring trivial subsystem {inst.channel.index} with dimension 1.") + + measurement_subsystems.append(inst.channel.index) + + memory_slot_indices.append(inst.mem_slot.index) + + measurement_subsystems_list.append(measurement_subsystems) + memory_slot_indices_list.append(memory_slot_indices) + + return t_span_list, measurement_subsystems_list, memory_slot_indices_list + + +def _to_schedule_list( + run_input: List[Union[QuantumCircuit, Schedule, ScheduleBlock]], backend: BackendV2 +): + """Convert all inputs to schedules, and store the number of classical registers present + in any circuits. + """ + if not isinstance(run_input, list): + run_input = [run_input] + + schedules = [] + num_memslots = [] + for sched in run_input: + num_memslots.append(None) + if isinstance(sched, ScheduleBlock): + schedules.append(block_to_schedule(sched)) + elif isinstance(sched, Schedule): + schedules.append(sched) + elif isinstance(sched, QuantumCircuit): + num_memslots[-1] = sum(creg.size for creg in sched.cregs) + schedules.append(build_schedule(sched, backend, dt=backend.options.solver._dt)) + else: + raise QiskitError(f"Type {type(sched)} cannot be converted to Schedule.") + return schedules, num_memslots + + +def _get_backend_channel_freqs( + backend_target: Optional[Target], + backend_config: PulseBackendConfiguration, + backend_defaults: Optional[PulseDefaults], + channels: List[str], +) -> Dict[str, float]: + """Extract frequencies of channels from a backend configuration and defaults. + + Args: + backend_target: A backend target object or ``None``. + backend_config: A backend configuration object. + backend_defaults: A backend defaults object or ``None``. + channels: Channel labels given as strings, assumed to be unique. + + Returns: + Dict: Mapping of channel labels to frequencies. + + Raises: + QiskitError: If the frequency for one of the channels cannot be found. + """ + + # partition types of channels + drive_channels = [] + meas_channels = [] + u_channels = [] + + for channel in channels: + if channel[0] == "d": + drive_channels.append(channel) + elif channel[0] == "m": + meas_channels.append(channel) + elif channel[0] == "u": + u_channels.append(channel) + else: + raise QiskitError("Unrecognized channel type requested.") + + # extract and validate channel frequency parameters + if drive_channels: + # get drive channel frequencies + drive_frequencies = [] + if (backend_target is not None) and (backend_target.qubit_properties is not None): + drive_frequencies = [q.frequency for q in backend_target.qubit_properties] + elif backend_defaults is not None: + drive_frequencies = backend_defaults.qubit_freq_est + else: + raise QiskitError( + "DriveChannels in model but frequencies not available in target or defaults." + ) + + if meas_channels: + if backend_defaults is not None: + meas_frequencies = backend_defaults.meas_freq_est + else: + raise QiskitError("MeasureChannels in model but defaults does not have meas_freq_est.") + + # backend_config.u_channel_lo is guaranteed to be a list + u_channel_lo = backend_config.u_channel_lo + + # populate frequencies + channel_freqs = {} + + for channel in drive_channels: + idx = int(channel[1:]) + if idx >= len(drive_frequencies): + raise QiskitError(f"DriveChannel index {idx} is out of bounds.") + channel_freqs[channel] = drive_frequencies[idx] + + for channel in meas_channels: + idx = int(channel[1:]) + if idx >= len(meas_frequencies): + raise QiskitError(f"MeasureChannel index {idx} is out of bounds.") + channel_freqs[channel] = meas_frequencies[idx] + + for channel in u_channels: + idx = int(channel[1:]) + if idx >= len(u_channel_lo): + raise QiskitError(f"ControlChannel index {idx} is out of bounds.") + freq = 0.0 + for channel_lo in u_channel_lo[idx]: + freq += drive_frequencies[channel_lo.q] * channel_lo.scale + + channel_freqs[channel] = freq + + # validate that all channels have frequencies + for channel in channels: + if channel not in channel_freqs: + raise QiskitError(f"No carrier frequency found for channel {channel}.") + + return channel_freqs +
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    Source code for qiskit_dynamics.dispatch.dispatch

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +"""Dispatch class"""
    +
    +import functools
    +from types import FunctionType
    +from typing import Optional, Union, Tuple, Callable
    +from .exceptions import DispatchError
    +
    +
    +class Dispatch:
    +    """Dispatch NumPy ufuncs to multiple array backends."""
    +
    +    # Registered backend names
    +    REGISTERED_BACKENDS = tuple()
    +
    +    # Set version of registered backend name strings
    +    _REGISTERED_BACKENDS = set()
    +
    +    # Registered backend array types
    +    REGISTERED_TYPES = tuple()
    +
    +    # Set version of registered backend array types
    +    _REGISTERED_TYPES = {}
    +
    +    # Default backend. If None the backend of the input array is used.
    +    DEFAULT_BACKEND = None
    +
    +    # Dispatch table from backend name to asarray function
    +    ASARRAY_DISPATCH = {}
    +
    +    # Dispatch table from backend name to repr function
    +    REPR_DISPATCH = {}
    +
    +    # Dispatch table from backend name to array_ufunc dispatcher
    +    ARRAY_UFUNC_DISPATCH = {}
    +
    +    # Dispatch table from backend name to array_function dispatcher
    +    ARRAY_FUNCTION_DISPATCH = {}
    +
    +    @classmethod
    +    def backend(
    +        cls, array: any, subclass: Optional[bool] = False, fallback: Optional[str] = None
    +    ) -> str:
    +        """Return the registered backend string of a array object.
    +
    +        Args:
    +            array: an array object.
    +            subclass: If True check if array type is a subclass of
    +                      registered types.
    +            fallback: Fallback backend to use if array does not match any
    +                      registered types.
    +
    +        Returns:
    +            str: The array backend name if the array type is registered,
    +                 or `use_default=True` and the type is not registered.
    +            None: If `use_default=False` and the array type is not registered.
    +
    +        Raises:
    +            DispatchError: if fallback backend is not valid.
    +        """
    +        backend = cls._REGISTERED_TYPES.get(type(array), None)
    +        if backend is not None:
    +            return backend
    +        if subclass:
    +            for key, backend in cls._REGISTERED_TYPES.items():
    +                if isinstance(array, key):
    +                    return backend
    +        if fallback is None or fallback in cls._REGISTERED_BACKENDS:
    +            return fallback
    +        raise DispatchError(f"fallback '{fallback}' is not a registered backend.")
    +
    +    @classmethod
    +    def validate_backend(cls, backend: str):
    +        """Raise an exception if backend is not registered.
    +
    +        Args:
    +            backend: array backend name.
    +
    +        Raises:
    +            DispatchError: if backend is not registered.
    +        """
    +        if backend not in cls._REGISTERED_BACKENDS:
    +            registered = cls.REGISTERED_BACKENDS if cls.REGISTERED_BACKENDS else None
    +            raise DispatchError(
    +                f"""'{backend}' is not a registered array backends
    +                (registered backends: {registered})"""
    +            )
    +
    +    @classmethod
    +    def array_ufunc(cls, backend: str, ufunc: callable, method: str) -> callable:
    +        """Return the ufunc for the specified array backend
    +
    +        Args:
    +            backend: the array backend name.
    +            ufunc: the numpy ufunc.
    +            method: the ufunc method.
    +
    +        Returns:
    +            callable: the ufunc for the specified array backend.
    +        """
    +        return cls.ARRAY_UFUNC_DISPATCH[backend](ufunc, method)
    +
    +    @classmethod
    +    def repr(cls, backend: str) -> callable:
    +        """Return the ufunc for the specified array backend
    +
    +        Args:
    +            backend: the array backend name.
    +
    +        Returns:
    +            callable: the repr function for the specified array backend.
    +        """
    +        return cls.REPR_DISPATCH[backend]
    +
    +    @classmethod
    +    def array_function(cls, backend: str, func: callable) -> callable:
    +        """Return the array function for the specified array backend
    +
    +        Args:
    +            backend: the array backend name.
    +            func: the numpy array function.
    +
    +        Returns:
    +            callable: the function for the specified array backend.
    +        """
    +        return cls.ARRAY_FUNCTION_DISPATCH[backend](func)
    +
    +    @classmethod
    +    def register_types(cls, name: str, array_types: Union[any, Tuple[any]]):
    +        """Register an asarray array backend.
    +
    +        Args:
    +            name: A string to identify the array backend.
    +            array_types: A class or list of classes to associate
    +                         with the array backend.
    +        """
    +        cls._REGISTERED_BACKENDS.add(name)
    +        cls.REGISTERED_BACKENDS = tuple(cls._REGISTERED_BACKENDS)
    +        if not isinstance(array_types, (list, tuple)):
    +            array_types = [array_types]
    +        for atype in array_types:
    +            cls._REGISTERED_TYPES[atype] = name
    +        cls.REGISTERED_TYPES = tuple(cls._REGISTERED_TYPES.keys())
    +
    +    @classmethod
    +    def register_asarray(
    +        cls, name: str, array_types: Optional[Union[any, Tuple[any]]] = None
    +    ) -> callable:
    +        """Decorator to register an asarray function for an array backend.
    +
    +        The function being wrapped must have signature
    +        `func(arg, dtype=None, order=None)`.
    +
    +        Args:
    +            name: A string to identify the array backend.
    +            array_types: Optional, the array types to register
    +                         for the backend.
    +
    +        Returns:
    +            callable: the decorated function.
    +        """
    +        if array_types:
    +            cls.register_types(name, array_types)
    +
    +        def decorator(func):
    +            cls.ASARRAY_DISPATCH[name] = func
    +            return func
    +
    +        return decorator
    +
    +    @classmethod
    +    def register_repr(
    +        cls, name: str, array_types: Optional[Union[any, Tuple[any]]] = None
    +    ) -> callable:
    +        """Decorator to register an asarray function for an array backend.
    +
    +        The function being wrapped must have signature
    +        `func(arg, dtype=None, order=None)`.
    +
    +        Args:
    +            name: A string to identify the array backend.
    +            array_types: Optional, the array types to register
    +                         for the backend.
    +
    +        Returns:
    +            callable: the decorated function.
    +        """
    +        if array_types:
    +            cls.register_types(name, array_types)
    +
    +        def decorator(func):
    +            cls.REPR_DISPATCH[name] = func
    +            return func
    +
    +        return decorator
    +
    +    @classmethod
    +    def register_array_ufunc(
    +        cls, name: str, array_types: Optional[Union[any, Tuple[any]]] = None
    +    ) -> callable:
    +        """Decorator to register a ufunc dispatch function.
    +
    +        This is used for handling of dispatch of NumPy ufuncs using
    +        `__array_ufunc__`. The function being wrapped must have
    +        signature `f(ufunc, method) -> callable(*args, **kwargs)`
    +
    +        Args:
    +            name: A string to identify the array backend.
    +            array_types: Optional, the array types to register
    +                         for the backend.
    +
    +        Returns:
    +            callable: the decorated function.
    +        """
    +        if array_types:
    +            cls.register_types(name, array_types)
    +
    +        def decorator(func):
    +            cls.ARRAY_UFUNC_DISPATCH[name] = func
    +            return func
    +
    +        return decorator
    +
    +    @classmethod
    +    def register_array_function(
    +        cls, name: str, array_types: Optional[Union[any, Tuple[any]]] = None
    +    ) -> callable:
    +        """Decorator to register an array function dispatch function.
    +
    +        This is used for handling of dispatch of NumPy functions using
    +        `__array_function__`. The function being wrapped must have
    +        signature `f(func) -> callable(*args, **kwargs)`.
    +
    +        Args:
    +            name: A string to identify the array backend.
    +            array_types: Optional, the array types to register
    +                         for the backend.
    +
    +        Returns:
    +            callable: the decorated function.
    +        """
    +        if array_types:
    +            cls.register_types(name, array_types)
    +
    +        def decorator(func):
    +            cls.ARRAY_FUNCTION_DISPATCH[name] = func
    +            return func
    +
    +        return decorator
    +
    +    @staticmethod
    +    def implements(np_function, dispatch_dict):
    +        """Register a numpy __array_function__ implementation."""
    +
    +        def decorator(func):
    +            dispatch_dict[np_function] = func
    +            return func
    +
    +        return decorator
    +
    +
    +
    +[docs] +def asarray( + array: any, + dtype: Optional[any] = None, + order: Optional[str] = None, + backend: Optional[str] = None, +) -> any: + """Convert input array to an array on the specified backend. + + This functions like `numpy.asarray` but optionally supports + casting to other registered array backends. + + Args: + array: An array_like input. + dtype: Optional. The dtype of the returned array. This value + must be supported by the specified array backend. + order: Optional. The array order. This value must be supported + by the specified array backend. + backend: A registered array backend name. If None the + default array backend will be used. + + Returns: + array: an array object of the form specified by the backend + kwarg. + """ + if backend: + Dispatch.validate_backend(backend) + else: + if Dispatch.DEFAULT_BACKEND: + backend = Dispatch.DEFAULT_BACKEND + else: + backend = Dispatch.backend(array, fallback="numpy") + return Dispatch.ASARRAY_DISPATCH[backend](array, dtype=dtype, order=order)
    + + + +
    +[docs] +def requires_backend(backend: str) -> Callable: + """Return a function and class decorator for checking a backend is available. + + If the the required backend is not in the list of :func:`available_backends` + any decorated function or method will raise an exception when called, and + any decorated class will raise an exeption when its ``__init__`` is called. + + Args: + backend: the backend name required by class or function. + + Returns: + Callable: A decorator that may be used to specify that a function, class, + or class method requires a specific backend to be installed. + """ + + def decorator(obj): + """Specify that the decorated object requires a specifc Array backend.""" + + def check_backend(descriptor): + if backend not in Dispatch.REGISTERED_BACKENDS: + raise DispatchError( + f"Array backend '{backend}' required by {descriptor} " + "is not installed. Please install the optional " + "library '{backend}'." + ) + + # Decorate a function or method + if isinstance(obj, FunctionType): + + @functools.wraps(obj) + def decorated_func(*args, **kwargs): + check_backend(f"function {obj}") + return obj(*args, **kwargs) + + return decorated_func + + # Decorate a class + elif isinstance(obj, type): + obj_init = obj.__init__ + + @functools.wraps(obj_init) + def decorated_init(self, *args, **kwargs): + check_backend(f"class {obj}") + obj_init(self, *args, **kwargs) + + obj.__init__ = decorated_init + return obj + + else: + raise Exception(f"Cannot decorate object {obj} that is not a class or function.") + + return decorator
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/models/generator_model.html b/stable/0.4/_modules/qiskit_dynamics/models/generator_model.html new file mode 100644 index 000000000..26771b87a --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/models/generator_model.html @@ -0,0 +1,914 @@ + + + + + + + + qiskit_dynamics.models.generator_model - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    +

    Source code for qiskit_dynamics.models.generator_model

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Generator models module.
    +"""
    +
    +from abc import ABC, abstractmethod
    +from typing import Tuple, Union, List, Optional
    +from warnings import warn
    +from copy import copy
    +import numpy as np
    +from scipy.sparse import csr_matrix, issparse, diags
    +
    +from qiskit import QiskitError
    +from qiskit.quantum_info.operators import Operator
    +from qiskit_dynamics.models.operator_collections import (
    +    BaseOperatorCollection,
    +    DenseOperatorCollection,
    +    SparseOperatorCollection,
    +    JAXSparseOperatorCollection,
    +)
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.signals import Signal, SignalList
    +from qiskit_dynamics.type_utils import to_numeric_matrix_type
    +from .rotating_frame import RotatingFrame
    +
    +try:
    +    import jax
    +except ImportError:
    +    pass
    +
    +
    +class BaseGeneratorModel(ABC):
    +    r"""Defines an interface for a time-dependent linear differential equation of the form
    +    :math:`\dot{y}(t) = \Lambda(t, y)`, where :math:`\Lambda` is linear in :math:`y`. The core
    +    functionality is evaluation of :math:`\Lambda(t, y)`, as well as, if possible, evaluation of the
    +    map :math:`\Lambda(t, \cdot)`.
    +
    +    Additionally, the class defines interfaces for:
    +
    +     * Setting a "rotating frame", specified either directly as a :class:`RotatingFrame`
    +        instance, or an operator from which a :class:`RotatingFrame` instance can be constructed.
    +        The exact meaning of this transformation is determined by the structure of
    +        :math:`\Lambda(t, y)`, and is therefore by handled by concrete subclasses.
    +     * Setting an internal "evaluation mode", to set the specific numerical methods to use
    +        when evaluating :math:`\Lambda(t, y)`.
    +    """
    +
    +    @property
    +    @abstractmethod
    +    def dim(self) -> int:
    +        """The matrix dimension."""
    +
    +    @property
    +    @abstractmethod
    +    def rotating_frame(self) -> RotatingFrame:
    +        """The rotating frame."""
    +
    +    @rotating_frame.setter
    +    @abstractmethod
    +    def rotating_frame(self, rotating_frame: RotatingFrame):
    +        pass
    +
    +    @property
    +    @abstractmethod
    +    def in_frame_basis(self) -> bool:
    +        """Whether or not the model is evaluated in the basis in which the frame is diagonalized."""
    +
    +    @in_frame_basis.setter
    +    @abstractmethod
    +    def in_frame_basis(self, in_frame_basis: bool):
    +        pass
    +
    +    @property
    +    @abstractmethod
    +    def evaluation_mode(self) -> str:
    +        """Numerical evaluation mode of the model."""
    +
    +    @evaluation_mode.setter
    +    @abstractmethod
    +    def evaluation_mode(self, new_mode: str):
    +        pass
    +
    +    @abstractmethod
    +    def evaluate(self, time: float) -> Array:
    +        r"""If possible, evaluate the map :math:`\Lambda(t, \cdot)`.
    +
    +        Args:
    +            time: The time to evaluate the model at.
    +        """
    +
    +    @abstractmethod
    +    def evaluate_rhs(self, time: float, y: Array) -> Array:
    +        r"""Evaluate the right hand side :math:`\dot{y}(t) = \Lambda(t, y)`.
    +
    +        Args:
    +            time: The time to evaluate the model at.
    +            y: State of the differential equation.
    +        """
    +
    +    def copy(self):
    +        """Return a copy of self."""
    +        return copy(self)
    +
    +    def __call__(self, time: float, y: Optional[Array] = None) -> Array:
    +        r"""Evaluate generator RHS functions. If ``y is None``, attemps to evaluate
    +        :math:`\Lambda(t, \cdot)`, otherwise, calculates :math:`\Lambda(t, y)`.
    +
    +        Args:
    +            time: The time to evaluate at.
    +            y: Optional state.
    +
    +        Returns:
    +            Array: Either the evaluated model, or the RHS for the given y.
    +        """
    +        return self.evaluate(time) if y is None else self.evaluate_rhs(time, y)
    +
    +
    +
    +[docs] +class GeneratorModel(BaseGeneratorModel): + r"""A model for a a linear matrix differential equation in standard form. + + :class:`GeneratorModel` is a concrete instance of :class:`BaseGeneratorModel`, where the map + :math:`\Lambda(t, y)` is explicitly constructed as: + + .. math:: + + \Lambda(t, y) = G(t)y, + + G(t) = \sum_i s_i(t) G_i + G_d + + where the :math:`G_i` are matrices (represented by :class:`Operator` or :class:`Array` objects), + the :math:`s_i(t)` are signals represented by a list of :class:`Signal` objects, and :math:`G_d` + is the constant-in-time static term of the generator. + """ + + def __init__( + self, + static_operator: Optional[Array] = None, + operators: Optional[Array] = None, + signals: Optional[Union[SignalList, List[Signal]]] = None, + rotating_frame: Optional[Union[Operator, Array, RotatingFrame]] = None, + in_frame_basis: bool = False, + evaluation_mode: str = "dense", + ): + """Initialize. + + Args: + static_operator: Constant part of the generator. + operators: A list of operators :math:`G_i`. + signals: Stores the terms :math:`s_i(t)`. While required for evaluation, + :class:`GeneratorModel` signals are not required at instantiation. + rotating_frame: Rotating frame operator. + in_frame_basis: Whether to represent the model in the basis in which the rotating frame + operator is diagonalized. + evaluation_mode: Evaluation mode to use. Supported options are ``'dense'`` and + ``'sparse'``. Call ``help(GeneratorModel.evaluation_mode)`` for more details. + Raises: + QiskitError: If model not sufficiently specified. + """ + if static_operator is None and operators is None: + raise QiskitError( + f"{type(self).__name__} requires at least one of static_operator or operators to " + "be specified at construction." + ) + + # initialize internal operator representation + self._operator_collection = construct_operator_collection( + evaluation_mode=evaluation_mode, static_operator=static_operator, operators=operators + ) + self._evaluation_mode = evaluation_mode + + # set frame + self._rotating_frame = None + self.rotating_frame = rotating_frame + + # set operation in frame basis + self._in_frame_basis = None + self.in_frame_basis = in_frame_basis + + # initialize signal-related attributes + self.signals = signals + + @property + def dim(self) -> int: + """The matrix dimension.""" + return self._operator_collection.dim + + @property + def evaluation_mode(self) -> str: + """Numerical evaluation mode of the model. + + Possible values: + + * ``"dense"``: Stores/evaluates operators using dense Arrays. + * ``"sparse"``: Stores/evaluates operators using sparse matrices. If the default Array + backend is JAX, implemented with JAX BCOO arrays, otherwise uses scipy + :class:`csr_matrix` sparse type. Note that JAX sparse mode is only recommended for use on + CPU. + + Raises: + NotImplementedError: If, when being set, ``new_mode`` is not one of the above supported + evaluation modes. + """ + return self._evaluation_mode + + @evaluation_mode.setter + def evaluation_mode(self, new_mode: str): + if new_mode != self._evaluation_mode: + self._operator_collection = construct_operator_collection( + new_mode, + self._operator_collection.static_operator, + self._operator_collection.operators, + ) + self._evaluation_mode = new_mode + + @property + def rotating_frame(self) -> RotatingFrame: + """The rotating frame. + + This property can be set with a :class:`RotatingFrame` instance, or any valid constructor + argument to this class. + + Setting this property updates the internal operator to use the new frame. + """ + return self._rotating_frame + + @rotating_frame.setter + def rotating_frame(self, rotating_frame: Union[Operator, Array, RotatingFrame]): + new_frame = RotatingFrame(rotating_frame) + + new_static_operator = transfer_static_operator_between_frames( + self._get_static_operator(in_frame_basis=True), + new_frame=new_frame, + old_frame=self.rotating_frame, + ) + new_operators = transfer_operators_between_frames( + self._get_operators(in_frame_basis=True), + new_frame=new_frame, + old_frame=self.rotating_frame, + ) + + self._rotating_frame = new_frame + + self._operator_collection = construct_operator_collection( + self.evaluation_mode, new_static_operator, new_operators + ) + + @property + def signals(self) -> SignalList: + """The signals in the model. + + Raises: + QiskitError: If set to ``None`` when operators exist, or when set to a number of signals + different then the number of operators. + """ + return self._signals + + @signals.setter + def signals(self, signals: Union[SignalList, List[Signal]]): + if signals is None: + self._signals = None + elif signals is not None and self.operators is None: + raise QiskitError("Signals must be None if operators is None.") + else: + # if signals is a list, instantiate a SignalList + if isinstance(signals, list): + signals = SignalList(signals) + + # if it isn't a SignalList by now, raise an error + if not isinstance(signals, SignalList): + raise QiskitError("Signals specified in unaccepted format.") + + # verify signal length is same as operators + if isinstance(self.operators, list): + len_operators = len(self.operators) + else: + len_operators = self.operators.shape[0] + if len(signals) != len_operators: + raise QiskitError("Signals needs to have the same length as operators.") + + self._signals = signals + + @property + def in_frame_basis(self) -> bool: + """Whether the model is represented in the basis that diagonalizes the frame operator.""" + return self._in_frame_basis + + @in_frame_basis.setter + def in_frame_basis(self, in_frame_basis: bool): + self._in_frame_basis = in_frame_basis + + @property + def operators(self) -> Array: + """The operators in the model.""" + return self._get_operators(in_frame_basis=self._in_frame_basis) + + @property + def static_operator(self) -> Array: + """The static operator.""" + return self._get_static_operator(in_frame_basis=self._in_frame_basis) + + @static_operator.setter + def static_operator(self, static_operator: Array): + self._set_static_operator( + new_static_operator=static_operator, operator_in_frame_basis=self._in_frame_basis + ) + + def _get_operators(self, in_frame_basis: Optional[bool] = False) -> Array: + """Get the operators used in the model construction. + + Args: + in_frame_basis: Flag indicating whether to return the operators + in the basis in which the rotating frame operator is diagonal. + Returns: + The operators in the basis specified by ``in_frame_basis``. + """ + ops = self._operator_collection.operators + if ops is not None and not in_frame_basis and self.rotating_frame is not None: + return self.rotating_frame.operator_out_of_frame_basis(ops) + return ops + + def _get_static_operator(self, in_frame_basis: Optional[bool] = False) -> Array: + """Get the constant term. + + Args: + in_frame_basis: Whether the returned static_operator should be in the basis in which the + frame is diagonal. + Returns: + The static operator term. + """ + op = self._operator_collection.static_operator + if not in_frame_basis and self.rotating_frame is not None: + return self.rotating_frame.operator_out_of_frame_basis(op) + return op + + def _set_static_operator( + self, + new_static_operator: Array, + operator_in_frame_basis: Optional[bool] = False, + ): + """Sets static term. Note that if the model has a rotating frame this will override any + contributions to the static term due to the frame transformation. + + Args: + new_static_operator: The static operator operator. + operator_in_frame_basis: Whether `new_static_operator` is already in the rotating frame + basis. + """ + if new_static_operator is None: + self._operator_collection.static_operator = None + else: + if not operator_in_frame_basis and self.rotating_frame is not None: + new_static_operator = self.rotating_frame.operator_into_frame_basis( + new_static_operator + ) + + self._operator_collection.static_operator = new_static_operator + +
    +[docs] + def evaluate(self, time: float) -> Array: + """Evaluate the model in array format as a matrix, independent of state. + + Args: + time: The time to evaluate the model at. + + Returns: + Array: The evaluated model as a matrix. + + Raises: + QiskitError: If model cannot be evaluated. + """ + if self._signals is None and self._operator_collection.operators is not None: + raise QiskitError( + f"{type(self).__name__} with non-empty operators must be evaluated signals." + ) + + # Evaluated in frame basis, but without rotations + op_combo = self._operator_collection(self._signals(time) if self._signals else None) + + # Apply rotations e^{-Ft}Ae^{Ft} in frame basis where F = D + return self.rotating_frame.operator_into_frame( + time, op_combo, operator_in_frame_basis=True, return_in_frame_basis=self._in_frame_basis + )
    + + +
    +[docs] + def evaluate_rhs(self, time: float, y: Array) -> Array: + r"""Evaluate ``G(t) @ y``. + + Args: + time: The time to evaluate the model at . + y: Array specifying system state. + + Returns: + Array defined by :math:`G(t) \times y`. + + Raises: + QiskitError: If model cannot be evaluated. + """ + if self._signals is None: + if self._operator_collection.operators is not None: + raise QiskitError( + f"{type(self).__name__} with non-empty operators must be evaluated signals." + ) + sig_vals = None + else: + sig_vals = self._signals.__call__(time) + + if self.rotating_frame is not None: + # First, compute e^{tF}y as a pre-rotation in the frame basis + out = self.rotating_frame.state_out_of_frame( + time, y, y_in_frame_basis=self._in_frame_basis, return_in_frame_basis=True + ) + # Then, compute the product Ae^{tF}y + out = self._operator_collection(sig_vals, out) + # Finally, we have the full operator e^{-tF}Ae^{tF}y + out = self.rotating_frame.state_into_frame( + time, out, y_in_frame_basis=True, return_in_frame_basis=self._in_frame_basis + ) + return out + + return self._operator_collection(sig_vals, y)
    +
    + + + +def transfer_static_operator_between_frames( + static_operator: Union[None, Array, csr_matrix], + new_frame: Optional[Union[Array, RotatingFrame]] = None, + old_frame: Optional[Union[Array, RotatingFrame]] = None, +) -> Tuple[Union[None, Array]]: + """Helper function for transforming the static operator of a model from one frame basis into + another. + + ``static_operator`` is additionally transformed as a generator: the old frame operator is added, + and the new one is subtracted. + + Args: + static_operator: Static operator of the model. None is treated as 0. + new_frame: New rotating frame. + old_frame: Old rotating frame. + + Returns: + static_operator: Transformed as described above. + """ + new_frame = RotatingFrame(new_frame) + old_frame = RotatingFrame(old_frame) + + static_operator = to_numeric_matrix_type(static_operator) + + # transform out of old frame basis, and add the old frame operator + if static_operator is not None: + static_operator = old_frame.generator_out_of_frame( + t=0.0, + operator=static_operator, + operator_in_frame_basis=True, + return_in_frame_basis=False, + ) + else: + # "add" the frame operator to 0 + if old_frame.frame_operator is not None: + if issparse(static_operator): + if old_frame.frame_operator.ndim == 1: + static_operator = diags(old_frame.frame_operator, format="csr") + else: + static_operator = csr_matrix(old_frame.frame_operator) + else: + if old_frame.frame_operator.ndim == 1: + static_operator = np.diag(old_frame.frame_operator) + else: + static_operator = old_frame.frame_operator + # transform into new frame basis, and add the new frame operator + if static_operator is not None: + static_operator = new_frame.generator_into_frame( + t=0.0, + operator=static_operator, + operator_in_frame_basis=False, + return_in_frame_basis=True, + ) + else: + # "subtract" the frame operator from 0 + if new_frame.frame_operator is not None: + if issparse(static_operator): + static_operator = -diags(new_frame.frame_diag, format="csr") + else: + static_operator = -np.diag(new_frame.frame_diag) + + return static_operator + + +def transfer_operators_between_frames( + operators: Union[None, Array, List[csr_matrix]], + new_frame: Optional[Union[Array, RotatingFrame]] = None, + old_frame: Optional[Union[Array, RotatingFrame]] = None, +) -> Tuple[Union[None, Array]]: + """Helper function for transforming a list of operators for a model from one frame basis into + another. + + Args: + operators: Operators of the model. If ``None``, remains as ``None``. + new_frame: New rotating frame. + old_frame: Old rotating frame. + + Returns: + operators: Transformed as described above. + """ + new_frame = RotatingFrame(new_frame) + old_frame = RotatingFrame(old_frame) + + operators = to_numeric_matrix_type(operators) + + # transform out of old frame basis + if operators is not None: + # For sparse case, if list, loop + if isinstance(operators, list): + operators = [old_frame.operator_out_of_frame_basis(op) for op in operators] + else: + operators = old_frame.operator_out_of_frame_basis(operators) + + # transform into new frame basis + if operators is not None: + # For sparse case, if list, loop + if isinstance(operators, list): + operators = [new_frame.operator_into_frame_basis(op) for op in operators] + else: + operators = new_frame.operator_into_frame_basis(operators) + + return operators + + +def construct_operator_collection( + evaluation_mode: str, + static_operator: Union[None, Array, csr_matrix], + operators: Union[None, Array, List[csr_matrix]], +) -> BaseOperatorCollection: + """Construct an operator collection for :class:`GeneratorModel`. + + Args: + evaluation_mode: Evaluation mode. + static_operator: Static operator of the model. + operators: Operators for the model. + + Returns: + BaseOperatorCollection: The relevant operator collection. + + Raises: + NotImplementedError: If the ``evaluation_mode`` is invalid. + """ + + if evaluation_mode == "dense": + return DenseOperatorCollection(static_operator=static_operator, operators=operators) + if evaluation_mode == "sparse" and Array.default_backend() == "jax": + # warn that sparse mode when using JAX is primarily recommended for use on CPU + if jax.default_backend() != "cpu": + warn( + """Using sparse mode with JAX is primarily recommended for use on CPU.""", + stacklevel=2, + ) + + return JAXSparseOperatorCollection(static_operator=static_operator, operators=operators) + if evaluation_mode == "sparse": + return SparseOperatorCollection(static_operator=static_operator, operators=operators) + + raise NotImplementedError( + f"Evaluation mode '{evaluation_mode}' is not supported. Call " + "help(GeneratorModel.evaluation_mode) for available options." + ) +
    +
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    + + Made with Sphinx and @pradyunsg's + + Furo +
    + Last updated on 2024/03/18
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/models/hamiltonian_model.html b/stable/0.4/_modules/qiskit_dynamics/models/hamiltonian_model.html new file mode 100644 index 000000000..66b3fc47e --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/models/hamiltonian_model.html @@ -0,0 +1,561 @@ + + + + + + + + qiskit_dynamics.models.hamiltonian_model - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    Source code for qiskit_dynamics.models.hamiltonian_model

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Hamiltonian models module.
    +"""
    +
    +from typing import Union, List, Optional
    +import numpy as np
    +from scipy.sparse import csr_matrix, issparse
    +from scipy.sparse.linalg import norm as spnorm
    +
    +from qiskit import QiskitError
    +from qiskit.quantum_info.operators import Operator
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.signals import Signal, SignalList
    +from qiskit_dynamics.type_utils import to_numeric_matrix_type, to_array
    +from .generator_model import (
    +    GeneratorModel,
    +    transfer_static_operator_between_frames,
    +    transfer_operators_between_frames,
    +    construct_operator_collection,
    +)
    +from .rotating_frame import RotatingFrame
    +
    +
    +
    +[docs] +class HamiltonianModel(GeneratorModel): + r"""A model of a Hamiltonian for the Schrodinger equation. + + This class represents a Hamiltonian as a time-dependent decomposition the form: + + .. math:: + H(t) = H_d + \sum_j s_j(t) H_j, + + where :math:`H_j` are Hermitian operators, :math:`H_d` is the static component, and the + :math:`s_j(t)` are either :class:`~qiskit_dynamics.signals.Signal` objects or numerical + constants. Constructing a :class:`~qiskit_dynamics.models.HamiltonianModel` requires specifying + the above decomposition, e.g.: + + .. code-block:: python + + hamiltonian = HamiltonianModel(static_operator=static_operator, + operators=operators, + signals=signals) + + This class inherits most functionality from :class:`GeneratorModel`, with the following + modifications: + + * The operators :math:`H_d` and :math:`H_j` are assumed and verified to be Hermitian. + * Rotating frames are dealt with assuming the structure of the Schrodinger equation. I.e. + Evaluating the Hamiltonian :math:`H(t)` in a frame :math:`F = -iH_0`, evaluates the + expression :math:`e^{-tF}H(t)e^{tF} - H_0`. + """ + + def __init__( + self, + static_operator: Optional[Array] = None, + operators: Optional[List[Operator]] = None, + signals: Optional[Union[SignalList, List[Signal]]] = None, + rotating_frame: Optional[Union[Operator, Array, RotatingFrame]] = None, + in_frame_basis: bool = False, + evaluation_mode: str = "dense", + validate: bool = True, + ): + """Initialize, ensuring that the operators are Hermitian. + + Args: + static_operator: Time-independent term in the Hamiltonian. + operators: List of Operator objects. + signals: List of coefficients :math:`s_i(t)`. Not required at instantiation, but + necessary for evaluation of the model. + rotating_frame: Rotating frame operator. + If specified with a 1d array, it is interpreted as the + diagonal of a diagonal matrix. Assumed to store + the antihermitian matrix F = -iH. + in_frame_basis: Whether to represent the model in the basis in which the rotating + frame operator is diagonalized. + evaluation_mode: Evaluation mode to use. Supported options are ``'dense'`` and + ``'sparse'``. Call ``help(HamiltonianModel.evaluation_mode)`` for more + details. + validate: If True check input operators are Hermitian. + + Raises: + QiskitError: if operators are not Hermitian + """ + + # verify operators are Hermitian, and if so instantiate + operators = to_numeric_matrix_type(operators) + static_operator = to_numeric_matrix_type(static_operator) + + if validate: + if (operators is not None) and (not is_hermitian(operators)): + raise QiskitError("""HamiltonianModel operators must be Hermitian.""") + if (static_operator is not None) and (not is_hermitian(static_operator)): + raise QiskitError("""HamiltonianModel static_operator must be Hermitian.""") + + super().__init__( + static_operator=static_operator, + operators=operators, + signals=signals, + rotating_frame=rotating_frame, + in_frame_basis=in_frame_basis, + evaluation_mode=evaluation_mode, + ) + + @property + def rotating_frame(self) -> RotatingFrame: + """The rotating frame. + + This property can be set with a :class:`RotatingFrame` instance, or any valid constructor + argument to this class. It can either be Hermitian or anti-Hermitian, and in either case + only the anti-Hermitian version :math:`F=-iH` will be stored. + + Setting this property updates the internal operator list to use the new frame. + """ + return super().rotating_frame + + @rotating_frame.setter + def rotating_frame(self, rotating_frame: Union[Operator, Array, RotatingFrame]) -> Array: + new_frame = RotatingFrame(rotating_frame) + + # convert static operator to new frame setup + static_op = self._get_static_operator(in_frame_basis=True) + if static_op is not None: + static_op = -1j * static_op + + new_static_operator = transfer_static_operator_between_frames( + static_op, + new_frame=new_frame, + old_frame=self.rotating_frame, + ) + + if new_static_operator is not None: + new_static_operator = 1j * new_static_operator + + # convert operators to new frame set up + new_operators = transfer_operators_between_frames( + self._get_operators(in_frame_basis=True), + new_frame=new_frame, + old_frame=self.rotating_frame, + ) + + self._rotating_frame = new_frame + + self._operator_collection = construct_operator_collection( + self.evaluation_mode, new_static_operator, new_operators + ) + +
    +[docs] + def evaluate(self, time: float) -> Array: + """Evaluate the model in array format as a matrix, independent of state. + + Args: + time: The time to evaluate the model at. + + Returns: + Array: The evaluated model as an anti-Hermitian matrix. + + Raises: + QiskitError: If model cannot be evaluated. + """ + return -1j * super().evaluate(time)
    + + +
    +[docs] + def evaluate_rhs(self, time: float, y: Array) -> Array: + r"""Evaluate ``-1j * H(t) @ y``. + + Args: + time: The time to evaluate the model at . + y: Array specifying system state. + + Returns: + Array defined by :math:`G(t) \times y`. + + Raises: + QiskitError: If model cannot be evaluated. + """ + return -1j * super().evaluate_rhs(time, y)
    +
    + + + +def is_hermitian( + operators: Union[Array, csr_matrix, List[csr_matrix], "BCOO"], tol: Optional[float] = 1e-10 +) -> bool: + """Validate that operators are Hermitian. + + Args: + operators: Either a 2d array representing a single operator, a 3d array representing a list + of operators, a ``csr_matrix``, or a list of ``csr_matrix``. + tol: Tolerance for checking zeros. + + Returns: + bool: Whether or not the operators are Hermitian to within tolerance. + + Raises: + QiskitError: If an unexpeted type is received. + """ + if isinstance(operators, (np.ndarray, Array)): + adj = None + if operators.ndim == 2: + adj = np.transpose(np.conjugate(operators)) + elif operators.ndim == 3: + adj = np.transpose(np.conjugate(operators), (0, 2, 1)) + return np.linalg.norm(adj - operators) < tol + elif issparse(operators): + return spnorm(operators - operators.conj().transpose()) < tol + elif isinstance(operators, list) and issparse(operators[0]): + return all(spnorm(op - op.conj().transpose()) < tol for op in operators) + elif type(operators).__name__ == "BCOO": + # fall back on array case for BCOO + return is_hermitian(to_array(operators)) + + raise QiskitError("is_hermitian got an unexpected type.") +
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/models/lindblad_model.html b/stable/0.4/_modules/qiskit_dynamics/models/lindblad_model.html new file mode 100644 index 000000000..b714076b9 --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/models/lindblad_model.html @@ -0,0 +1,1059 @@ + + + + + + + + qiskit_dynamics.models.lindblad_model - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    Source code for qiskit_dynamics.models.lindblad_model

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Lindblad model module.
    +"""
    +
    +from typing import Tuple, Union, List, Optional
    +from warnings import warn
    +from scipy.sparse import csr_matrix
    +
    +from qiskit import QiskitError
    +from qiskit.quantum_info.operators import Operator
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.type_utils import to_numeric_matrix_type
    +from qiskit_dynamics.signals import Signal, SignalList
    +from .generator_model import (
    +    BaseGeneratorModel,
    +    transfer_static_operator_between_frames,
    +    transfer_operators_between_frames,
    +)
    +from .hamiltonian_model import HamiltonianModel, is_hermitian
    +from .operator_collections import (
    +    BaseLindbladOperatorCollection,
    +    DenseLindbladCollection,
    +    DenseVectorizedLindbladCollection,
    +    SparseLindbladCollection,
    +    JAXSparseLindbladCollection,
    +    SparseVectorizedLindbladCollection,
    +    JAXSparseVectorizedLindbladCollection,
    +)
    +from .rotating_frame import RotatingFrame
    +
    +try:
    +    import jax
    +except ImportError:
    +    pass
    +
    +
    +
    +[docs] +class LindbladModel(BaseGeneratorModel): + r"""A model of a quantum system in terms of the Lindblad master equation. + + The Lindblad master equation models the evolution of a density matrix according to: + + .. math:: + + \dot{\rho}(t) = -i[H(t), \rho(t)] + \mathcal{D}_0(\rho(t)) + \mathcal{D}(t)(\rho(t)), + + where :math:`\mathcal{D}_0` is the static dissipator portion, and :math:`\mathcal{D}(t)` is the + time-dependent dissipator portion of the equation, given by + + .. math:: + + \mathcal{D}_0(\rho(t)) = \sum_j N_j \rho N_j^\dagger + - \frac{1}{2} \{N_j^\dagger N_j, \rho\}, + + and + + .. math:: + + \mathcal{D}(t)(\rho(t)) = \sum_j \gamma_j(t) L_j \rho L_j^\dagger + - \frac{1}{2} \{L_j^\dagger L_j, \rho\}, + + respectively. In the above: + + - :math:`[\cdot, \cdot]` and :math:`\{\cdot, \cdot\}` respectively denote the matrix + commutator and anti-commutator, + - :math:`H(t)` denotes the Hamiltonian, + - :math:`N_j` denotes the operators appearing in the static dissipator, + - :math:`L_j` denotes the operators appearing in the time-dpendent portion of the + dissipator, and + - :math:`\gamma_j(t)` denotes the signal corresponding to the + :math:`j^{th}` time-dependent dissipator operator. + + Instantiating an instance of :class:`~qiskit_dynamics.models.LindbladModel` requires specifying + the above decomposition: + + .. code-block:: python + + lindblad_model = LindbladModel( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=hamiltonian_operators, + hamiltonian_signals=hamiltonian_signals, + static_dissipators=static_dissipators, + dissipator_operators=dissipator_operators, + dissipator_signals=dissipator_signals + ) + + where the arguments ``hamiltonian_operators``, ``hamiltonian_signals``, and + ``static_hamiltonian`` are for the Hamiltonian decomposition as in + :class:`~qiskit_dynamics.models.HamiltonianModel`, + and the ``static_dissipators`` correspond to the :math:`N_j`, the ``dissipator_operators`` + to the :math:`L_j`, and the ``dissipator_signals`` the :math:`\gamma_j(t)`. + """ + + def __init__( + self, + static_hamiltonian: Optional[Union[Array, csr_matrix]] = None, + hamiltonian_operators: Optional[Union[Array, List[csr_matrix]]] = None, + hamiltonian_signals: Optional[Union[List[Signal], SignalList]] = None, + static_dissipators: Optional[Union[Array, csr_matrix]] = None, + dissipator_operators: Optional[Union[Array, List[csr_matrix]]] = None, + dissipator_signals: Optional[Union[List[Signal], SignalList]] = None, + rotating_frame: Optional[Union[Operator, Array, RotatingFrame]] = None, + in_frame_basis: bool = False, + evaluation_mode: Optional[str] = "dense", + validate: bool = True, + ): + """Initialize. + + Args: + static_hamiltonian: Constant term in Hamiltonian. + hamiltonian_operators: List of operators in Hamiltonian with time-dependent + coefficients. + hamiltonian_signals: Time-dependent coefficients for hamiltonian_operators. + static_dissipators: List of dissipators with coefficient 1. + dissipator_operators: List of dissipator operators with time-dependent coefficients. + dissipator_signals: Time-dependent coefficients for dissipator_operators. + rotating_frame: Rotating frame in which calcualtions are to be done. If provided, it is + assumed that all operators were already in the frame basis. + in_frame_basis: Whether to represent the model in the basis in which the rotating + frame operator is diagonalized. + evaluation_mode: Evaluation mode to use. Call ``help(LindbladModel.evaluation_mode)`` + for more details. + validate: If True check input hamiltonian_operators and static_hamiltonian are + Hermitian. + + Raises: + QiskitError: If model insufficiently or incorrectly specified. + """ + + if ( + static_hamiltonian is None + and hamiltonian_operators is None + and static_dissipators is None + and dissipator_operators is None + ): + raise QiskitError( + f"{type(self).__name__} requires at least one of static_hamiltonian " + "hamiltonian_operators, static_dissipators, or dissipator_operators " + "to be specified at construction." + ) + + static_hamiltonian = to_numeric_matrix_type(static_hamiltonian) + hamiltonian_operators = to_numeric_matrix_type(hamiltonian_operators) + if validate: + if (hamiltonian_operators is not None) and (not is_hermitian(hamiltonian_operators)): + raise QiskitError("""LinbladModel hamiltonian_operators must be Hermitian.""") + if (static_hamiltonian is not None) and (not is_hermitian(static_hamiltonian)): + raise QiskitError("""LinbladModel static_hamiltonian must be Hermitian.""") + + self._operator_collection = construct_lindblad_operator_collection( + evaluation_mode=evaluation_mode, + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=hamiltonian_operators, + static_dissipators=static_dissipators, + dissipator_operators=dissipator_operators, + ) + self._evaluation_mode = evaluation_mode + self.vectorized_operators = "vectorized" in evaluation_mode + + self._rotating_frame = None + self.rotating_frame = rotating_frame + self._in_frame_basis = None + self.in_frame_basis = in_frame_basis + + self.signals = (hamiltonian_signals, dissipator_signals) + +
    +[docs] + @classmethod + def from_hamiltonian( + cls, + hamiltonian: HamiltonianModel, + static_dissipators: Optional[Union[Array, csr_matrix]] = None, + dissipator_operators: Optional[Union[Array, List[csr_matrix]]] = None, + dissipator_signals: Optional[Union[List[Signal], SignalList]] = None, + evaluation_mode: Optional[str] = None, + ): + """Construct from a :class:`HamiltonianModel`. + + Args: + hamiltonian: The :class:`HamiltonianModel`. + static_dissipators: List of dissipators with coefficient 1. + dissipator_operators: List of dissipators with time-dependent coefficients. + dissipator_signals: List time-dependent coefficients for dissipator_operators. + evaluation_mode: Evaluation mode. Call ``help(LindbladModel.evaluation_mode)`` for more + information. + + Returns: + LindbladModel: Linblad model from parameters. + """ + + if evaluation_mode is None: + evaluation_mode = hamiltonian.evaluation_mode + + ham_copy = hamiltonian.copy() + ham_copy.rotating_frame = None + + return cls( + static_hamiltonian=ham_copy._get_static_operator(in_frame_basis=False), + hamiltonian_operators=ham_copy._get_operators(in_frame_basis=False), + hamiltonian_signals=ham_copy.signals, + static_dissipators=static_dissipators, + dissipator_operators=dissipator_operators, + dissipator_signals=dissipator_signals, + rotating_frame=hamiltonian.rotating_frame, + in_frame_basis=hamiltonian.in_frame_basis, + evaluation_mode=evaluation_mode, + )
    + + + @property + def dim(self) -> int: + """The matrix dimension.""" + if self._operator_collection.static_hamiltonian is not None: + return self._operator_collection.static_hamiltonian.shape[-1] + elif self._operator_collection.hamiltonian_operators is not None: + return self._operator_collection.hamiltonian_operators[0].shape[-1] + elif self._operator_collection.static_dissipators is not None: + return self._operator_collection.static_dissipators[0].shape[-1] + else: + return self._operator_collection.dissipator_operators[0].shape[-1] + + @property + def signals(self) -> Tuple[SignalList]: + """The model's signals as tuple with the 0th entry storing the Hamiltonian signals and the + 1st entry storing the dissipator signals. + + Raises: + QiskitError: If, when setting this property, the given signals are incompatible with + operator structure. + """ + return (self._hamiltonian_signals, self._dissipator_signals) + + @signals.setter + def signals(self, new_signals: Tuple[List[Signal]]): + hamiltonian_signals, dissipator_signals = new_signals + + # set Hamiltonian signals + if hamiltonian_signals is None: + self._hamiltonian_signals = None + elif hamiltonian_signals is not None and self.hamiltonian_operators is None: + raise QiskitError("Hamiltonian signals must be None if hamiltonian_operators is None.") + else: + # if signals is a list, instantiate a SignalList + if isinstance(hamiltonian_signals, list): + hamiltonian_signals = SignalList(hamiltonian_signals) + + # if it isn't a SignalList by now, raise an error + if not isinstance(hamiltonian_signals, SignalList): + raise QiskitError("Hamiltonian signals specified in unaccepted format.") + + # verify signal length is same as operators + if isinstance(self.hamiltonian_operators, list): + len_hamiltonian_operators = len(self.hamiltonian_operators) + else: + len_hamiltonian_operators = self.hamiltonian_operators.shape[0] + if len(hamiltonian_signals) != len_hamiltonian_operators: + raise QiskitError( + "Hamiltonian signals need to have the same length as Hamiltonian operators." + ) + + self._hamiltonian_signals = hamiltonian_signals + + # set dissipator signals + if dissipator_signals is None: + self._dissipator_signals = None + elif dissipator_signals is not None and self.dissipator_operators is None: + raise QiskitError("Dissipator signals must be None if dissipator_operators is None.") + else: + # if signals is a list, instantiate a SignalList + if isinstance(dissipator_signals, list): + dissipator_signals = SignalList(dissipator_signals) + + # if it isn't a SignalList by now, raise an error + if not isinstance(dissipator_signals, SignalList): + raise QiskitError("Dissipator signals specified in unaccepted format.") + + # verify signal length is same as operators + if isinstance(self.dissipator_operators, list): + len_dissipator_operators = len(self.dissipator_operators) + else: + len_dissipator_operators = self.dissipator_operators.shape[0] + if len(dissipator_signals) != len_dissipator_operators: + raise QiskitError( + "Dissipator signals need to have the same length as dissipator operators." + ) + + self._dissipator_signals = dissipator_signals + + @property + def in_frame_basis(self) -> bool: + """Whether to represent the model in the basis in which the frame operator is + diagonalized. + """ + return self._in_frame_basis + + @in_frame_basis.setter + def in_frame_basis(self, in_frame_basis: bool): + self._in_frame_basis = in_frame_basis + + @property + def static_hamiltonian(self) -> Array: + """The static Hamiltonian term.""" + return self._get_static_hamiltonian(in_frame_basis=self._in_frame_basis) + + @static_hamiltonian.setter + def static_hamiltonian(self, static_hamiltonian: Array): + self._set_static_hamiltonian( + new_static_hamiltonian=static_hamiltonian, operator_in_frame_basis=self._in_frame_basis + ) + + @property + def hamiltonian_operators(self) -> Array: + """The Hamiltonian operators.""" + return self._get_hamiltonian_operators(in_frame_basis=self._in_frame_basis) + + @property + def static_dissipators(self) -> Array: + """The static dissipator operators.""" + return self._get_static_dissipators(in_frame_basis=self._in_frame_basis) + + @property + def dissipator_operators(self) -> Array: + """The dissipator operators.""" + return self._get_dissipator_operators(in_frame_basis=self._in_frame_basis) + + def _get_static_hamiltonian(self, in_frame_basis: Optional[bool] = False) -> Array: + """Get the constant Hamiltonian term. + + Args: + in_frame_basis: Flag for whether the returned ``static_operator`` should be in the basis + in which the frame is diagonal. + + Returns: + The static operator term. + """ + op = self._operator_collection.static_hamiltonian + if not in_frame_basis and self.rotating_frame is not None: + return self.rotating_frame.operator_out_of_frame_basis(op) + else: + return op + + def _set_static_hamiltonian( + self, + new_static_hamiltonian: Array, + operator_in_frame_basis: Optional[bool] = False, + ): + """Set the constant Hamiltonian term. + + Note that if the model has a rotating frame this will override any contributions to the + static term due to the frame transformation. + + Args: + new_static_hamiltonian: The static operator operator. + operator_in_frame_basis: Whether ``new_static_operator`` is already in the rotating + frame basis. + """ + if new_static_hamiltonian is None: + self._operator_collection.static_hamiltonian = None + else: + if not operator_in_frame_basis and self.rotating_frame is not None: + new_static_hamiltonian = self.rotating_frame.operator_into_frame_basis( + new_static_hamiltonian + ) + + self._operator_collection.static_hamiltonian = new_static_hamiltonian + + def _get_hamiltonian_operators(self, in_frame_basis: Optional[bool] = False) -> Tuple[Array]: + """Get the Hamiltonian operators, either in the frame basis or not. + + Args: + in_frame_basis: Whether to return in frame basis or not. + + Returns: + Hamiltonian operators. + """ + ham_ops = self._operator_collection.hamiltonian_operators + if not in_frame_basis and self.rotating_frame is not None: + ham_ops = self.rotating_frame.operator_out_of_frame_basis(ham_ops) + + return ham_ops + + def _get_static_dissipators(self, in_frame_basis: Optional[bool] = False) -> Tuple[Array]: + """Get the static dissipators, either in the frame basis or not. + + Args: + in_frame_basis: Whether to return in frame basis or not. + + Returns: + Dissipator operators. + """ + diss_ops = self._operator_collection.static_dissipators + if not in_frame_basis and self.rotating_frame is not None: + diss_ops = self.rotating_frame.operator_out_of_frame_basis(diss_ops) + + return diss_ops + + def _get_dissipator_operators(self, in_frame_basis: Optional[bool] = False) -> Tuple[Array]: + """Get the dissipator operators, either in the frame basis or not. + + Args: + in_frame_basis: Whether to return in frame basis or not. + + Returns: + Dissipator operators. + """ + diss_ops = self._operator_collection.dissipator_operators + if not in_frame_basis and self.rotating_frame is not None: + diss_ops = self.rotating_frame.operator_out_of_frame_basis(diss_ops) + + return diss_ops + + @property + def evaluation_mode(self) -> str: + """Numerical evaluation mode of the model. + + Available options: + + * ``'dense'``: Stores Hamiltonian and dissipator terms as dense Array types. + * ``'dense_vectorized'``: Stores the Hamiltonian and dissipator terms as + :math:`(dim^2,dim^2)` matrices that acts on a vectorized density matrix by + left-multiplication. Allows for direct evaluate generator. + * ``'sparse'``: Like dense, but matrices stored in sparse format. If the default Array + backend is JAX, uses JAX BCOO sparse arrays, otherwise uses scipy :class:`csr_matrix` + sparse type. + * ```sparse_vectorized```: Like dense_vectorized, but matrices stored in sparse format. If + the default Array backend is JAX, uses JAX BCOO sparse arrays, otherwise uses scipy + :class:`csr_matrix` sparse type. Note that JAX sparse mode is only recommended for use + on CPU. + + Raises: + NotImplementedError: If this property is set to something other than one of the above + modes. + """ + return self._evaluation_mode + + @evaluation_mode.setter + def evaluation_mode(self, new_mode: str): + if new_mode != self._evaluation_mode: + self._operator_collection = construct_lindblad_operator_collection( + evaluation_mode=new_mode, + static_hamiltonian=self._operator_collection.static_hamiltonian, + hamiltonian_operators=self._operator_collection.hamiltonian_operators, + static_dissipators=self._operator_collection.static_dissipators, + dissipator_operators=self._operator_collection.dissipator_operators, + ) + + self.vectorized_operators = "vectorized" in new_mode + self._evaluation_mode = new_mode + + @property + def rotating_frame(self): + """The rotating frame. + + This property can be set with a :class:`RotatingFrame` instance, or any valid constructor + argument to this class. + + Setting this property updates the internal operator to use the new frame. + """ + return self._rotating_frame + + @rotating_frame.setter + def rotating_frame(self, rotating_frame: Union[Operator, Array, RotatingFrame]): + new_frame = RotatingFrame(rotating_frame) + + # convert static hamiltonian to new frame setup + static_ham = self._get_static_hamiltonian(in_frame_basis=True) + if static_ham is not None: + static_ham = -1j * static_ham + + new_static_hamiltonian = transfer_static_operator_between_frames( + static_ham, + new_frame=new_frame, + old_frame=self.rotating_frame, + ) + + if new_static_hamiltonian is not None: + new_static_hamiltonian = 1j * new_static_hamiltonian + + # convert hamiltonian operators and dissipator operators + ham_ops = self._get_hamiltonian_operators(in_frame_basis=True) + static_diss_ops = self._get_static_dissipators(in_frame_basis=True) + diss_ops = self._get_dissipator_operators(in_frame_basis=True) + + new_hamiltonian_operators = transfer_operators_between_frames( + ham_ops, + new_frame=new_frame, + old_frame=self.rotating_frame, + ) + new_static_dissipators = transfer_operators_between_frames( + static_diss_ops, + new_frame=new_frame, + old_frame=self.rotating_frame, + ) + new_dissipator_operators = transfer_operators_between_frames( + diss_ops, + new_frame=new_frame, + old_frame=self.rotating_frame, + ) + + self._rotating_frame = new_frame + + self._operator_collection = construct_lindblad_operator_collection( + evaluation_mode=self.evaluation_mode, + static_hamiltonian=new_static_hamiltonian, + hamiltonian_operators=new_hamiltonian_operators, + static_dissipators=new_static_dissipators, + dissipator_operators=new_dissipator_operators, + ) + +
    +[docs] + def evaluate_hamiltonian(self, time: float) -> Array: + """Evaluates Hamiltonian matrix at a given time. + + Args: + time: The time at which to evaluate the Hamiltonian. + + Returns: + Array: Hamiltonian matrix. + """ + + hamiltonian_sig_vals = None + if self._hamiltonian_signals is not None: + hamiltonian_sig_vals = self._hamiltonian_signals(time) + + ham = self._operator_collection.evaluate_hamiltonian(hamiltonian_sig_vals) + if self.rotating_frame.frame_diag is not None: + ham = self.rotating_frame.operator_into_frame( + time, + ham, + operator_in_frame_basis=True, + return_in_frame_basis=self._in_frame_basis, + vectorized_operators=self.vectorized_operators, + ) + + return ham
    + + +
    +[docs] + def evaluate(self, time: float) -> Array: + """Evaluate the model in array format as a matrix, independent of state. + + Args: + time: The time to evaluate the model at. + + Returns: + Array: The evaluated model as an anti-Hermitian matrix. + + Raises: + QiskitError: If model cannot be evaluated. + NotImplementedError: If the model is currently unvectorized. + """ + hamiltonian_sig_vals = None + if self._hamiltonian_signals is not None: + hamiltonian_sig_vals = self._hamiltonian_signals(time) + elif self._operator_collection.hamiltonian_operators is not None: + raise QiskitError( + f"{type(self).__name__} with non-empty hamiltonian operators cannot be evaluated " + "without hamiltonian signals." + ) + + dissipator_sig_vals = None + if self._dissipator_signals is not None: + dissipator_sig_vals = self._dissipator_signals(time) + elif self._operator_collection.dissipator_operators is not None: + raise QiskitError( + f"{type(self).__name__} with non-empty dissipator operators cannot be evaluated " + "without dissipator signals." + ) + + if self.vectorized_operators: + out = self._operator_collection.evaluate(hamiltonian_sig_vals, dissipator_sig_vals) + return self.rotating_frame.vectorized_map_into_frame( + time, out, operator_in_frame_basis=True, return_in_frame_basis=self._in_frame_basis + ) + else: + raise NotImplementedError( + "Non-vectorized Lindblad models cannot be represented without a given state." + )
    + + +
    +[docs] + def evaluate_rhs(self, time: Union[float, int], y: Array) -> Array: + """Evaluates the Lindblad model at a given time. + + Args: + time: The time at which the model should be evaluated. + y: Density matrix as an (n,n) Array if not using a vectorized evaluation_mode, or an + (n^2) Array if using vectorized evaluation. + + Returns: + Array: Either the evaluated generator or the state. + + Raises: + QiskitError: If signals not sufficiently specified. + """ + + hamiltonian_sig_vals = None + if self._hamiltonian_signals is not None: + hamiltonian_sig_vals = self._hamiltonian_signals(time) + elif self._operator_collection.hamiltonian_operators is not None: + raise QiskitError( + f"{type(self).__name__} with non-empty hamiltonian operators cannot be evaluated " + "without hamiltonian signals." + ) + + dissipator_sig_vals = None + if self._dissipator_signals is not None: + dissipator_sig_vals = self._dissipator_signals(time) + elif self._operator_collection.dissipator_operators is not None: + raise QiskitError( + f"{type(self).__name__} with non-empty dissipator operators cannot be evaluated " + "without dissipator signals." + ) + + if self.rotating_frame.frame_diag is not None: + # Take y out of the frame, but keep in the frame basis + rhs = self.rotating_frame.operator_out_of_frame( + time, + y, + operator_in_frame_basis=self._in_frame_basis, + return_in_frame_basis=True, + vectorized_operators=self.vectorized_operators, + ) + + rhs = self._operator_collection.evaluate_rhs( + hamiltonian_sig_vals, dissipator_sig_vals, rhs + ) + + # Put rhs back into the frame, potentially converting its basis. + rhs = self.rotating_frame.operator_into_frame( + time, + rhs, + operator_in_frame_basis=True, + return_in_frame_basis=self._in_frame_basis, + vectorized_operators=self.vectorized_operators, + ) + + else: + rhs = self._operator_collection.evaluate_rhs( + hamiltonian_sig_vals, dissipator_sig_vals, y + ) + + return rhs
    +
    + + + +def construct_lindblad_operator_collection( + evaluation_mode: str, + static_hamiltonian: Union[None, Array, csr_matrix], + hamiltonian_operators: Union[None, Array, List[csr_matrix]], + static_dissipators: Union[None, Array, csr_matrix], + dissipator_operators: Union[None, Array, List[csr_matrix]], +) -> BaseLindbladOperatorCollection: + """Construct a Lindblad operator collection. + + Args: + evaluation_mode: String specifying new mode. Available options are ``'dense'``, + ``'sparse'``, ``'dense_vectorized'``, and ``'sparse_vectorized'``. + static_hamiltonian: Constant part of the Hamiltonian. + hamiltonian_operators: Operators in Hamiltonian with time-dependent coefficients. + static_dissipators: Dissipation operators with coefficient 1. + dissipator_operators: Dissipation operators with variable coefficients. + + Returns: + BaseLindbladOperatorCollection: Right-hand side evaluation object. + + Raises: + NotImplementedError: If ``evaluation_mode`` is not one of the above supported evaluation + modes. + """ + + # raise warning if sparse mode set with JAX not on cpu + if ( + Array.default_backend() == "jax" + and "sparse" in evaluation_mode + and jax.default_backend() != "cpu" + ): + warn( + """Using sparse mode with JAX is primarily recommended for use on CPU.""", + stacklevel=2, + ) + + if evaluation_mode == "dense": + CollectionClass = DenseLindbladCollection + elif evaluation_mode == "sparse": + if Array.default_backend() == "jax": + CollectionClass = JAXSparseLindbladCollection + else: + CollectionClass = SparseLindbladCollection + elif evaluation_mode == "dense_vectorized": + CollectionClass = DenseVectorizedLindbladCollection + elif evaluation_mode == "sparse_vectorized": + if Array.default_backend() == "jax": + CollectionClass = JAXSparseVectorizedLindbladCollection + else: + CollectionClass = SparseVectorizedLindbladCollection + else: + raise NotImplementedError( + f"Evaluation mode '{evaluation_mode}' is not supported. See " + "help(LindbladModel.evaluation_mode) for available options." + ) + + return CollectionClass( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=hamiltonian_operators, + static_dissipators=static_dissipators, + dissipator_operators=dissipator_operators, + ) +
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    Source code for qiskit_dynamics.models.rotating_frame

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2021.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Module for rotating frame handling classes.
    +"""
    +
    +from typing import Union, List, Optional
    +import numpy as np
    +from scipy.sparse import issparse, csr_matrix
    +
    +from qiskit import QiskitError
    +from qiskit.quantum_info.operators import Operator
    +from qiskit.quantum_info.operators.predicates import is_hermitian_matrix
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.type_utils import to_array, to_BCOO, to_numeric_matrix_type
    +
    +try:
    +    import jax.numpy as jnp
    +    from jax.experimental import sparse as jsparse
    +
    +    jsparse_matmul = jsparse.sparsify(jnp.matmul)
    +except ImportError:
    +    pass
    +
    +
    +
    +[docs] +class RotatingFrame: + r"""Class for representing a rotation frame transformation. + + This class provides functionality for transforming various objects into or out-of a rotating + frame specified by an anti-Hermitian operator :math:`F = -iH`. For example: + + * Bringing a "state" into/out of the frame: :math:`t, y \mapsto e^{\mp tF}y` + * Bringing an "operator" into/out of the frame: :math:`t, A \mapsto e^{\mp tF}Ae^{\pm tF}` + * Bringing a generator for a LMDE into/out of the frame: + :math:`t, G \mapsto e^{\mp tF}Ge^{\pm tF} - F` + + This class also contains functions for bringing states/operators into/out of the basis in which + :math:`F` is diagonalized, which we refer to as the "frame basis". All previously mentioned + functions also include optional arguments specifying whether the input/output are meant to be in + the frame basis. + + .. note:: + :class:`~qiskit_dynamics.models.RotatingFrame` can be instantiated + with a 1d array, which is understood to correspond to the diagonal entries + of a diagonal :math:`H` or :math:`F = -i H`. + + """ + + def __init__( + self, frame_operator: Union[Array, Operator], atol: float = 1e-10, rtol: float = 1e-10 + ): + """Initialize with a frame operator. + + Args: + frame_operator: The frame operator, which must be either Hermitian or anti-Hermitian. + atol: Absolute tolerance when verifying that the ``frame_operator`` is Hermitian or + anti-Hermitian. + rtol: Relative tolerance when verifying that the ``frame_operator`` is Hermitian or + anti-Hermitian. + """ + if isinstance(frame_operator, RotatingFrame): + frame_operator = frame_operator.frame_operator + + self._frame_operator = frame_operator + frame_operator = to_array(frame_operator) + + if frame_operator is None: + self._dim = None + self._frame_diag = None + self._frame_basis = None + self._frame_basis_adjoint = None + # if frame_operator is a 1d array, assume already diagonalized + elif frame_operator.ndim == 1: + # verify Hermitian or anti-Hermitian + # if Hermitian convert to anti-Hermitian + frame_operator = _enforce_anti_herm(frame_operator, atol=atol, rtol=rtol) + + self._frame_diag = Array(frame_operator) + self._frame_basis = None + self._frame_basis_adjoint = None + self._dim = len(self._frame_diag) + # if not, diagonalize it + else: + # verify Hermitian or anti-Hermitian + # if Hermitian convert to anti-Hermitian + frame_operator = _enforce_anti_herm(frame_operator, atol=atol, rtol=rtol) + + # diagonalize with eigh, utilizing assumption of anti-hermiticity + frame_diag, frame_basis = np.linalg.eigh(1j * frame_operator) + + self._frame_diag = Array(-1j * frame_diag) + self._frame_basis = Array(frame_basis) + self._frame_basis_adjoint = frame_basis.conj().transpose() + self._dim = len(self._frame_diag) + + # lazily evaluate change-of-basis matrices for vectorized operators. + self._vectorized_frame_basis = None + self._vectorized_frame_basis_adjoint = None + + @property + def dim(self) -> int: + """The dimension of the frame.""" + return self._dim + + @property + def frame_operator(self) -> Array: + """The original frame operator.""" + return self._frame_operator + + @property + def frame_diag(self) -> Array: + """The diagonal of the frame operator.""" + return self._frame_diag + + @property + def frame_basis(self) -> Array: + """The array containing diagonalizing unitary.""" + return self._frame_basis + + @property + def frame_basis_adjoint(self) -> Array: + """The adjoint of the diagonalizing unitary.""" + return self._frame_basis_adjoint + +
    +[docs] + def state_into_frame_basis(self, y: Array) -> Array: + r"""Take a state into the frame basis, i.e. return ``self.frame_basis_adjoint @ y``. + + Args: + y: The state. + + Returns: + Array: The state in the frame basis. + """ + y = to_numeric_matrix_type(y) + if self.frame_basis_adjoint is None: + return y + + return self.frame_basis_adjoint @ y
    + + +
    +[docs] + def state_out_of_frame_basis(self, y: Array) -> Array: + r"""Take a state out of the frame basis, i.e. ``return self.frame_basis @ y``. + + Args: + y: The state. + + Returns: + Array: The state in the frame basis. + """ + y = to_numeric_matrix_type(y) + if self.frame_basis is None: + return y + + return self.frame_basis @ y
    + + +
    +[docs] + def operator_into_frame_basis( + self, + op: Union[Operator, List[Operator], Array, csr_matrix, None], + convert_type: bool = True, + ) -> Array: + r"""Take an operator into the frame basis, i.e. return + ``self.frame_basis_adjoint @ A @ self.frame_basis`` + + Args: + op: The operator or array of operators. + convert_type: Whether or not to initially convert ``op`` into an expected type. Should + only be set to ``False`` in situations in which it is gauranteed that + ``op`` is a handled input type. + + Returns: + Array: The operator in the frame basis. + """ + if convert_type: + op = to_numeric_matrix_type(op) + + if self.frame_basis is None or op is None: + return op + + if isinstance(op, list): + return [self.operator_into_frame_basis(x, convert_type=False) for x in op] + elif type(op).__name__ == "BCOO": + return self.frame_basis_adjoint @ jsparse_matmul(op, self.frame_basis.data) + else: + # parentheses are necessary for sparse op evaluation + return self.frame_basis_adjoint @ (op @ self.frame_basis)
    + + +
    +[docs] + def operator_out_of_frame_basis( + self, + op: Union[Operator, List[Operator], Array, csr_matrix, None], + convert_type: bool = True, + ) -> Array: + r"""Take an operator out of the frame basis, i.e. return + ``self.frame_basis @ to_array(op) @ self.frame_basis_adjoint``. + + Args: + op: The operator or array of operators. + convert_type: Whether or not to initially convert ``op`` into an expected type. Should + only be set to ``False`` in situations in which it is gauranteed that + that ``op`` is a handled input type. + + Returns: + Array: The operator in the frame basis. + """ + if convert_type: + op = to_numeric_matrix_type(op) + + if self.frame_basis is None or op is None: + return op + + if isinstance(op, list): + return [self.operator_out_of_frame_basis(x, convert_type=False) for x in op] + elif type(op).__name__ == "BCOO": + return self.frame_basis @ jsparse_matmul(op, self.frame_basis_adjoint.data) + else: + # parentheses are necessary for sparse op evaluation + return self.frame_basis @ (op @ self.frame_basis_adjoint)
    + + +
    +[docs] + def state_into_frame( + self, + t: float, + y: Array, + y_in_frame_basis: Optional[bool] = False, + return_in_frame_basis: Optional[bool] = False, + ): + """Take a state into the rotating frame, i.e. return ``exp(-tF) @ y``. + + Args: + t: The time. + y: The state. + y_in_frame_basis: Whether or not the array y is already in the basis in which the frame + is diagonal. + return_in_frame_basis: Whether or not to return the result in the frame basis. + + Returns: + Array: The state in the rotating frame. + """ + y = to_numeric_matrix_type(y) + if self._frame_operator is None: + return y + + out = y + + # if not in frame basis convert it + if not y_in_frame_basis: + out = self.state_into_frame_basis(out) + + # go into the frame using fast diagonal matrix multiplication + out = (np.exp(self.frame_diag * (-t)) * out.transpose()).transpose() # = e^{tF}out + + # if output is requested to not be in the frame basis, convert it + if not return_in_frame_basis: + out = self.state_out_of_frame_basis(out) + + return out
    + + +
    +[docs] + def state_out_of_frame( + self, + t: float, + y: Array, + y_in_frame_basis: Optional[bool] = False, + return_in_frame_basis: Optional[bool] = False, + ) -> Array: + r"""Take a state out of the rotating frame, i.e. return ``exp(tF) @ y``. + + Calls ``self.state_into_frame`` with time reversed. + + Args: + t: The time. + y: The state.. + y_in_frame_basis: Whether or not the array y is already in the basis in which the frame + is diagonal. + return_in_frame_basis: Whether or not to return the result in the frame basis. + + Returns: + Array: The state out of the rotating frame. + """ + return self.state_into_frame(-t, y, y_in_frame_basis, return_in_frame_basis)
    + + + def _conjugate_and_add( + self, + t: float, + operator: Union[Array, csr_matrix], + op_to_add_in_fb: Optional[Array] = None, + operator_in_frame_basis: Optional[bool] = False, + return_in_frame_basis: Optional[bool] = False, + vectorized_operators: Optional[bool] = False, + ) -> Union[Array, csr_matrix]: + r"""General helper function for computing :math:`\exp(-tF)G\exp(tF) + B`. + + Note: :math:`B` is added in the frame basis before any potential final change + out of the frame basis. + + Note that there are two conventions for passing multiple operators at the same time. For + evaluation with ``vectorized_operators=False``, these operators should be passed as ``(k, + dim, dim)`` array objects, with the :math:`i^{th}` operator being stored as the ``[i,:,:]`` + entry. For ``vectorized_operators = True``, these (vectorized) operators should be passed as + a ``(dim**2, k)`` array, with the :math:`i^{th}` vectorized operator stored as the ``[:,i]`` + entry. + + Args: + t: The time. + operator: The operator :math:`G`. + op_to_add_in_fb: The additional operator :math:`B`. + operator_in_fame_basis: Whether ``operator`` is already in the basis in which the frame + operator is diagonal. + vectorized_operators: Whether ``operator`` is passed as a vectorized, ``(dim**2,)`` + Array, rather than a ``(dim,dim)`` Array. + + Returns: + Array of the newly conjugated operator. + """ + operator = to_numeric_matrix_type(operator) + op_to_add_in_fb = to_numeric_matrix_type(op_to_add_in_fb) + + if vectorized_operators: + # If passing vectorized operator, undo vectorization temporarily + if self._frame_operator is None: + if op_to_add_in_fb is None: + return operator + else: + return operator + op_to_add_in_fb + if len(operator.shape) == 2: + operator = operator.T + operator = operator.reshape(operator.shape[:-1] + (self.dim, self.dim), order="F") + + if self._frame_operator is None: + if op_to_add_in_fb is None: + return operator + else: + if op_to_add_in_fb is not None: + if issparse(operator): + op_to_add_in_fb = csr_matrix(op_to_add_in_fb) + elif type(operator).__name__ == "BCOO": + op_to_add_in_fb = to_BCOO(op_to_add_in_fb) + + return operator + op_to_add_in_fb + + out = operator + + # if not in frame basis convert it + if not operator_in_frame_basis: + out = self.operator_into_frame_basis(out) + + # get frame transformation matrix in diagonal basis + # assumption that F is anti-Hermitian implies conjugation of + # diagonal gives inversion + exp_freq = np.exp(self.frame_diag * t) + frame_mat = exp_freq.conj().reshape(self.dim, 1) * exp_freq + if issparse(out): + out = out.multiply(frame_mat) + elif type(out).__name__ == "BCOO": + out = out * frame_mat.data + else: + out = frame_mat * out + + if op_to_add_in_fb is not None: + if issparse(out): + op_to_add_in_fb = csr_matrix(op_to_add_in_fb) + elif type(out).__name__ == "BCOO": + op_to_add_in_fb = to_BCOO(op_to_add_in_fb) + + out = out + op_to_add_in_fb + + # if output is requested to not be in the frame basis, convert it + if not return_in_frame_basis: + out = self.operator_out_of_frame_basis(out) + + if vectorized_operators: + # If a vectorized output is required, reshape correctly + out = out.reshape(out.shape[:-2] + (self.dim**2,), order="F") + if len(out.shape) == 2: + out = out.T + + return out + +
    +[docs] + def operator_into_frame( + self, + t: float, + operator: Union[Operator, Array, csr_matrix], + operator_in_frame_basis: Optional[bool] = False, + return_in_frame_basis: Optional[bool] = False, + vectorized_operators: Optional[bool] = False, + ) -> Array: + r"""Bring an operator into the frame, i.e. return + ``exp(-tF) @ operator @ exp(tF)``. + + The default implementation is to use ``self._conjugate_and_add``. + + Args: + t: The time. + operator: An array of appropriate size. + operator_in_frame_basis: Whether or not the operator is already in the basis in which + the frame is diagonal. + return_in_frame_basis: Whether or not to return the result in the frame basis. + vectorized_operators: Whether ``operator`` is passed as a vectorized, + ``(dim**2,)`` Array, rather than a ``(dim,dim)`` Array. + + Returns: + Array: The operator in the rotating frame. + """ + return self._conjugate_and_add( + t, + operator, + operator_in_frame_basis=operator_in_frame_basis, + return_in_frame_basis=return_in_frame_basis, + vectorized_operators=vectorized_operators, + )
    + + +
    +[docs] + def operator_out_of_frame( + self, + t: float, + operator: Union[Operator, Array, csr_matrix], + operator_in_frame_basis: Optional[bool] = False, + return_in_frame_basis: Optional[bool] = False, + vectorized_operators: Optional[bool] = False, + ): + r"""Bring an operator into the rotating frame, i.e. return + ``exp(tF) @ operator @ exp(-tF)``. + + The default implmentation is to use `self.operator_into_frame`. + + Args: + t: Time. + operator: An array of appropriate size. + operator_in_frame_basis: Whether or not the operator is already in the basis in which + the frame is diagonal. + return_in_frame_basis: Whether or not to return the result in the frame basis. + vectorized_operators: Whether ``operator`` is passed as a vectorized, ``(dim**2,)`` + Array, rather than a ``(dim,dim)`` Array. + + Returns: + Array: The operator out of the rotating frame. + """ + return self.operator_into_frame( + -t, + operator, + operator_in_frame_basis=operator_in_frame_basis, + return_in_frame_basis=return_in_frame_basis, + vectorized_operators=vectorized_operators, + )
    + + +
    +[docs] + def generator_into_frame( + self, + t: float, + operator: Union[Operator, Array, csr_matrix], + operator_in_frame_basis: Optional[bool] = False, + return_in_frame_basis: Optional[bool] = False, + vectorized_operators: Optional[bool] = False, + ): + r"""Take an generator into the rotating frame, i.e. return + ``exp(-tF) @ operator @ exp(tF) - F``. + + The default implementation is to use :meth:`_conjugate_and_add`. + + Args: + t: Time. + operator: Generator (array of appropriate size). + operator_in_frame_basis: Whether or not the generator is already in the basis in which + the frame is diagonal. + return_in_frame_basis: Whether or not to return the result in the frame basis. + vectorized_operators: Whether ``operator`` is passed as a vectorized, ``(dim**2,)`` + Array, rather than a ``(dim,dim)`` Array. + + Returns: + Array: The generator in the rotating frame. + """ + if self.frame_operator is None: + return to_numeric_matrix_type(operator) + else: + # conjugate and subtract the frame diagonal + return self._conjugate_and_add( + t, + operator, + op_to_add_in_fb=-np.diag(self.frame_diag), + operator_in_frame_basis=operator_in_frame_basis, + return_in_frame_basis=return_in_frame_basis, + vectorized_operators=vectorized_operators, + )
    + + +
    +[docs] + def generator_out_of_frame( + self, + t: float, + operator: Union[Operator, Array, csr_matrix], + operator_in_frame_basis: Optional[bool] = False, + return_in_frame_basis: Optional[bool] = False, + ) -> Array: + r"""Take an operator out of the frame using the generator transformaton rule, i.e. return + ``exp(tF) @ operator @ exp(-tF) + F``. + + The default implementation is to use ``self._conjugate_and_add``. + + Args: + t: The time + operator: Generator (array of appropriate size). + operator_in_frame_basis: Whether or not the operator is already in the basis in which + the frame is diagonal. + return_in_frame_basis: Whether or not to return the result in the frame basis. + + Returns: + Array: The generator out of the rotating frame. + """ + if self.frame_operator is None: + return to_numeric_matrix_type(operator) + else: + # conjugate and add the frame diagonal + return self._conjugate_and_add( + -t, + operator, + op_to_add_in_fb=Array(np.diag(self.frame_diag)), + operator_in_frame_basis=operator_in_frame_basis, + return_in_frame_basis=return_in_frame_basis, + )
    + + + @property + def vectorized_frame_basis(self): + """Lazily evaluated operator for mapping vectorized operators into the frame basis.""" + + if self.frame_basis is None: + return None + + if self._vectorized_frame_basis is None: + self._vectorized_frame_basis = np.kron(self.frame_basis.conj(), self.frame_basis) + self._vectorized_frame_basis_adjoint = self._vectorized_frame_basis.conj().transpose() + + return self._vectorized_frame_basis + + @property + def vectorized_frame_basis_adjoint(self): + """Lazily evaluated operator for mapping vectorized operators out of the frame basis.""" + + if self.frame_basis is None: + return None + + if self._vectorized_frame_basis_adjoint is None: + # trigger lazy evaluation of vectorized_frame_basis + # pylint: disable=pointless-statement + self.vectorized_frame_basis + + return self._vectorized_frame_basis_adjoint + +
    +[docs] + def vectorized_map_into_frame( + self, + time: float, + op: Array, + operator_in_frame_basis: Optional[bool] = False, + return_in_frame_basis: Optional[bool] = False, + ) -> Array: + r"""Given an operator ``op`` of dimension ``dim**2`` assumed to represent vectorized linear + map in column stacking convention, returns: + + .. math:: + ((e^{tF})^T \otimes e^{-tF}) \times op \times ((e^{-tF})^T \otimes e^{tF}). + + Utilizes element-wise multiplication :math:`op \to \Delta\otimes\bar{\Delta} \odot op`, + where :math:`\Delta_{ij}=\exp((-d_i+d_j)t)` is the frame difference matrix, as well as + caches array :math:`\bar{C}\otimes C`, where ``C = self.frame_basis`` for future use. + + Args: + time: The time :math:`t`. + op: The ``(dim**2,dim**2)`` Array. + operator_in_frame_basis: Whether the operator is in the frame basis. + return_in_frame_basis: Whether the operator should be returned in the frame basis. + + Returns: + ``op`` in the frame. + """ + if self.frame_diag is not None: + # Put the vectorized operator into the frame basis + if not operator_in_frame_basis and self.frame_basis is not None: + op = self.vectorized_frame_basis_adjoint @ (op @ self.vectorized_frame_basis) + + expvals = np.exp(self.frame_diag * time) # = e^{td_i} = e^{it*Im(d_i)} + # = kron(e^{-it*Im(d_i)},e^{it*Im(d_i)}), but ~3x faster + temp_outer = (expvals.conj().reshape(self.dim, 1) * expvals).flatten() + delta_bar_otimes_delta = np.outer( + temp_outer.conj(), temp_outer + ) # = kron(delta.conj(),delta) but >3x faster + if issparse(op): + op = op.multiply(delta_bar_otimes_delta) + else: + op = delta_bar_otimes_delta * op # hadamard product + + if not return_in_frame_basis and self.frame_basis is not None: + op = self.vectorized_frame_basis @ (op @ self.vectorized_frame_basis_adjoint) + + return op
    +
    + + + +def _enforce_anti_herm(mat: Array, atol: Optional[float] = 1e-10, rtol: Optional[float] = 1e-10): + r"""Given ``mat``, the logic of this function is: + - if ``mat`` is hermitian, return ``-1j * mat`` + - if ``mat`` is anti-hermitian, return ``mat`` + - otherwise: + - if ``mat.backend == 'jax'`` return ``jnp.inf * mat`` + - otherwise raise an error + + The main purpose of this function is to hide the pecularities of implementing the above logic in + a compileable way in ``jax``. + + Args: + mat: The array to check. + atol: The absolute tolerance. + rtol: The relative tolerance. + + Returns: + Array: Anti-hermitian version of ``mat``, if applicable. + + Raises: + ImportError: If the backend is jax and jax is not installed. + QiskitError: If ``mat`` is not Hermitian or anti-Hermitian. + """ + mat = to_array(mat) + mat = Array(mat, dtype=complex) + + if mat.backend == "jax": + from jax.lax import cond + + mat = mat.data + + if mat.ndim == 1: + # this function checks if pure imaginary. If yes it returns the + # array, otherwise it multiplies it by jnp.nan to raise an error + # Note: pathways in conditionals in jax cannot raise Exceptions + def anti_herm_conditional(b): + aherm_pred = jnp.allclose(b, -b.conj(), atol=atol, rtol=rtol) + return cond(aherm_pred, lambda A: A, lambda A: jnp.nan * A, b) + + # Check if it is purely real, if not apply anti_herm_conditional + herm_pred = jnp.allclose(mat, mat.conj(), atol=atol, rtol=rtol) + return Array(cond(herm_pred, lambda A: -1j * A, anti_herm_conditional, mat)) + else: + # this function checks if anti-hermitian, if yes returns the array, + # otherwise it multiplies it by jnp.nan + def anti_herm_conditional(b): + aherm_pred = jnp.allclose(b, -b.conj().transpose(), atol=atol, rtol=rtol) + return cond(aherm_pred, lambda A: A, lambda A: jnp.nan * A, b) + + # the following lines check if a is hermitian, otherwise it feeds + # it into the anti_herm_conditional + herm_pred = jnp.allclose(mat, mat.conj().transpose(), atol=atol, rtol=rtol) + return Array(cond(herm_pred, lambda A: -1j * A, anti_herm_conditional, mat)) + + else: + if mat.ndim == 1: + if np.allclose(mat, mat.conj(), atol=atol, rtol=rtol): + return -1j * mat + elif np.allclose(mat, -mat.conj(), atol=atol, rtol=rtol): + return mat + else: + if is_hermitian_matrix(mat, rtol=rtol, atol=atol): + return -1j * mat + elif is_hermitian_matrix(1j * mat, rtol=rtol, atol=atol): + return mat + + # raise error if execution has made it this far + raise QiskitError("""frame_operator must be either a Hermitian or anti-Hermitian matrix.""") +
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/models/rotating_wave_approximation.html b/stable/0.4/_modules/qiskit_dynamics/models/rotating_wave_approximation.html new file mode 100644 index 000000000..829ed127c --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/models/rotating_wave_approximation.html @@ -0,0 +1,653 @@ + + + + + + + + qiskit_dynamics.models.rotating_wave_approximation - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    +

    Source code for qiskit_dynamics.models.rotating_wave_approximation

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2021.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name, inconsistent-return-statements
    +
    +"""Functions for performing the Rotating Wave Approximation
    +on Model classes."""
    +
    +
    +from typing import List, Optional, Union
    +import numpy as np
    +from qiskit_dynamics.models import (
    +    BaseGeneratorModel,
    +    GeneratorModel,
    +    HamiltonianModel,
    +    LindbladModel,
    +    RotatingFrame,
    +)
    +from qiskit_dynamics.signals import SignalSum, Signal, SignalList
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.type_utils import to_array
    +
    +
    +
    +[docs] +def rotating_wave_approximation( + model: BaseGeneratorModel, cutoff_freq: float, return_signal_map: Optional[bool] = False +) -> BaseGeneratorModel: + r"""Construct a new model by performing the rotating wave approximation with a given cutoff + frequency. The outputs of this function can be used in JAX-transformable functions, however this + function itself cannot (see below). + + Performs elementwise rotating wave approximation (RWA) with cutoff frequency ``cutoff_freq`` on + each operator in a model, returning a new model. The new model contains a modified list of + signal coefficients, and setting the optional argument ``return_signal_map=True`` results in + the additional return of the function ``f`` which maps the signals of the input model to those + of the output RWA model, such that the code blocks: + + .. code-block:: python + + model.signals = new_signals + rwa_model = rotating_wave_approximation(model, cutoff_freq) + + and + + .. code-block:: python + + rwa_model, f = rotating_wave_approximation(model, cutoff_freq, return_signal_map=True) + rwa_model.signals = f(new_signals) + + result in an ``rwa_model`` with the same updated signals. + + .. note:: + The ``rotating_wave_approximation`` function itself cannot be included in a function + to-be JAX-transformed, however the resulting model and ``signal_map`` can. For example, + the following function is **not** JAX-transformable: + + .. code-block:: python + + def function_with_rwa(t): + operators = ... + signals = ... + model = GeneratorModel(operators=operators, signals=signals) + rwa_model = rotating_wave_approximation(model, cutoff_freq) + return rwa_model(t) + + Whereas, defining: + + .. code-block:: python + + rwa_model, signal_map = rotating_wave_approximation(model, + cutoff_freq, + return_signal_map=True) + + The following function **is** JAX-transformable: + + .. code-block:: python + + def jax_transformable_func(t): + rwa_model_copy = rwa_model.copy() + rwa_model_copy.signals = signal_map(new_signals) + return rwa_model_copy(t) + + In this way, the outputs of ``rotating_wave_approximation`` can be used in JAX-transformable + functions, however ``rotating_wave_approximation`` itself cannot. + + + We now describe the formalism. When considering :math:`s_i(t) e^{-tF}G_ie^{tF}`, in the basis in + which :math:`F` is diagonal, the :math:`(j, k)` element of :math:`G_i` has effective frequency + :math:`\tilde\nu_{ijk}^\pm = \pm\nu_i + Im[-d_j+d_k]/2\pi`, where the :math:`\pm\nu_i` comes + from expressing :math:`s_i(t) = Re[a_i(t)e^{2\pi i\nu_i t}] = a_i(t)e^{i(2\pi\nu_i t+\phi_i)}/2 + + c.c.` and the other term comes from the rotating frame. Define :math:`G_i^\pm` the matrix + whose entries :math:`(G_i^\pm)_{jk}` are the entries of :math:`G_i` s.t. + :math:`|\nu_{ijk}^\pm|<\nu_*` for some cutoff frequency :math:`\nu_*`. Then, after the RWA, we + may write + + .. math:: + s_i(t)G_i \to G_i^+ a_ie^{i(2\pi \nu_i t+\phi_i)}/2 + + G_i^- \overline{a_i}e^{-i(2\pi \nu_i t+\phi_i)}/2. + + When we regroup these to use only the real components of the signal, we find that + + .. math:: + s_i(t)G_i \to s_i(t)(G_i^+ + G_i^-)/2 + s_i'(t)(iG_i^+-iG_i^-) + + where :math:`s_i'(t)` is a signal with the same frequency and amplitude as :math:`s_i`, but with + a phase shift of :math:`\phi_i - \pi/2`. + + Args: + model: The model to approximate. + cutoff_freq: The cutoff frequency for the approximation. + return_signal_map: Whether to also return the function for mapping pre-RWA signals to + post-RWA signals. + + Returns: + :class:`GeneratorModel` with twice as many terms, and, if ``return_signal_map``, + also the function ``f``. + + Raises: + ValueError: If the model has no signals. + """ + + n = model.dim + + frame_freqs = None + if model.rotating_frame is None or model.rotating_frame.frame_diag is None: + frame_freqs = np.zeros((n, n), dtype=complex) + else: + diag = model.rotating_frame.frame_diag + diff_matrix = np.broadcast_to(diag, (n, n)) - np.broadcast_to(diag, (n, n)).T + frame_freqs = diff_matrix.imag / (2 * np.pi) + + if model.rotating_frame.frame_diag is not None: + frame_shift = np.diag(model.rotating_frame.frame_diag) + if isinstance(model, (HamiltonianModel, LindbladModel)): + frame_shift = 1j * frame_shift + else: + frame_shift = np.zeros((n, n), dtype=complex) + + if isinstance(model, GeneratorModel): + if model.signals is None and model.operators is not None: + raise ValueError("Model must have nontrivial signals to perform the RWA.") + + cur_drift = to_array(model._get_static_operator(True)) + if cur_drift is not None: + cur_drift = cur_drift + frame_shift + rwa_drift = cur_drift * (abs(frame_freqs) < cutoff_freq).astype(int) + rwa_drift = model.rotating_frame.operator_out_of_frame_basis(rwa_drift) + else: + rwa_drift = None + + rwa_operators = get_rwa_operators( + to_array(model._get_operators(True)), + model.signals, + model.rotating_frame, + frame_freqs, + cutoff_freq, + ) + rwa_signals = get_rwa_signals(model.signals) + + # works for both GeneratorModel and HamiltonianModel + rwa_model = model.__class__( + static_operator=rwa_drift, + operators=rwa_operators, + signals=rwa_signals, + rotating_frame=model.rotating_frame, + in_frame_basis=model.in_frame_basis, + evaluation_mode=model.evaluation_mode, + ) + if return_signal_map: + return rwa_model, get_rwa_signals + return rwa_model + + elif isinstance(model, LindbladModel): + if model.signals[0] is None and model.hamiltonian_operators is not None: + raise ValueError("Model must have nontrivial Hamiltonian signals to perform the RWA.") + + if model.signals[1] is None and model.dissipator_operators is not None: + raise ValueError("Model must have nontrivial dissipator signals to perform the RWA.") + + # static hamiltonian part + cur_drift = to_array(model._get_static_hamiltonian(True)) + frame_shift + rwa_drift = cur_drift * (abs(frame_freqs) < cutoff_freq).astype(int) + rwa_drift = model.rotating_frame.operator_out_of_frame_basis(rwa_drift) + + # static dissipator part + cur_static_dis = to_array(model._get_static_dissipators(in_frame_basis=True)) + rwa_static_dis = None + if cur_static_dis is not None: + rwa_static_dis = [] + for op in cur_static_dis: + op = Array(op) + rwa_op = op * (abs(frame_freqs) < cutoff_freq).astype(int) + rwa_op = model.rotating_frame.operator_out_of_frame_basis(rwa_op) + rwa_static_dis.append(rwa_op) + + cur_ham_ops = to_array(model._get_hamiltonian_operators(in_frame_basis=True)) + cur_dis_ops = to_array(model._get_dissipator_operators(in_frame_basis=True)) + + cur_ham_sig, cur_dis_sig = model.signals + + rwa_ham_ops = get_rwa_operators( + cur_ham_ops, cur_ham_sig, model.rotating_frame, frame_freqs, cutoff_freq + ) + rwa_ham_sig = get_rwa_signals(cur_ham_sig) + + rwa_dis_ops = get_rwa_operators( + cur_dis_ops, cur_dis_sig, model.rotating_frame, frame_freqs, cutoff_freq + ) + + rwa_dis_sig = get_rwa_signals(cur_dis_sig) + + rwa_model = LindbladModel( + static_hamiltonian=rwa_drift, + hamiltonian_operators=rwa_ham_ops, + hamiltonian_signals=rwa_ham_sig, + static_dissipators=rwa_static_dis, + dissipator_operators=rwa_dis_ops, + dissipator_signals=rwa_dis_sig, + rotating_frame=model.rotating_frame, + in_frame_basis=model.in_frame_basis, + evaluation_mode=model.evaluation_mode, + ) + + if return_signal_map: + signal_translator = lambda a: (get_rwa_signals(a[0]), get_rwa_signals(a[1])) + return rwa_model, signal_translator + return rwa_model
    + + + +def get_rwa_operators( + current_ops: Array, + current_sigs: SignalList, + rotating_frame: RotatingFrame, + frame_freqs: Array, + cutoff_freq: float, +): + r"""Given a set of operators as a ``(k,n,n)`` array, a set of frequencies + :math:`\operatorname{frame_freqs}_{jk} = \operatorname{Im}[-d_j+d_k]` where :math:`d_i` the + :math:`i^{th}` eigenlvalue of the frame operator :math:`F`, the current signals of a model, and + a cutoff frequency, returns the new operators and signals that should be passed to create a new + Model class after the RWA. + + Args: + current_ops: The current operator list, a ``(k,n,n)`` array. + current_sigs: ``(k,)`` length :class:`SignalList`. + rotating_frame: The current :class:`~RotatingFrame` object of the pre-RWA model + frame_freqs: The effective frequencies of different matrix elements due to the conjugation + by :math:`e^{\pm Ft}` in the rotating frame. + cutoff_freq: The maximum frequency allowed under the RWA. + + Returns: + SignaLList: ``(2k,n,n)`` array of new operators post RWA. + """ + if current_ops is None: + return None + + current_sigs = current_sigs.flatten() + carrier_freqs = np.zeros(len(current_ops)) + + for i, sig_sum in enumerate(current_sigs.components): + sig = sig_sum.components[0] + carrier_freqs[i] = sig.carrier_freq + + num_components = len(carrier_freqs) + n = current_ops[0].shape[-1] + + frame_freqs = np.broadcast_to(frame_freqs, (num_components, n, n)) + carrier_freqs = carrier_freqs.reshape((num_components, 1, 1)) + + pos_pass = np.abs(carrier_freqs + frame_freqs) < cutoff_freq + pos_terms = current_ops * pos_pass.astype(int) # G_i^+ + + neg_pass = np.abs(-carrier_freqs + frame_freqs) < cutoff_freq + neg_terms = current_ops * neg_pass.astype(int) # G_i^- + + real_component = pos_terms / 2 + neg_terms / 2 + imag_component = 1j * pos_terms / 2 - 1j * neg_terms / 2 + + return rotating_frame.operator_out_of_frame_basis( + np.append(real_component, imag_component, axis=0) + ) + + +def get_rwa_signals(curr_signal_list: Union[List[Signal], SignalList]): + """Helper function that converts pre-RWA signals to post-RWA signals. + + Args: + curr_signal_list: The pre-RWA signals. + + Returns: + The post-RWA signals. + """ + if curr_signal_list is None: + return curr_signal_list + + real_signal_components = [] + imag_signal_components = [] + + if not isinstance(curr_signal_list, SignalList): + curr_signal_list = SignalList(curr_signal_list) + + curr_signal_list = curr_signal_list.flatten() + + for sig_sum in curr_signal_list.components: + sig = sig_sum.components[0] + real_signal_components.append(sig) + imag_signal_components.append( + SignalSum(Signal(sig.envelope, sig.carrier_freq, sig.phase - np.pi / 2)) + ) + + return SignalList(real_signal_components + imag_signal_components) +
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/perturbation/array_polynomial.html b/stable/0.4/_modules/qiskit_dynamics/perturbation/array_polynomial.html new file mode 100644 index 000000000..89d4e5653 --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/perturbation/array_polynomial.html @@ -0,0 +1,1280 @@ + + + + + + + + qiskit_dynamics.perturbation.array_polynomial - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    Source code for qiskit_dynamics.perturbation.array_polynomial

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2022.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +
    +"""
    +Array polynomial.
    +"""
    +
    +from typing import List, Optional, Callable, Tuple, Union
    +from copy import copy
    +from itertools import product
    +
    +from multiset import Multiset
    +
    +import numpy as np
    +from numpy.typing import DTypeLike
    +
    +from qiskit import QiskitError
    +
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.perturbation.multiset_utils import (
    +    _validate_non_negative_ints,
    +    _get_all_submultisets,
    +    _sorted_multisets,
    +    _submultisets_and_complements,
    +    _multiset_to_sorted_list,
    +)
    +from qiskit_dynamics.perturbation.custom_binary_op import _CustomBinaryOp
    +
    +try:
    +    import jax.numpy as jnp
    +except ImportError:
    +    pass
    +
    +
    +
    +[docs] +class ArrayPolynomial: + r"""A polynomial with array-valued coefficients. + + This class represents a multi-variable function of the form: + + .. math:: + f(c_1, \dots, c_r) = A_\emptyset + \sum_{I \in S} c_I A_I, + + where in the above: + + - :math:`S` is a finite set of multisets + indicating non-zero monomial terms, + - For a given multiset of non-negative integers :math:`I=(i_1, \dots, i_k)`, + :math:`c_I = c_{i_1} \times \dots \times c_{i_k}`, and + - The :math:`A_I` are arrays of the same shape, indexed by the first dimension. + + See the :ref:`multiset and power series notation section <multiset power series>` + of the perturbation review for an explanation of the multiset notation. + + An :class:`.ArrayPolynomial` is instantiated with the arguments: + + - ``constant_term`` specifying the array :math:`A_\emptyset`. + - ``array_coefficients`` specifying a list of the arrays :math:`A_I`, or as a single array + whose first index lists the :math:`A_I`, + - ``monomial_labels`` specifying the set :math:`S` as a list of + ``Multiset`` instances ordered in + correspondence with ``array_coefficients``. + + For example, the :class:`.ArrayPolynomial` corresponding to the mathematical polynomial + + .. math:: + + f(c_0, c_1) = A_\emptyset + + c_{(0)} A_{(0)} + c_{(0, 1)}A_{(0, 1)} + c_{(1, 1)}A_{(1, 1)} + + for arrays :math:`A_\emptyset, A_{(0)}, A_{(0, 1)}, A_{(1, 1)}` stored in variables + ``A_c``, ``A0``, ``A01``, and ``A11`` can be instantiated with + + .. code-block:: python + + ap = ArrayPolynomial( + constant_term = A_c + array_coefficients=[A0, A01, A11], + monomial_labels=[Multiset({0: 1}), Multiset({0: 1, 1: 1}), Multiset({1: 2})] + ) + + Once instantiated, the polynomial can be evaluated on an array of variable values, e.g. + + .. code-block:: python + + c = np.array([c0, c1]) + ap(c) # polynomial evaluated on variables + + :class:`.ArrayPolynomial` supports some array properties, e.g. ``ap.shape`` and ``ap.ndim`` + return the shape and number of dimensions of the output of the polynomial. Some array + methods are also supported, such as ``transpose`` and ``trace``, and their output produces + a new :class:`.ArrayPolynomial` which evaluates to the array one would obtain by first + evaluating the original, then calling the array method. E.g. + + .. code-block:: python + + ap2 = ap1.transpose() + ap2(c) == ap1(c).transpose() + + Finally, :class:`.ArrayPolynomial` supports algebraic operations, e.g. + + .. code-block:: python + + ap3 = ap1 @ ap2 + ap3(c) == ap1(c) @ ap2(c) + + It also has specialized algebraic methods that perform algebraic operations while + "ignoring" terms. E.g., for two instances ``ap1`` and ``ap2``, the call + + .. code-block:: python + + ap1.matmul(ap2, monomial_filter=lambda x: len(x) <= 3) + + is similar to ``ap1 @ ap2``, but will result in an :class:`.ArrayPolynomial` in which all + terms of degree larger than ``3`` will not be included in the results. + """ + __array_priority__ = 20 + + def __init__( + self, + constant_term: Optional[Array] = None, + array_coefficients: Optional[Array] = None, + monomial_labels: Optional[List[Multiset]] = None, + ): + """Construct a multivariable matrix polynomial. + + Args: + constant_term: An array representing the constant term of the polynomial. + array_coefficients: A 3d array representing a list of array coefficients. + monomial_labels: A list of multisets with non-negative integer entries of the same + length as ``array_coefficients`` indicating the monomial coefficient + for each corresponding ``array_coefficients``. + Raises: + QiskitError: If insufficient information is supplied to define an ArrayPolynomial, + or if monomial labels contain anything other than non-negative integers. + """ + + if array_coefficients is None and constant_term is None: + raise QiskitError( + "At least one of array_coefficients and constant_term must be specified." + ) + + if monomial_labels is not None: + self._monomial_labels = [Multiset(m) for m in monomial_labels] + for m in self._monomial_labels: + _validate_non_negative_ints(m) + else: + self._monomial_labels = [] + + # If operating in jax mode, wrap in Arrays + if Array.default_backend() == "jax": + if array_coefficients is not None: + self._array_coefficients = Array(array_coefficients) + else: + self._array_coefficients = None + + if constant_term is not None: + self._constant_term = Array(constant_term) + else: + self._constant_term = None + + self._compute_monomials = _get_monomial_compute_function_jax(self._monomial_labels) + else: + if constant_term is not None: + self._constant_term = np.array(constant_term) + else: + self._constant_term = None + + if array_coefficients is not None: + self._array_coefficients = np.array(array_coefficients) + else: + self._array_coefficients = None + + self._compute_monomials = _get_monomial_compute_function(self._monomial_labels) + + @property + def monomial_labels(self) -> Union[List, None]: + """The monomial labels corresponding to non-constant terms.""" + return self._monomial_labels + + @property + def array_coefficients(self) -> Union[Array, None]: + """The array coefficients for non-constant terms.""" + return self._array_coefficients + + @property + def constant_term(self) -> Union[Array, None]: + """The constant term.""" + return self._constant_term + +
    +[docs] + def compute_monomials(self, c: Array) -> Union[Array, None]: + """Vectorized computation of all scalar monomial terms in the polynomial as specified by + ``self.monomial_labels``. + + Args: + c: Array of variables. + Returns: + Array of all monomial terms ordered according to ``self.monomial_labels``. + """ + return self._compute_monomials(c)
    + + + @property + def shape(self) -> Tuple[int]: + """Shape of the arrays in the polynomial.""" + if self._constant_term is not None: + return self._constant_term.shape + else: + return self._array_coefficients.shape[1:] + + @property + def ndim(self) -> int: + """Number of dimensions of the coefficients of the polynomial.""" + if self._constant_term is not None: + return self._constant_term.ndim + else: + return self._array_coefficients.ndim - 1 + +
    +[docs] + def conj(self) -> "ArrayPolynomial": + """Return an ArrayPolynomial that is the conjugate of self.""" + + constant_term = None + coefficients = None + + if self._constant_term is not None: + constant_term = np.conj(self._constant_term) + + if self._array_coefficients is not None: + coefficients = np.conj(self._array_coefficients) + + return ArrayPolynomial( + array_coefficients=coefficients, + monomial_labels=copy(self._monomial_labels), + constant_term=constant_term, + )
    + + +
    +[docs] + def transpose(self, axes: Optional[Tuple[int]] = None) -> "ArrayPolynomial": + """Return the ArrayPolynomial when transposing all coefficients.""" + + constant_term = None + coefficients = None + + if self._constant_term is not None: + constant_term = np.transpose(self._constant_term, axes) + + if self._array_coefficients is not None: + if axes is None: + axes = tuple(range(1, self.ndim + 1)[::-1]) + else: + axes = tuple(ax + 1 for ax in axes) + axes = (0,) + axes + coefficients = np.transpose(self._array_coefficients, axes) + + return ArrayPolynomial( + array_coefficients=coefficients, + monomial_labels=copy(self._monomial_labels), + constant_term=constant_term, + )
    + + +
    +[docs] + def trace( + self, + offset: Optional[int] = 0, + axis1: Optional[int] = 0, + axis2: Optional[int] = 1, + dtype: Optional[DTypeLike] = None, + ) -> "ArrayPolynomial": + """Take the trace of the coefficients.""" + + if self.ndim < 2: + raise QiskitError("ArrayPolynomial.trace() requires ArrayPolynomial.ndim at least 2.") + + constant_term = None + coefficients = None + + if self._constant_term is not None: + constant_term = np.trace( + self._constant_term, offset=offset, axis1=axis1, axis2=axis2, dtype=dtype + ) + + if self._array_coefficients is not None: + coefficients = np.trace( + self._array_coefficients, + offset=offset, + axis1=axis1 + 1, + axis2=axis2 + 1, + dtype=dtype, + ) + + return ArrayPolynomial( + array_coefficients=coefficients, + monomial_labels=copy(self._monomial_labels), + constant_term=constant_term, + )
    + + +
    +[docs] + def sum(self, axis: Optional[Union[int, Tuple[int]]] = None, dtype: Optional[DTypeLike] = None): + """Perform a sum on the coefficients.""" + + constant_term = None + coefficients = None + + # constant term can be handled normally + if self.constant_term is not None: + constant_term = self.constant_term.sum(axis=axis, dtype=dtype) + + # axis must be shifted for array coefficients + if self.array_coefficients is not None: + if self.ndim == 0 and axis is None: + coefficients = np.array(self.array_coefficients, dtype=dtype) + else: + if axis is None: + axis = tuple(k for k in range(1, self.ndim + 1)) + elif isinstance(axis, int): + axis = axis + 1 + elif isinstance(axis, tuple): + axis = tuple(k + 1 for k in axis) + + coefficients = self.array_coefficients.sum(axis=axis, dtype=dtype) + + return ArrayPolynomial( + array_coefficients=coefficients, + monomial_labels=copy(self._monomial_labels), + constant_term=constant_term, + )
    + + + @property + def real(self) -> "ArrayPolynomial": + """Return the real part of self.""" + + constant_term = None + array_coefficients = None + + if self.constant_term is not None: + constant_term = self.constant_term.real + + if self.array_coefficients is not None: + array_coefficients = self.array_coefficients.real + + return ArrayPolynomial( + array_coefficients=array_coefficients, + monomial_labels=copy(self._monomial_labels), + constant_term=constant_term, + ) + +
    +[docs] + def add( + self, + other: Union["ArrayPolynomial", int, float, complex, Array], + monomial_filter: Optional[Callable] = None, + ) -> "ArrayPolynomial": + """Add two polynomials with bounds on which terms to keep. + + Optionally, a function ``monomial_filter`` can be provided to limit which monomials + appear in the output. It must accept as input a ``Multiset`` and return a ``bool``, + and a term with label given by ``multiset`` will be included only if + ``monomial_filter(multiset) == True``, and will not be computed if + ``monomial_filter(multiset) == False``. + + Args: + other: Other to add to self. + monomial_filter: Function determining which terms to compute and keep. + Returns: + ArrayPolynomial achieved by adding both self and other. + Raises: + QiskitError: if other cannot be cast as an ArrayPolynomial. + """ + + if isinstance(other, (int, float, complex, np.ndarray, Array)): + other = ArrayPolynomial(constant_term=other) + + if isinstance(other, ArrayPolynomial): + return _array_polynomial_addition(self, other, monomial_filter=monomial_filter) + + raise QiskitError( + "Only types castable as an ArrayPolynomial can be added to an ArrayPolynomial." + )
    + + +
    +[docs] + def matmul( + self, + other: Union["ArrayPolynomial", int, float, complex, np.ndarray, Array], + monomial_filter: Optional[Callable] = None, + ) -> "ArrayPolynomial": + """Matmul self @ other with bounds on which terms to keep. + + Optionally, a function ``monomial_filter`` can be provided to limit which monomials + appear in the output. It must accept as input a ``Multiset`` and return a ``bool``, + and a term with label given by ``multiset`` will be included only if + ``monomial_filter(multiset) == True``, and will not be computed if + ``monomial_filter(multiset) == False``. + + Args: + other: Other to add to self. + monomial_filter: Function determining which terms to compute and keep. + Returns: + ArrayPolynomial achieved by matmul of self and other. + Raises: + QiskitError: if other cannot be cast as an ArrayPolynomial. + """ + if isinstance(other, (int, float, complex, np.ndarray, Array)): + other = ArrayPolynomial(constant_term=other) + + if isinstance(other, ArrayPolynomial): + return _array_polynomial_distributive_binary_op( + self, other, lambda A, B: A @ B, monomial_filter=monomial_filter + ) + + raise QiskitError(f"Type {type(other)} not supported by ArrayPolynomial.matmul.")
    + + +
    +[docs] + def mul( + self, + other: Union["ArrayPolynomial", int, float, complex, np.ndarray, Array], + monomial_filter: Optional[Callable] = None, + ) -> "ArrayPolynomial": + """Entrywise multiplication of two ArrayPolynomials with bounds on which terms to keep. + + Optionally, a function ``monomial_filter`` can be provided to limit which monomials + appear in the output. It must accept as input a ``Multiset`` and return a ``bool``, + and a term with label given by ``multiset`` will be included only if + ``monomial_filter(multiset) == True``, and will not be computed if + ``monomial_filter(multiset) == False``. + + Args: + other: Other to add to self. + monomial_filter: Function determining which terms to compute and keep. + Returns: + ArrayPolynomial achieved by matmul of self and other. + Raises: + QiskitError: if other cannot be cast as an ArrayPolynomial. + """ + + if isinstance(other, (int, float, complex, np.ndarray, Array)): + other = ArrayPolynomial(constant_term=other) + + if isinstance(other, ArrayPolynomial): + return _array_polynomial_distributive_binary_op( + self, other, lambda A, B: A * B, monomial_filter=monomial_filter + ) + + raise QiskitError(f"Type {type(other)} not supported by ArrayPolynomial.mul.")
    + + + def __add__( + self, other: Union["ArrayPolynomial", int, float, complex, Array] + ) -> "ArrayPolynomial": + """Dunder method for addition of two ArrayPolynomials.""" + return self.add(other) + + def __radd__( + self, other: Union["ArrayPolynomial", int, float, complex, Array] + ) -> "ArrayPolynomial": + """Dunder method for right-addition of two ArrayPolynomials.""" + return self.add(other) + + def __neg__(self) -> "ArrayPolynomial": + constant_term = None + if self.constant_term is not None: + # pylint: disable=invalid-unary-operand-type + constant_term = -self.constant_term + + array_coefficients = None + if self.array_coefficients is not None: + # pylint: disable=invalid-unary-operand-type + array_coefficients = -self.array_coefficients + + return ArrayPolynomial( + constant_term=constant_term, + monomial_labels=self.monomial_labels, + array_coefficients=array_coefficients, + ) + + def __sub__( + self, other: Union["ArrayPolynomial", int, float, complex, Array] + ) -> "ArrayPolynomial": + return self + (-other) + + def __rsub__( + self, other: Union["ArrayPolynomial", int, float, complex, Array] + ) -> "ArrayPolynomial": + return other + (-self) + + def __mul__( + self, other: Union["ArrayPolynomial", int, float, complex, Array] + ) -> "ArrayPolynomial": + """Dunder method for entry-wise multiplication.""" + return self.mul(other) + + def __rmul__( + self, other: Union["ArrayPolynomial", int, float, complex, Array] + ) -> "ArrayPolynomial": + """Dunder method for right-multiplication.""" + return self.mul(other) + + def __matmul__(self, other: Union["ArrayPolynomial", Array]) -> "ArrayPolynomial": + """Dunder method for matmul.""" + return self.matmul(other) + + def __rmatmul__(self, other: Union["ArrayPolynomial", Array]) -> "ArrayPolynomial": + """Dunder method for rmatmul.""" + if isinstance(other, (int, float, complex, np.ndarray, Array)): + other = ArrayPolynomial(constant_term=other) + + if isinstance(other, ArrayPolynomial): + return other.matmul(self) + + raise QiskitError(f"Type {type(other)} not supported by ArrayPolynomial.__rmatmul__.") + + def __getitem__(self, idx) -> "ArrayPolynomial": + """Index the ArrayPolynomial similarly to an array.""" + constant_term = None + array_coefficients = None + + if self.constant_term is not None: + constant_term = self.constant_term[idx] + + if self.array_coefficients is not None: + array_coefficients = self.array_coefficients[(slice(None),) + idx] + + return ArrayPolynomial( + array_coefficients=array_coefficients, + monomial_labels=copy(self._monomial_labels), + constant_term=constant_term, + ) + + def __len__(self) -> int: + """Number of terms in the polynomial.""" + num_terms = 0 + if self.array_coefficients is not None: + num_terms = num_terms + len(self.array_coefficients) + + if self.constant_term is not None: + num_terms = num_terms + 1 + + return num_terms + + def __call__(self, c: Optional[Array] = None) -> Array: + """Evaluate the polynomial. + + Args: + c: Array of variables. + Returns: + Value of the polynomial at c. + """ + + if self._array_coefficients is not None and self._constant_term is not None: + monomials = self._compute_monomials(c) + return self._constant_term + np.tensordot( + self._array_coefficients, monomials, axes=(0, 0) + ) + elif self._array_coefficients is not None: + monomials = self._compute_monomials(c) + return np.tensordot(self._array_coefficients, monomials, axes=(0, 0)) + else: + return self._constant_term
    + + + +def _get_monomial_compute_function(multisets: List[Multiset]) -> Callable: + """Construct a vectorized function for computing multivariable monomial terms indicated by + multisets. + + The returned function takes in the individual variables as an array, and returns an array + of computed monomial terms in the order indicated by multisets. + + The returned function is vectorized in the sense that the supplied first order terms can be + arrays. + + The algorithm computes monomial terms of increasing order, recursively utilizing lower + order terms. + + Args: + multisets: list of multisets. + + Returns: + Callable: Vectorized function for computing monomials. + """ + if multisets is None or len(multisets) == 0: + return lambda c: None + + complete_multiset_list = _get_all_submultisets(multisets) + + ( + first_order_terms, + first_order_range, + left_indices, + right_indices, + update_ranges, + ) = _get_recursive_monomial_rule(complete_multiset_list) + + multiset_len = len(complete_multiset_list) + + location_list = np.array( + [complete_multiset_list.index(multiset) for multiset in multisets], dtype=int + ) + + def monomial_function(c): + shape = [multiset_len] + list(c.shape[1:]) + mono_vec = np.empty(shape=shape, dtype=complex) + mono_vec[first_order_range[0] : first_order_range[1]] = c[first_order_terms] + + for left_index, right_index, update_range in zip( + left_indices, right_indices, update_ranges + ): + mono_vec[update_range[0] : update_range[1]] = ( + mono_vec[left_index] * mono_vec[right_index] + ) + + return mono_vec[location_list] + + return monomial_function + + +# pylint: disable=invalid-name +def _get_monomial_compute_function_jax(multisets: List) -> Callable: + """JAX version of _get_monomial_compute_function.""" + + if multisets is None or len(multisets) == 0: + return lambda c: None + + complete_multiset_list = _get_all_submultisets(multisets) + + first_order_terms, _, left_indices, right_indices, _ = _get_recursive_monomial_rule( + complete_multiset_list + ) + location_list = np.array( + [complete_multiset_list.index(multiset) for multiset in multisets], dtype=int + ) + + # initial function sets up required first order terms + def monomial_function_init(c): + return c[first_order_terms] + + monomial_function = monomial_function_init + + # function for generating next update and compositions to avoid looping reference issues + def get_next_update_func(left_index, right_index): + def update_next(mono_vec): + return jnp.append(mono_vec, mono_vec[left_index] * mono_vec[right_index], axis=0) + + return update_next + + def compose_functions(f, g): + def new_func(x): + return g(f(x)) + + return new_func + + # recursively compose updates with monomial_function + for left_index, right_index in zip(left_indices, right_indices): + next_update = get_next_update_func(left_index, right_index) + monomial_function = compose_functions(monomial_function, next_update) + + # return only the requested terms + def trimmed_output_function(c): + return monomial_function(c)[location_list] + + return trimmed_output_function + + +def _get_recursive_monomial_rule(complete_multisets: List) -> Tuple: + """Helper function for _get_monomial_compute_function and _get_monomial_compute_function_jax; + computes a representation of the algorithm for computing monomials that is used by both + functions. + + complete_multisets is assumed to be closed under taking submultisets and in canonical order. + + Args: + complete_multisets: Description of monomial terms. + + Returns: + Tuple: Collection of lists organizing computation for both + _get_monomial_compute_function and _get_monomial_compute_function_jax. + """ + + # first, construct representation of recursive rule explicitly in terms of multisets + first_order_terms = [] + left_terms = [] + right_terms = [] + current_left = -1 + current_right_list = [] + current_len = 2 + + # convert multisets to list representation + complete_multisets = [_multiset_to_sorted_list(multiset) for multiset in complete_multisets] + + for multiset in complete_multisets: + if len(multiset) == 1: + first_order_terms.append(multiset[0]) + else: + if multiset[0] != current_left or len(multiset) != current_len: + current_len = len(multiset) + if current_left != -1: + left_terms.append(current_left) + right_terms.append(current_right_list) + + current_left = multiset[0] + current_right_list = [multiset[1:]] + else: + current_right_list.append(multiset[1:]) + + # if current_left is still -1, then only first order terms exist + if current_left == -1: + return np.array(first_order_terms), [0, len(first_order_terms)], [], [], [] + + # proceed assuming at least one term above first order exists + # append the last one + left_terms.append(current_left) + right_terms.append(current_right_list) + + # convert representation of rule in terms of multisets into one in terms of + # array indices + + # set up arrays + first_order_terms = np.array(first_order_terms, dtype=int) + + left_indices = [] + right_indices = [] + for left_term, right_term in zip(left_terms, right_terms): + left_indices.append(complete_multisets.index([left_term])) + + right_index_list = [] + for term in right_term: + right_index_list.append(complete_multisets.index(term)) + + right_indices.append(np.array(right_index_list, dtype=int)) + + # set up index updating ranges + first_order_range = [0, len(first_order_terms)] + update_ranges = [] + current_idx = first_order_range[1] + for right_index in right_indices: + next_idx = current_idx + len(right_index) + update_ranges.append([current_idx, next_idx]) + current_idx = next_idx + + return ( + np.array(first_order_terms), + first_order_range, + np.array(left_indices), + right_indices, + update_ranges, + ) + + +def _array_polynomial_distributive_binary_op( + ap1: ArrayPolynomial, + ap2: ArrayPolynomial, + binary_op: Callable, + monomial_filter: Optional[Callable] = None, +) -> ArrayPolynomial: + """Apply a distributive binary op on two array polynomials.""" + + # determine list of Multisets required for monomial labels, including filtering + all_multisets = [] + + # if no filter is provided, set to always return True + if monomial_filter is None: + monomial_filter = lambda x: True + + if ap1.constant_term is not None: + for multiset in ap2.monomial_labels: + if monomial_filter(multiset) and multiset not in all_multisets: + all_multisets.append(multiset) + if ap2.constant_term is not None: + for multiset in ap1.monomial_labels: + if monomial_filter(multiset) and multiset not in all_multisets: + all_multisets.append(multiset) + + for I, J in product(ap1.monomial_labels, ap2.monomial_labels): + IuJ = I + J + if monomial_filter(IuJ) and IuJ not in all_multisets: + all_multisets.append(IuJ) + + all_multisets = _sorted_multisets(all_multisets) + + # setup constant term + new_constant_term = None + if ( + ap1.constant_term is not None + and ap2.constant_term is not None + and monomial_filter(Multiset({})) + ): + new_constant_term = binary_op(ap1.constant_term, ap2.constant_term) + + # return constant case + if not all_multisets: + return ArrayPolynomial(constant_term=new_constant_term) + + # iteratively construct custom multiplication rule, + # temporarily treating the constant terms as index -1 + operation_rule = [] + for multiset in all_multisets: + rule_indices = [] + + if multiset in ap1.monomial_labels: + idx = ap1.monomial_labels.index(multiset) + rule_indices.append([idx, -1]) + + if multiset in ap2.monomial_labels: + idx = ap2.monomial_labels.index(multiset) + rule_indices.append([-1, idx]) + + if len(multiset) > 1: + for I, J in zip(*_submultisets_and_complements(multiset)): + if I in ap1.monomial_labels and J in ap2.monomial_labels: + rule_indices.append( + [ap1.monomial_labels.index(I), ap2.monomial_labels.index(J)] + ) + + # if non-empty, + if rule_indices: + operation_rule.append((np.ones(len(rule_indices)), np.array(rule_indices))) + + lmats = None + if ap1.constant_term is not None: + lmats = np.expand_dims(ap1.constant_term, 0) + else: + lmats = np.expand_dims(np.zeros_like(Array(ap1.array_coefficients[0])), 0) + + if ap1.array_coefficients is not None: + lmats = np.append(lmats, ap1.array_coefficients, axis=0) + + rmats = None + if ap2.constant_term is not None: + rmats = np.expand_dims(ap2.constant_term, 0) + else: + rmats = np.expand_dims(np.zeros_like(Array(ap2.array_coefficients[0])), 0) + + if ap2.array_coefficients is not None: + rmats = np.append(rmats, ap2.array_coefficients, axis=0) + + custom_binary_op = _CustomBinaryOp( + operation_rule=operation_rule, + binary_op=binary_op, + index_offset=1, + ) + new_array_coefficients = custom_binary_op(lmats, rmats) + + return ArrayPolynomial( + array_coefficients=new_array_coefficients, + monomial_labels=all_multisets, + constant_term=new_constant_term, + ) + + +def _array_polynomial_addition( + ap1: ArrayPolynomial, + ap2: ArrayPolynomial, + monomial_filter: Optional[Callable] = None, +) -> ArrayPolynomial: + """Add two ArrayPolynomials.""" + + for a, b in zip(ap1.shape[::-1], ap2.shape[::-1]): + if not (a == 1 or b == 1 or a == b): + raise QiskitError( + "ArrayPolynomial addition requires shapes be broadcastable to eachother." + ) + + if monomial_filter is None: + monomial_filter = lambda x: True + + # construct constant term + new_constant_term = None + + # if constant term is to be included, determine what it is + if monomial_filter(Multiset({})): + if ap1.constant_term is not None and ap2.constant_term is not None: + new_constant_term = ap1.constant_term + ap2.constant_term + elif ap1.constant_term is not None: + new_constant_term = ap1.constant_term + elif ap2.constant_term is not None: + new_constant_term = ap2.constant_term + + # exit early if both polynomials are constant + if ap1.array_coefficients is None and ap2.array_coefficients is None: + return ArrayPolynomial(constant_term=new_constant_term) + + # construct list of admissable multisets and sort into canonical order + new_multisets = [] + for multiset in ap1.monomial_labels + ap2.monomial_labels: + if monomial_filter(multiset) and multiset not in new_multisets: + new_multisets.append(multiset) + new_multisets = _sorted_multisets(new_multisets) + + # construct index order mapping for each polynomial + idx1 = [] + idx2 = [] + for multiset in new_multisets: + if multiset in ap1.monomial_labels: + idx1.append(ap1.monomial_labels.index(multiset)) + else: + idx1.append(-1) + + if multiset in ap2.monomial_labels: + idx2.append(ap2.monomial_labels.index(multiset)) + else: + idx2.append(-1) + + # if either is empty, pad with single -1, then convert to array + idx1 = idx1 or [-1] + idx2 = idx2 or [-1] + idx1 = np.array(idx1) + idx2 = np.array(idx2) + + # append zero to the coefficient arrays + array_coefficients1 = np.zeros((1,) + ap1.shape, dtype=complex) + array_coefficients2 = np.zeros((1,) + ap1.shape, dtype=complex) + if ap1.array_coefficients is not None: + array_coefficients1 = np.append(ap1.array_coefficients, array_coefficients1, axis=0) + if ap2.array_coefficients is not None: + array_coefficients2 = np.append(ap2.array_coefficients, array_coefficients2, axis=0) + + new_coefficients = array_coefficients1[idx1] + array_coefficients2[idx2] + + return ArrayPolynomial( + array_coefficients=new_coefficients, + monomial_labels=new_multisets, + constant_term=new_constant_term, + ) +
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    Source code for qiskit_dynamics.perturbation.perturbation_data

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2022.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +
    +r"""
    +Class for storing results of perturbation theory computations.
    +"""
    +
    +from typing import List, Mapping, Optional
    +from dataclasses import dataclass
    +
    +from multiset import Multiset
    +
    +from qiskit import QiskitError
    +from qiskit_dynamics.array import Array
    +
    +
    +@dataclass
    +class _LabeledData:
    +    """Container for arbitrarily "labeled data", i.e. data whose indices are arbitrary python
    +    objects. The method ``get_item`` looks up an item according to the label.
    +    """
    +
    +    data: Mapping[int, any]
    +    labels: List[any]
    +    metadata: Optional[any] = None
    +
    +    def get_item(self, label: any) -> any:
    +        """Look up an item in self.data according to the location of label in self.labels."""
    +        label = self._preprocess_label(label)
    +
    +        if label in self.labels:
    +            return self._post_process_item(self.data[self.labels.index(label)])
    +
    +        raise QiskitError("label is not present in self.labels.")
    +
    +    def _preprocess_label(self, label: any) -> any:
    +        return label
    +
    +    def _post_process_item(self, item: any) -> any:
    +        return item
    +
    +
    +
    +[docs] +class PowerSeriesData(_LabeledData): + """Storage container for power series data. Labels are assumed to be ``Multiset`` instances, + and data is assumed to be an ``Array``. + """ + + def _preprocess_label(self, label: Multiset) -> Multiset: + """Cast to a Multiset.""" + return Multiset(label) + + def _post_process_item(self, item: Array) -> Array: + """Wrap in an Array.""" + return Array(item, backend=self.data.backend)
    + + + +
    +[docs] +class DysonLikeData(_LabeledData): + """Storage container for DysonLike series data. Labels are assumed to be lists of ints, + and data is assumed to be an ``Array``. + """ + + def _preprocess_label(self, label: list) -> list: + """Cast to a list.""" + return list(label) + + def _post_process_item(self, item: Array) -> Array: + """Wrap in an array.""" + return Array(item, backend=self.data.backend)
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    Source code for qiskit_dynamics.perturbation.solve_lmde_perturbation

    +# -*- coding: utf-8 -*-
    +
    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2022.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may obtain a copy of this license
    +# in the LICENSE.txt file in the root directory of this source tree or at
    +# http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this copyright notice, and modified
    +# files need to carry a notice indicating that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +r"""
    +Compute perturbation theory terms for an LMDE.
    +"""
    +
    +from typing import List, Optional, Callable
    +
    +from scipy.integrate._ivp.ivp import OdeResult  # pylint: disable=unused-import
    +
    +from multiset import Multiset
    +
    +from qiskit import QiskitError
    +
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.perturbation.multiset_utils import _clean_multisets
    +from qiskit_dynamics.perturbation.perturbation_utils import (
    +    _merge_multiset_expansion_order_labels,
    +    _merge_list_expansion_order_labels,
    +)
    +
    +from qiskit_dynamics.perturbation.dyson_magnus import (
    +    _solve_lmde_dyson,
    +    _solve_lmde_magnus,
    +    _solve_lmde_dyson_jax,
    +    _solve_lmde_magnus_jax,
    +)
    +
    +
    +
    +[docs] +def solve_lmde_perturbation( + perturbations: List[Callable], + t_span: Array, + expansion_method: str, + expansion_order: Optional[int] = None, + expansion_labels: Optional[List[Multiset]] = None, + perturbation_labels: Optional[List[Multiset]] = None, + generator: Optional[Callable] = None, + y0: Optional[Array] = None, + dyson_in_frame: Optional[bool] = True, + integration_method: Optional[str] = "DOP853", + t_eval: Optional[Array] = None, + **kwargs, +) -> OdeResult: + r"""Compute time-dependent perturbation theory terms for an LMDE. + + This function computes multi-variable Dyson or Magnus expansion terms via the algorithm in + :footcite:`puzzuoli_sensitivity_2022`, or Dyson-like terms via the algorithm in + :footcite:`haas_engineering_2019`. See the + :ref:`review on time-dependent perturbation theory <perturbation review>` + to understand the details and notation used in this documentation. + + Which expansion is used is specified by the ``expansion_method`` argument, which impacts the + interpretation of several of the function arguments (described below). Regardless of + ``expansion_method``, the main computation is performed by solving a differential equation, + utilizing :func:`.solve_ode`, and as such several of the function arguments are direct inputs + into this function: + + - ``integration_method`` is the ODE method used (passed as ``method`` to + :func:`.solve_ode`), ``t_span`` is the integration interval, and ``t_eval`` is an optional + set of points to evaluate the perturbation terms at. + - ``kwargs`` are passed directly to :func:`.solve_ode`, enabling passing through of + tolerance or step size arguments. + + Other arguments which are treated the same regardless off ``expansion_method`` are: + + - ``generator`` is the unperturbed generator, and the computation is performed in the + toggling frame of this generator. + + If ``expansion_method in ['dyson', 'magnus']``, this function computes either multivariable + Dyson series or Magnus expansion terms. That is, given a (finitely truncated) power series for + the generator: + + .. math:: + + G(t, c_0, \dots, c_{r-1}) = G_\emptyset(t) + + \sum_{k=1}^\infty \sum_{I \in \mathcal{I}_k(r)} c_I G_I(t), + + this function computes, in the toggling frame of :math:`G_\emptyset(t)` given by ``generator``, + either a collection of multivariable Dyson terms :math:`\mathcal{D}_I(t)` or multivariable + Magnus terms :math:`\mathcal{O}_I(t)`, whose definitions are given in the + :ref:`perturbation theory review <perturbation review>`. In this case, the arguments to the + function are interpreted as follows: + + - ``perturbations`` and ``perturbation_labels`` specify the truncated generator power + series. ``perturbations`` provides a list of python callable functions for the non-zero + :math:`G_I(t)`, and the ``perturbation_labels`` is a list of the corresponding multiset + labels :math:`I`, in the form of ``Multiset`` instances. If not specified, the labels are + assumed to be ``[Multiset({0: 1}), ..., Multiset({len(perturbations) - 1: 1})]``. + - ``expansion_order`` and ``expansion_labels`` specify which terms in the chosen expansion + are to be computed. ``expansion_order`` specifies that all expansion terms up to a given + order are to be computed, and ``expansion_labels`` specifies individual terms to be + computed, specified as ``Multiset`` instances. At least one of ``expansion_order`` and + ``expansion_labels`` must be specified. If both are specified, then all terms up to + ``expansion_order`` will be computed, along with any additional specific terms given by + ``expansion_labels``. + + Note that in the above, this function requires that the Multisets consist of non-negative + integers. Arguments requiring lists of ``Multiset`` instances also accept lists of any valid + format acceptable to the ``Multiset`` constructor (modulo the non-negative integer constraint). + + If ``expansion_method == 'dyson_like'``, the setup is different. In this case, for a list of + matrix-valued functions :math:`G_0(t), \dots, G_{r-1}(t)`, this function computes integrals of + the form + + .. math:: + \int_{t_0}^{t_F} dt_1 \int_{t_0}^{t_1} dt_2 \dots \int_{t_0}^{t_{k-1}}dt_k + \tilde{G}_{i_1}(t_1) \dots \tilde{G}_{i_k}(t_k), + + for lists of integers :math:`[i_1, \dots, i_k]`, and similar to the other cases, + :math:`\tilde{G}_j(t) = V(t)^\dagger G_j(t)V(t)`, i.e. the computation is performed in the + toggling frame specified by ``generator``. + + - ``perturbations`` gives the list of matrix functions as callables + :math:`G_0(t), \dots, G_{r-1}(t)`. + - ``perturbation_labels`` is not used in this mode. + - ``expansion_order`` specifies that all possible integrals of the above form should be + computed up to a given order (i.e. integrals up to a given order with all possible + orderings of the :math:`G_0(t), \dots, G_{r-1}(t)`). + - ``expansion_labels`` allows for specification of specific terms to be computed. In this + case, a term is specified by a list of ``int``\s, where the length of the list is the + order of the integral, and the :math:`G_0(t), \dots, G_{r-1}(t)` appear in the integral in + the order given by the list. + + Finally, additional optional arguments which can be used in the ``'dyson'`` and ``'dyson_like'`` + cases are: + + - ``dyson_in_frame`` controls which frame the results are returned in. The default is + ``True``, in which case the results are returned as described above. If ``False``, the + returned results include a pre-factor of :math:`V(t)`, the solution of the unperturbed + generator, e.g. :math:`V(t)\mathcal{D}_I(t)`. If ``expansion_method=='magnus'``, this + argument has no effect on the computation. + - ``y0`` is the initial state for the LMDE given by the unperturbed generator. The effect of + this argument on the output is to multiply all outputs by ``y0`` on the right. If ``y0`` + is supplied, the argument ``dyson_in_frame`` must be ``False``, as the operator + :math:`V(t)` is never explicitly computed, and therefore it cannot be removed from the + results. If ``y0`` is 1d, it will first be transformed into a 2d column vector to ensure + consistent usage of matrix multiplication. + + Regardless of the value of ``expansion_method``, results are returned in an ``OdeResult`` + instance in the same manner as :func:`.solve_ode`. The result object stores the solution of the + LMDE for ``generator`` and ``y0`` as if these were passed directly to :func:`.solve_ode` before, + as well as the computed perturbation theory terms in the additional attribute + ``perturbation_data``. If ``expansion_method in ['dyson', 'magnus']``, the ``perturbation_data`` + attribute stores a :class:`.PowerSeriesData` instance, and if + ``expansion_method == 'dyson_like'``, it stores a :class:`.DysonLikeData` instance. In either + case, these are data container classes with the following attributes: + + - ``metadata``: Containing expansion information. + - ``labels``: Index labels for all computed perturbation terms. In the case of the Dyson or + Magnus expansion, the labels are ``Multiset`` instances, and in the `'dyson_like'` case, + they are lists of ``int``\s. + - ``data``: A 4d array storing all computed terms. The first axis indexes the expansion + terms in the same ordering as ``labels``, and the second axis indexes the perturbation + terms evaluated at the times in ``results.t`` in the same manner as ``results.y``. + + Additionally, both the :meth:`.PowerSeriesData.get_item` and :meth:`.DysonLikeData.get_item` + methods can be used to retrieve the results for a given perturbation term according to its + label. E.g. the results for the term with label ``[0, 1]`` is retrievable via + ``results.perturbation_data.get_term([0, 1])``. + + Args: + perturbations: List of matrix-valued callables. + t_span: Integration bounds. + expansion_method: Either ``'dyson'``, ``'magnus'``, or ``'dyson_like'``. + expansion_order: Order of perturbation terms to compute up to. Specifying this argument + results in computation of all terms up to the given order. Can be used in conjunction + with ``expansion_labels``. + expansion_labels: Specific perturbation terms to compute. If both ``expansion_order`` + and ``expansion_labels`` are specified, then all terms up to ``expansion_order`` are + computed, along with the additional terms specified in ``expansion_labels``. + perturbation_labels: Optional description of power series terms specified by + ``perturbations``. To only be used with ``'dyson'`` and ``'magnus'`` methods. + generator: Optional frame generator. Defaults to ``0``. + y0: Optional initial state for frame generator LMDE. Defaults to the identity matrix. + dyson_in_frame: For ``expansion_method`` ``'dyson'`` or ``'dyson_like'``, whether or not + to remove the frame transformation pre-factor from the Dyson terms. + integration_method: Integration method to use. + t_eval: Points at which to evaluate the system. + **kwargs: Additional arguments to pass to ode integration method used to compute terms. + + Returns: + OdeResult: Results object containing standard ODE results for LMDE given by ``generator`` + and ``y0``, with additional ``perturbation_data`` attribute containing the requested + perturbation theory terms. + + Raises: + QiskitError: If problem with inputs, either ``expansion_method`` is unsupported, + or both of ``expansion_order`` and ``expansion_labels`` unspecified. + + .. footbibliography:: + """ + + # validation checks + if y0 is not None: + if "magnus" in expansion_method: + raise QiskitError("""Argument y0 cannot be used for expansion_method=='magnus'.""") + + if dyson_in_frame: + raise QiskitError( + """If expansion_method in ['dyson', 'dyson_like'] + and y0 passed, dyson_in_frame must be False.""" + ) + + # if 1d in a dyson case, turn into a column vector + if y0.ndim == 1: + y0 = Array([y0]).transpose() + + if perturbation_labels is not None and expansion_method == "dyson_like": + raise QiskitError( + """perturbation_labels argument not usable with + expansion_method='dyson_like'.""" + ) + + # clean and validate perturbation_labels, and setup expansion terms to compute + if expansion_method in ["dyson", "magnus"]: + if perturbation_labels is None: + perturbation_labels = [Multiset({idx: 1}) for idx in range(len(perturbations))] + else: + # validate perturbation_labels + perturbations_len = len(perturbation_labels) + perturbation_labels = [Multiset(x) for x in perturbation_labels] + cleaned_perturbation_labels = _clean_multisets(perturbation_labels) + if len(cleaned_perturbation_labels) != perturbations_len: + raise QiskitError("perturbation_labels argument contains duplicates as multisets.") + + expansion_labels = _merge_multiset_expansion_order_labels( + perturbation_labels=perturbation_labels, + expansion_order=expansion_order, + expansion_labels=expansion_labels, + ) + elif expansion_method in ["dyson_like"]: + expansion_labels = _merge_list_expansion_order_labels( + perturbation_num=len(perturbations), + expansion_order=expansion_order, + expansion_labels=expansion_labels, + ) + + if expansion_method in ["dyson", "dyson_like"]: + dyson_like = expansion_method == "dyson_like" + if not Array.default_backend() == "jax": + return _solve_lmde_dyson( + perturbations=perturbations, + t_span=t_span, + dyson_terms=expansion_labels, + perturbation_labels=perturbation_labels, + generator=generator, + y0=y0, + dyson_in_frame=dyson_in_frame, + dyson_like=dyson_like, + integration_method=integration_method, + t_eval=t_eval, + **kwargs, + ) + else: + return _solve_lmde_dyson_jax( + perturbations=perturbations, + t_span=t_span, + dyson_terms=expansion_labels, + perturbation_labels=perturbation_labels, + generator=generator, + y0=y0, + dyson_in_frame=dyson_in_frame, + dyson_like=dyson_like, + integration_method=integration_method, + t_eval=t_eval, + **kwargs, + ) + elif expansion_method == "magnus": + if not Array.default_backend() == "jax": + return _solve_lmde_magnus( + perturbations=perturbations, + t_span=t_span, + magnus_terms=expansion_labels, + perturbation_labels=perturbation_labels, + generator=generator, + y0=y0, + integration_method=integration_method, + t_eval=t_eval, + **kwargs, + ) + else: + return _solve_lmde_magnus_jax( + perturbations=perturbations, + t_span=t_span, + magnus_terms=expansion_labels, + perturbation_labels=perturbation_labels, + generator=generator, + y0=y0, + integration_method=integration_method, + t_eval=t_eval, + **kwargs, + ) + + # raise error if none apply + raise QiskitError(f"expansion_method {expansion_method} not supported.")
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    + Last updated on 2024/03/18
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/pulse/pulse_to_signals.html b/stable/0.4/_modules/qiskit_dynamics/pulse/pulse_to_signals.html new file mode 100644 index 000000000..db5e747a2 --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/pulse/pulse_to_signals.html @@ -0,0 +1,736 @@ + + + + + + + + qiskit_dynamics.pulse.pulse_to_signals - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    Source code for qiskit_dynamics.pulse.pulse_to_signals

    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +
    +"""
    +Pulse schedule to Signals converter.
    +"""
    +
    +from typing import Callable, Dict, List, Optional
    +import functools
    +from warnings import warn
    +
    +import numpy as np
    +import sympy as sym
    +
    +from qiskit.pulse import (
    +    Schedule,
    +    Play,
    +    ShiftPhase,
    +    SetPhase,
    +    ShiftFrequency,
    +    SetFrequency,
    +    Waveform,
    +    MeasureChannel,
    +    DriveChannel,
    +    ControlChannel,
    +    AcquireChannel,
    +)
    +from qiskit.pulse.exceptions import PulseError
    +from qiskit.pulse.library import SymbolicPulse
    +from qiskit import QiskitError
    +
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.signals import DiscreteSignal
    +
    +try:
    +    import jax
    +    import jax.numpy as jnp
    +except ImportError:
    +    pass
    +
    +
    +
    +[docs] +class InstructionToSignals: + """Converts pulse instructions to signals to be used in models. + + The :class:`InstructionsToSignals` class converts a pulse schedule to a list of signals that can + be given to a model. This conversion is done by calling the :meth:`get_signals` method on a + schedule. The converter applies to instances of :class:`~qiskit.pulse.Schedule`. Instances of + :class:`~qiskit.pulse.ScheduleBlock` must first be converted to :class:`~qiskit.pulse.Schedule` + using the :func:`~qiskit.pulse.transforms.block_to_schedule` function in Qiskit Pulse. + + The converter can be initialized with the optional arguments ``carriers`` and ``channels``. When + ``channels`` is given, only the signals specified by name in ``channels`` are returned. The + ``carriers`` dictionary specifies the analog carrier frequency of each channel. Here, the keys + are the channel name, e.g. ``d12`` for drive channel number ``12``, and the values are the + corresponding frequency. If a channel is not present in ``carriers`` it is assumed that the + analog carrier frequency is zero. + + See the :meth:`get_signals` method documentation for a detailed description of how pulse + schedules are interpreted and translated into :class:`.DiscreteSignal` objects. + """ + + def __init__( + self, + dt: float, + carriers: Optional[Dict[str, float]] = None, + channels: Optional[List[str]] = None, + ): + """Initialize pulse schedule to signals converter. + + Args: + dt: Length of the samples. This is required by the converter as pulse schedule are + specified in units of dt and typically do not carry the value of dt with them. + carriers: A dict of analog carrier frequencies. The keys are the names of the channels + and the values are the corresponding carrier frequency. + channels: A list of channels that the :meth:`get_signals` method should return. This + argument will cause :meth:`get_signals` to return the signals in the same order as + the channels. Channels present in the schedule but absent from channels will not be + included in the returned object. If None is given (the default) then all channels + present in the pulse schedule are returned. + """ + + self._dt = dt + self._channels = channels + self._carriers = carriers or {} + +
    +[docs] + def get_signals(self, schedule: Schedule) -> List[DiscreteSignal]: + r"""Convert a schedule to a corresponding list of DiscreteSignal instances. + + Which channels are converted, and the order they are returned, is controlled by the + ``channels`` argument at instantiation. The ``carriers`` instantiation argument sets the + analog carrier frequency for each channel, which is fixed for the full duration. For a given + channel, the :math:`k^{th}` envelope sample for the corresponding :class:`.DiscreteSignal` + is determined according to the following formula: + + .. math:: + f(k) \exp(i(2\pi \Delta\nu(k) k dt + \phi(k) + 2 \pi \phi_a(k))), + + where: + + * :math:`f(k)` is the waveform value at the :math:`k^{th}` time step as specified by + ``Play`` instructions. + * :math:`\Delta\nu(k)` is the frequency deviation at time step :math:`k` from the analog + carrier as the result of ``SetFrequency`` and ``ShiftFrequency`` instructions. As evident + by the formula, carrier frequency deviations as a result of these instructions are handled + digitally, with the analog carrier frequency being fixed for the entirety of the schedule. + * :math:`dt` is the sample rate as specified by the ``dt`` instantiation argument. + * :math:`\phi(k)` is the channel phase at time step :math:`k`, as determined by + ``ShiftPhase`` and ``SetPhase`` instructions. + * :math:`\phi_a(k)` is the phase correction term at time step :math:`k`, impacted by + ``SetFrequency`` and ``ShiftFrequency`` instructions, described below. + + In detail, the sample array for the output signal for each channel is generated by iterating + over each instruction in the schedule in temporal order. New samples are appended with every + ``Play`` instruction on the given channel, using the waveform values and the current value + of the tracked parameters :math:`\Delta\nu`, :math:`\phi`, and :math:`\phi_a`, which are + initialized to :math:`0`. Explicitly, each instruction is interpreted as follows: + + * ``Play`` instructions add new samples to the sample array, according to the above formula, + using the waveform specified in the instruction and the current values of + :math:`\Delta\nu`, :math:`\phi`, and :math:`\phi_a`. + * ``ShiftPhase``, with a phase value :math:`\psi`, updates :math:`\phi \mapsto \phi + \psi`. + * ``SetPhase``, with a phase value :math:`\psi`, updates :math:`\phi \mapsto \psi`. + * ``ShiftFrequency``, with a frequency value :math:`\mu` at time-step :math:`k`, updates + :math:`\phi_a \mapsto \phi_a - \mu k dt` and :math:`\Delta\nu \mapsto \Delta\nu + \mu`. + The simultaneous shifting of both :math:`\Delta\nu` and :math:`\phi_a` ensures that the + carrier wave, as a combination of the analog and digital components, is continuous across + ``ShiftFrequency`` instructions (up to the sampling rate :math:`dt`). + * ``SetFrequency``, with a frequency value :math:`\mu` at time-step :math:`k`, updates + :math:`\phi_a \mapsto \phi_a - (\mu - (\Delta\nu + \nu)) k dt` and + :math:`\Delta\nu \mapsto \mu - \nu`, where :math:`\nu` is the analog carrier frequency. + Similarly to ``ShiftFrequency``, the shift rule for :math:`\phi_a` is defined to maintain + carrier wave continuity. + + If, at any sample point :math:`k`, :math:`\Delta\nu(k)` is larger than the Nyquist sampling + rate given by ``dt``, a warning will be raised. + + Args: + schedule: The schedule to represent in terms of signals. Instances of + :class:`~qiskit.pulse.ScheduleBlock` must first be converted to + :class:`~qiskit.pulse.Schedule` using the + :func:`~qiskit.pulse.transforms.block_to_schedule` function in Qiskit Pulse. + + Returns: + A list of :class:`.DiscreteSignal` instances. + """ + + signals, phases, frequency_shifts, phase_accumulations = {}, {}, {}, {} + + if self._channels is not None: + schedule = schedule.filter(channels=[self._get_channel(ch) for ch in self._channels]) + + for chan in schedule.channels: + phases[chan.name] = 0.0 + frequency_shifts[chan.name] = 0.0 + phase_accumulations[chan.name] = 0.0 + + carrier_freq = self._carriers.get(chan.name, 0.0) + + signals[chan.name] = DiscreteSignal( + samples=[], + dt=self._dt, + name=chan.name, + carrier_freq=carrier_freq, + ) + + for start_sample, inst in schedule.instructions: + # get channel name if instruction has it + chan = inst.channel.name if hasattr(inst, "channel") else None + + if isinstance(inst, Play): + # get the instruction samples + inst_samples = None + if isinstance(inst.pulse, Waveform): + inst_samples = inst.pulse.samples + else: + inst_samples = get_samples(inst.pulse) + + # build sample array to append to signal + times = self._dt * (start_sample + np.arange(len(inst_samples))) + samples = inst_samples * np.exp( + Array( + 2.0j * np.pi * frequency_shifts[chan] * times + + 1.0j * phases[chan] + + 2.0j * np.pi * phase_accumulations[chan] + ) + ) + signals[chan].add_samples(start_sample, samples) + + if isinstance(inst, ShiftPhase): + phases[chan] += inst.phase + + if isinstance(inst, SetPhase): + phases[chan] = inst.phase + + if isinstance(inst, ShiftFrequency): + frequency_shifts[chan] = frequency_shifts[chan] + Array(inst.frequency) + phase_accumulations[chan] = ( + phase_accumulations[chan] - inst.frequency * start_sample * self._dt + ) + _nyquist_warn(frequency_shifts[chan], self._dt, chan) + + if isinstance(inst, SetFrequency): + phase_accumulations[chan] = phase_accumulations[chan] - ( + (inst.frequency - (frequency_shifts[chan] + signals[chan].carrier_freq)) + * start_sample + * self._dt + ) + frequency_shifts[chan] = inst.frequency - signals[chan].carrier_freq + _nyquist_warn(frequency_shifts[chan], self._dt, chan) + + # ensure all signals have the same number of samples + max_duration = 0 + for sig in signals.values(): + max_duration = max(max_duration, sig.duration) + + for sig in signals.values(): + if sig.duration < max_duration: + sig.add_samples( + start_sample=sig.duration, + samples=np.zeros(max_duration - sig.duration, dtype=complex), + ) + + # filter the channels + if self._channels is None: + return list(signals.values()) + + return_signals = [] + for chan_name in self._channels: + signal = signals.get( + chan_name, DiscreteSignal(samples=[], dt=self._dt, name=chan_name, carrier_freq=0.0) + ) + + return_signals.append(signal) + return return_signals
    + + +
    +[docs] + @staticmethod + def get_awg_signals( + signals: List[DiscreteSignal], if_modulation: float + ) -> List[DiscreteSignal]: + r""" + Create signals that correspond to the output ports of an Arbitrary Waveform Generator + to be used with IQ mixers. For each signal in the list the number of signals is double + to create the I and Q components. The I and Q signals represent the real and imaginary + parts, respectively, of + + .. math:: + \Omega(t) e^{i \omega_{if} t} + + where :math:`\Omega` is the complex-valued pulse envelope and :math:`\omega_{if}` is the + intermediate frequency. + + Args: + signals: A list of signals for which to create I and Q. + if_modulation: The intermediate frequency with which the AWG modulates the pulse + envelopes. + + Returns: + iq signals: A list of signals which is twice as long as the input list of signals. + For each input signal get_awg_signals returns two + """ + new_signals = [] + + for sig in signals: + new_freq = sig.carrier_freq + if_modulation + + samples_i = sig.samples + samples_q = np.imag(samples_i) - 1.0j * np.real(samples_i) + + sig_i = DiscreteSignal( + sig.dt, + samples_i, + sig.start_time, + new_freq, + sig.phase, + sig.name + "_i", + ) + sig_q = DiscreteSignal( + sig.dt, + samples_q, + sig.start_time, + new_freq, + sig.phase, + sig.name + "_q", + ) + + new_signals += [sig_i, sig_q] + + return new_signals
    + + + def _get_channel(self, channel_name: str): + """Return the channel corresponding to the given name.""" + + try: + prefix = channel_name[0] + index = int(channel_name[1:]) + + if prefix == "d": + return DriveChannel(index) + + if prefix == "m": + return MeasureChannel(index) + + if prefix == "u": + return ControlChannel(index) + + if prefix == "a": + return AcquireChannel(index) + + raise QiskitError( + f"Unsupported channel name {channel_name} in {self.__class__.__name__}" + ) + + except (KeyError, IndexError, ValueError) as error: + raise QiskitError( + f"Invalid channel name {channel_name} given to {self.__class__.__name__}." + ) from error
    + + + +def get_samples(pulse: SymbolicPulse) -> np.ndarray: + """Return samples filled according to the formula that the pulse + represents and the parameter values it contains. + + Args: + pulse: SymbolicPulse class. + Returns: + Samples of the pulse. + Raises: + PulseError: When parameters are not assigned. + PulseError: When expression for pulse envelope is not assigned. + PulseError: When a free symbol value is not defined in the pulse instance parameters. + """ + envelope = pulse.envelope + pulse_params = pulse.parameters + if pulse.is_parameterized(): + raise PulseError("Unassigned parameter exists. All parameters must be assigned.") + + if envelope is None: + raise PulseError("Pulse envelope expression is not assigned.") + + args = [] + for symbol in sorted(envelope.free_symbols, key=lambda s: s.name): + if symbol.name == "t": + times = Array(np.arange(0, pulse_params["duration"]) + 1 / 2) + args.insert(0, times.data) + continue + try: + args.append(pulse_params[symbol.name]) + except KeyError as ex: + raise PulseError( + f"Pulse parameter '{symbol.name}' is not defined for this instance. " + "Please check your waveform expression is correct." + ) from ex + return _lru_cache_expr(envelope, Array.default_backend())(*args) + + +@functools.lru_cache(maxsize=None) +def _lru_cache_expr(expr: sym.Expr, backend) -> Callable: + """A helper function to get lambdified expression. + + Args: + expr: Symbolic expression to evaluate. + backend: Array backend. + Returns: + lambdified expression. + """ + params = [] + for param in sorted(expr.free_symbols, key=lambda s: s.name): + if param.name == "t": + params.insert(0, param) + continue + params.append(param) + return sym.lambdify(params, expr, modules=backend) + + +def _nyquist_warn(frequency_shift: Array, dt: float, channel: str): + """Raise a warning if the frequency shift is above the Nyquist frequency given by ``dt``.""" + + if ( + Array(frequency_shift).backend != "jax" or not isinstance(jnp.array(0), jax.core.Tracer) + ) and np.abs(frequency_shift) > 0.5 / dt: + warn( + "Due to SetFrequency and ShiftFrequency instructions, the digital carrier frequency " + f"of channel {channel} is larger than the Nyquist frequency of the envelope sample " + "size dt. As shifts of the frequency from the analog frequency are handled digitally, " + "this will result in aliasing effects." + ) +
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/signals/signals.html b/stable/0.4/_modules/qiskit_dynamics/signals/signals.html new file mode 100644 index 000000000..e607ff33a --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/signals/signals.html @@ -0,0 +1,1550 @@ + + + + + + + + qiskit_dynamics.signals.signals - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    +

    Source code for qiskit_dynamics.signals.signals

    +# -*- coding: utf-8 -*-
    +
    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2021.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name, unidiomatic-typecheck, super-init-not-called
    +
    +"""
    +Module for representation of model coefficients.
    +"""
    +
    +from typing import List, Callable, Union, Optional, Tuple
    +import itertools
    +import operator
    +
    +import numpy as np
    +from matplotlib import pyplot as plt
    +
    +try:
    +    import jax.numpy as jnp
    +except ImportError:
    +    pass
    +
    +from qiskit import QiskitError
    +from qiskit_dynamics.array import Array
    +
    +
    +
    +[docs] +class Signal: + r"""General signal class. + + Represents a function of the form: + + .. math:: + Re[f(t)e^{i (2 \pi \nu t + \phi)}] + = Re[f(t)]\cos(2 \pi \nu t + \phi) - Im[f(t)]\sin(2 \pi \nu t + \phi), + + where + + - :math:`f(t)` is the envelope function. + - :math:`\nu` is the carrier frequency. + - :math:`\phi` is the phase. + + The envelope function can be specified either as a constant numeric value + (indicating a constant function), or as a complex-valued callable, + and the frequency and phase must be real. + + + .. note:: + + :class:`~qiskit_dynamics.signals.Signal` assumes the envelope ``f`` is + *array vectorized* in the sense that ``f`` can operate on arrays of arbitrary shape + and satisfy ``f(x)[idx] == f(x[idx])`` for a multidimensional index ``idx``. This + can be ensured either by writing ``f`` to be vectorized, or by using the ``vectorize`` + function in ``numpy`` or ``jax.numpy``. + + For example, for an unvectorized envelope function ``f``: + + .. code-block:: python + + import numpy as np + vectorized_f = np.vectorize(f) + signal = Signal(envelope=vectorized_f, carrier_freq=2.) + """ + + def __init__( + self, + envelope: Union[Callable, complex, float, int, Array], + carrier_freq: Union[float, List, Array] = 0.0, + phase: Union[float, List, Array] = 0.0, + name: Optional[str] = None, + ): + """ + Initializes a signal given by an envelope and a carrier. + + Args: + envelope: Envelope function of the signal, must be vectorized. + carrier_freq: Frequency of the carrier. Subclasses such as SignalSums + represent the carriers of each signal in an array. + phase: The phase of the carrier. Subclasses such as SignalSums + represent the phase of each signal in an array. + name: Name of the signal. + """ + self._name = name + self._is_constant = False + + if isinstance(envelope, (complex, float, int)): + envelope = Array(complex(envelope)) + + if isinstance(envelope, Array): + # if envelope is constant and the carrier is zero, this is a constant signal + try: + # try block is for catching JAX tracer errors + if carrier_freq == 0.0: + self._is_constant = True + except Exception: # pylint: disable=broad-except + pass + + if envelope.backend == "jax": + self._envelope = lambda t: envelope * jnp.ones_like(Array(t).data) + else: + self._envelope = lambda t: envelope * np.ones_like(t) + elif callable(envelope): + if Array.default_backend() == "jax": + self._envelope = lambda t: Array(envelope(t)) + else: + self._envelope = envelope + + # set carrier and phase + self.carrier_freq = carrier_freq + self.phase = phase + + @property + def name(self) -> str: + """Return the name of the signal.""" + return self._name + + @property + def is_constant(self) -> bool: + """Whether or not the signal is constant.""" + return self._is_constant + + @property + def carrier_freq(self) -> Array: + """The carrier frequency of the signal.""" + return self._carrier_freq + + @carrier_freq.setter + def carrier_freq(self, carrier_freq: Union[float, list, Array]): + """Carrier frequency setter. List handling is to support subclasses storing a + list of frequencies.""" + if type(carrier_freq) == list: + carrier_freq = [Array(entry).data for entry in carrier_freq] + self._carrier_freq = Array(carrier_freq) + self._carrier_arg = 1j * 2 * np.pi * self._carrier_freq + + @property + def phase(self) -> Array: + """The phase of the signal.""" + return self._phase + + @phase.setter + def phase(self, phase: Union[float, list, Array]): + """Phase setter. List handling is to support subclasses storing a + list of phases.""" + if type(phase) == list: + phase = [Array(entry).data for entry in phase] + self._phase = Array(phase) + self._phase_arg = 1j * self._phase + +
    +[docs] + def envelope(self, t: Union[float, np.array, Array]) -> Union[complex, np.array, Array]: + """Vectorized evaluation of the envelope at time t.""" + return self._envelope(t)
    + + +
    +[docs] + def complex_value(self, t: Union[float, np.array, Array]) -> Union[complex, np.array, Array]: + """Vectorized evaluation of the complex value at time t.""" + arg = self._carrier_arg * t + self._phase_arg + return self.envelope(t) * np.exp(arg)
    + + + def __call__(self, t: Union[float, np.array, Array]) -> Union[complex, np.array, Array]: + """Vectorized evaluation of the signal at time(s) t.""" + return np.real(self.complex_value(t)) + + def __str__(self) -> str: + """Return string representation.""" + if self.name is not None: + return str(self.name) + + if self.is_constant: + return f"Constant({str(self(0.0))})" + + return f"Signal(carrier_freq={str(self.carrier_freq)}, phase={str(self.phase)})" + + def __add__(self, other: "Signal") -> "SignalSum": + return signal_add(self, other) + + def __radd__(self, other: "Signal") -> "SignalSum": + return self.__add__(other) + + def __mul__(self, other: "Signal") -> "SignalSum": + return signal_multiply(self, other) + + def __rmul__(self, other: "Signal") -> "SignalSum": + return self.__mul__(other) + + def __neg__(self) -> "SignalSum": + return -1 * self + + def __sub__(self, other: "Signal") -> "SignalSum": + return self + (-other) + + def __rsub__(self, other: "Signal") -> "SignalSum": + return other + (-self) + +
    +[docs] + def conjugate(self): + """Return a new signal whose complex value is the complex conjugate of this one.""" + + def conj_env(t): + return np.conjugate(self.envelope(t)) + + return Signal(conj_env, -self.carrier_freq, -self.phase)
    + + +
    +[docs] + def draw( + self, + t0: float, + tf: float, + n: int, + function: Optional[str] = "signal", + axis: Optional[plt.axis] = None, + title: Optional[str] = None, + ): + """Plot the signal over an interval. + + The ``function`` arg specifies which function to + plot: + + - ``function == 'signal'`` plots the full signal. + - ``function == 'envelope'`` plots the complex envelope. + - ``function == 'complex_value'`` plots the ``complex_value``. + + Args: + t0: Initial time. + tf: Final time. + n: Number of points to sample in interval. + function: Which function to plot. + axis: The axis to use for plotting. + title: Title of plot. + """ + + if axis is None: + plotter = plt + plotter.title(title) + else: + plotter = axis + plotter.set_title(title) + + t_vals = np.linspace(t0, tf, n) + + y_vals = None + data_type = "real" + if function == "signal": + y_vals = self(t_vals) + title = title or "Value of " + str(self) + elif function == "envelope": + y_vals = self.envelope(t_vals) + data_type = "complex" + title = title or "Envelope of " + str(self) + elif function == "complex_value": + y_vals = self.complex_value(t_vals) + data_type = "complex" + title = title or "Complex value of " + str(self) + + legend = False + if data_type == "complex": + plotter.plot(t_vals, np.real(y_vals), label="Real") + plotter.plot(t_vals, np.imag(y_vals), label="Imag") + legend = True + else: + plotter.plot(t_vals, y_vals) + + if legend: + plotter.legend()
    +
    + + + +
    +[docs] +class DiscreteSignal(Signal): + r"""Piecewise constant signal implemented as an array of samples. + + The envelope is specified by an array of samples ``s = [s_0, ..., s_k]``, sample width ``dt``, + and a start time ``t_0``, with the envelope being evaluated as + :math:`f(t) =` ``s[floor((t - t0)/dt)]`` if ``t`` is in the interval with endpoints + ``start_time`` and ``start_time + dt * len(samples)``, and ``0.0`` otherwise. + By default a :class:`~qiskit_dynamics.signals.DiscreteSignal` is defined to start at + :math:`t=0` but a custom start time can be set via the ``start_time`` kwarg. + """ + + def __init__( + self, + dt: float, + samples: Union[Array, List], + start_time: float = 0.0, + carrier_freq: Union[float, List, Array] = 0.0, + phase: Union[float, List, Array] = 0.0, + name: str = None, + ): + """Initialize a piecewise constant signal. + + Args: + dt: The duration of each sample. + samples: The array of samples. + start_time: The time at which the signal starts. + carrier_freq: Frequency of the carrier. Subclasses such as SignalSums + represent the carriers of each signal in an array. + phase: The phase of the carrier. Subclasses such as SignalSums + represent the phase of each signal in an array. + name: name of the signal. + """ + self._dt = dt + + samples = Array(samples) + + if len(samples) == 0: + zero_pad = np.array([0]) + else: + zero_pad = np.expand_dims(np.zeros_like(Array(samples[0])), 0) + self._padded_samples = np.append(samples, zero_pad, axis=0) + + self._start_time = start_time + + # define internal envelope function + if samples.backend == "jax": + + def envelope(t): + t = Array(t).data + idx = jnp.clip( + jnp.array((t - self._start_time) // self._dt, dtype=int), + -1, + len(self.samples), + ) + return self._padded_samples[idx] + + else: + + def envelope(t): + t = Array(t).data + idx = np.clip( + np.array((t - self._start_time) // self._dt, dtype=int), + -1, + len(self.samples), + ) + return self._padded_samples[idx] + + Signal.__init__(self, envelope=envelope, carrier_freq=carrier_freq, phase=phase, name=name) + +
    +[docs] + @classmethod + def from_Signal( + cls, + signal: Signal, + dt: float, + n_samples: int, + start_time: Optional[float] = 0.0, + sample_carrier: Optional[bool] = False, + ): + r"""Constructs a ``DiscreteSignal`` object by sampling a ``Signal``\. + + The optional argument ``sample_carrier`` controls whether or not to include the carrier + in the sampling. I.e.: + + - If ``sample_carrier == False``\, a ``DiscreteSignal`` is constructed with: + - ``samples`` obtained by sampling ``signal.envelope``\. + - ``carrier_freq = signal.carrier_freq``\. + - ``phase = signal.phase``\. + + - If ``sample_carrier == True``\, a ``DiscreteSignal`` is constructed with: + - ``samples`` obtained by sampling ``signal`` (as a ``callable``\) + - ``carrier_freq = 0``\. + - ``phase = signal.phase``\. + + In either case, samples are obtained from the midpoint of each interval. + + Args: + signal: Signal to sample. + dt: Time increment to use. + n_samples: Number of steps to resample with. + start_time: Start time from which to resample. + sample_carrier: Whether or not to include the carrier in the sampling. + + Returns: + DiscreteSignal: The discretized ``Signal``\. + """ + + times = start_time + (np.arange(n_samples) + 0.5) * dt + freq = signal.carrier_freq + + if sample_carrier: + freq = 0.0 + samples = signal(times) + else: + samples = signal.envelope(times) + + return DiscreteSignal( + dt, + samples, + start_time=start_time, + carrier_freq=freq, + phase=signal.phase, + name=signal.name, + )
    + + + @property + def duration(self) -> int: + """ + Returns: + duration: The duration of the signal in samples. + """ + return len(self.samples) + + @property + def dt(self) -> float: + """ + Returns: + dt: the duration of each sample. + """ + return self._dt + + @property + def samples(self) -> Array: + """ + Returns: + samples: the samples of the piecewise constant signal. + """ + return Array(self._padded_samples[:-1]) + + @property + def start_time(self) -> float: + """ + Returns: + start_time: The time at which the list of samples start. + """ + return self._start_time + +
    +[docs] + def conjugate(self): + return self.__class__( + dt=self._dt, + samples=np.conjugate(self.samples), + start_time=self._start_time, + carrier_freq=-self.carrier_freq, + phase=-self.phase, + )
    + + +
    +[docs] + def add_samples(self, start_sample: int, samples: List): + """ + Appends samples to the pulse starting at start_sample, filling any gap with zeros. + + Args: + start_sample: Index of the sample at which the new samples should be appended. + samples: List of samples to append. + + Raises: + QiskitError: If start_sample is less than the current length of samples. + """ + samples = Array(samples) + + if len(samples) < 1: + return + + if start_sample < len(self.samples): + raise QiskitError("Samples can only be added afer the last sample.") + + zero_pad = np.expand_dims(np.zeros_like(Array(samples[0])), 0) + + new_samples = self.samples + if len(self.samples) < start_sample: + new_samples = np.append( + new_samples, np.repeat(zero_pad, start_sample - len(self.samples)) + ) + + new_samples = np.append(new_samples, samples) + self._padded_samples = np.append(new_samples, zero_pad, axis=0)
    + + + def __str__(self) -> str: + """Return string representation.""" + if self.name is not None: + return str(self.name) + + return f"""DiscreteSignal(dt={self.dt}, carrier_freq={str(self.carrier_freq)}, + phase={str(self.phase)})"""
    + + + +class SignalCollection: + """Base class for a list-like collection of signals.""" + + def __init__(self, signal_list: List[Signal]): + """Initialize by storing list of signals. + + Args: + signal_list: List of signals. + """ + self._is_constant = False + self._components = signal_list + + @property + def components(self) -> List[Signal]: + """The list of components.""" + return self._components + + def __len__(self): + """Number of components.""" + return len(self.components) + + def __getitem__( + self, idx: Union[int, List, np.array, slice] + ) -> Union[Signal, "SignalCollection"]: + """Get item with NumPy-style subscripting, as if this class were a 1d array.""" + + if type(idx) == np.ndarray and idx.ndim > 0: + idx = list(idx) + + # get a list of the subcomponents + if type(idx) == list: + # handle lists + sublist = operator.itemgetter(*idx)(self.components) + + # output will either be a single signal or a tuple of Signals + # convert to list if tuple + if type(sublist) == tuple: + sublist = list(sublist) + else: + # handle slices or singletons + sublist = operator.itemgetter(idx)(self.components) + + # at this point sublist should either be a single Signal, or a list of Signals + if isinstance(sublist, list): + return self.__class__(sublist) + else: + return sublist + + def __iter__(self): + """Return iterator over component list.""" + return self.components.__iter__() + + def conjugate(self) -> "SignalCollection": + """Return the conjugation of this collection.""" + return self.__class__([sig.conjugate() for sig in self.components]) + + +
    +[docs] +class SignalSum(SignalCollection, Signal): + r"""Represents a sum of signals. + + I.e. a sum of ``Signal`` objects: + + .. math:: + s_1(t) + \dots + s_k(t) + + For basic evaluation, this class behaves in the same manner as ``Signal``: + + - ``__call__`` evaluates the sum. + - ``complex_value`` evaluates the sum of the complex values of the individual summands. + + Attributes ``carrier_freq`` and ``phase`` here correspond to an ``Array`` of + frequencies/phases for each term in the sum, and the ``envelope`` method returns an + ``Array`` of the envelopes for each summand. + + Internally, the signals are stored as a list in the ``components`` attribute, which can + be accessed via direct subscripting of the object. + """ + + def __init__(self, *signals, name: Optional[str] = None): + r"""Initialize with a list of Signal objects through ``args``\. + + Args: + signals: ``Signal`` subclass objects. + name: Name of the sum. + + Raises: + QiskitError: If ``signals`` are not subclasses of ``Signal``\. + """ + self._name = name + + components = [] + for sig in signals: + if isinstance(sig, list): + sig = SignalSum(*sig) + + if isinstance(sig, SignalSum): + components += sig.components + elif isinstance(sig, Signal): + components.append(sig) + elif isinstance(sig, (int, float, complex)) or ( + isinstance(sig, Array) and sig.ndim == 0 + ): + components.append(Signal(sig)) + else: + raise QiskitError( + "Components of a SignalSum must be instances of a Signal subclass." + ) + + SignalCollection.__init__(self, components) + + # set up routine for evaluating envelopes if jax + if Array.default_backend() == "jax": + jax_arraylist_eval = array_funclist_evaluate([sig.envelope for sig in self.components]) + + def envelope(t): + return np.moveaxis(jax_arraylist_eval(t), 0, -1) + + else: + + def envelope(t): + return np.moveaxis([sig.envelope(t) for sig in self.components], 0, -1) + + carrier_freqs = [] + for sig in self.components: + carrier_freqs.append(sig.carrier_freq) + + phases = [] + for sig in self.components: + phases.append(sig.phase) + + Signal.__init__( + self, envelope=envelope, carrier_freq=carrier_freqs, phase=phases, name=name + ) + +
    +[docs] + def complex_value(self, t: Union[float, np.array, Array]) -> Union[complex, np.array, Array]: + """Return the sum of the complex values of each component.""" + if Array.default_backend() == "jax": + t = Array(t) + exp_phases = np.exp(np.expand_dims(t, -1) * self._carrier_arg + self._phase_arg) + return np.sum(self.envelope(t) * exp_phases, axis=-1)
    + + + def __str__(self): + if self.name is not None: + return str(self.name) + + if len(self) == 0: + return "SignalSum()" + + default_str = str(self[0]) + for sig in self.components[1:]: + default_str += f" + {str(sig)}" + + return default_str + +
    +[docs] + def flatten(self) -> Signal: + r"""Merge into a single ``Signal``\. The output frequency is given by the + average. + """ + + if len(self) == 0: + return Signal(0.0) + elif len(self) == 1: + return self.components[0] + + ave_freq = np.sum(self.carrier_freq) / len(self) + shifted_arg = self._carrier_arg - (1j * 2 * np.pi * ave_freq) + + def merged_env(t): + exp_phases = np.exp(np.expand_dims(Array(t), -1) * shifted_arg + self._phase_arg) + return np.sum(self.envelope(t) * exp_phases, axis=-1) + + return Signal(envelope=merged_env, carrier_freq=ave_freq, name=str(self))
    +
    + + + +
    +[docs] +class DiscreteSignalSum(DiscreteSignal, SignalSum): + """Represents a sum of piecewise constant signals, all with the same + time parameters: dt, number of samples, and start time. + """ + + def __init__( + self, + dt: float, + samples: Union[List, Array], + start_time: float = 0.0, + carrier_freq: Union[List, np.array, Array] = None, + phase: Union[List, np.array, Array] = None, + name: str = None, + ): + r"""Directly initialize a ``DiscreteSignalSum``\. Samples of all terms in the + sum are specified as a 2d array, with 0th axis indicating time, and 1st axis + indicating a term in the sum. + + Args: + dt: The duration of each sample. + samples: The 2d array representing a list whose elements are all envelope values + at a given time. + start_time: The time at which the signal starts. + carrier_freq: Array with the carrier frequencies of each term in the sum. + phase: Array with the phases of each term in the sum. + name: name of the signal. + """ + + samples = Array(samples) + if carrier_freq is None: + carrier_freq = np.zeros(samples.shape[-1], dtype=float) + + if phase is None: + phase = np.zeros(samples.shape[-1], dtype=float) + + DiscreteSignal.__init__( + self, + dt=dt, + samples=samples, + start_time=start_time, + carrier_freq=carrier_freq, + phase=phase, + name=name, + ) + + # construct individual components so they can be accessed as in SignalSum + components = [] + for sample_row, freq, phi in zip(self.samples.transpose(), carrier_freq, phase): + components.append( + DiscreteSignal( + dt=self.dt, + samples=sample_row, + start_time=self.start_time, + carrier_freq=freq, + phase=phi, + ) + ) + + self._components = components + +
    +[docs] + @classmethod + def from_SignalSum( + cls, + signal_sum: SignalSum, + dt: float, + n_samples: int, + start_time: Optional[float] = 0.0, + sample_carrier: Optional[bool] = False, + ): + r"""Constructs a ``DiscreteSignalSum`` object by sampling a ``SignalSum``\. + + The optional argument ``sample_carrier`` controls whether or not to include the carrier + in the sampling. I.e.: + + - If ``sample_carrier == False``, a ``DiscreteSignalSum`` is constructed with: + - ``samples`` obtained by sampling ``signal_sum.envelope``\. + - ``carrier_freq = signal_sum.carrier_freq``\. + - ``phase = signal_sum.phase``\. + + - If ``sample_carrier == True``\, a ``DiscreteSignal`` is constructed with: + - ``samples`` obtained by sampling ``signal_sum`` (as a ``callable``\) + - ``carrier_freq = 0``\. + - ``phase = signal_sum.phase``\. + + In either case, samples are obtained from the midpoint of each interval. + + Args: + signal_sum: SignalSum to sample. + dt: Time increment to use. + n_samples: Number of steps to resample with. + start_time: Start time from which to resample. + sample_carrier: Whether or not to include the carrier in the sampling. + + Returns: + DiscreteSignalSum: The discretized ``SignalSum``\. + """ + + times = start_time + (np.arange(n_samples) + 0.5) * dt + + freq = signal_sum.carrier_freq + + if sample_carrier: + freq = 0.0 * freq + exp_phases = np.exp(np.expand_dims(Array(times), -1) * signal_sum._carrier_arg) + samples = signal_sum.envelope(times) * exp_phases + else: + samples = signal_sum.envelope(times) + + return DiscreteSignalSum( + dt, + samples, + start_time=start_time, + carrier_freq=freq, + phase=signal_sum.phase, + name=signal_sum.name, + )
    + + + def __str__(self): + """Get the string rep.""" + if self.name is not None: + return str(self.name) + + if len(self) == 0: + return "DiscreteSignalSum()" + + default_str = str(self[0]) + for sig in self.components[1:]: + default_str += f" + {str(sig)}" + + return default_str + + def __getitem__(self, idx: Union[int, List, np.array, slice]) -> Signal: + """Enables numpy-style subscripting, as if this class were a 1d array.""" + + if type(idx) == int and idx >= len(self): + raise IndexError("index out of range for DiscreteSignalSum of length " + str(len(self))) + + samples = self.samples[:, idx] + carrier_freqs = self.carrier_freq[idx] + phases = self.phase[idx] + + if samples.ndim == 1: + samples = Array([samples]) + + if carrier_freqs.ndim == 0: + carrier_freqs = Array([carrier_freqs]) + + if phases.ndim == 0: + phases = Array([phases]) + + if len(samples) == 1: + return DiscreteSignal( + dt=self.dt, + samples=samples[0], + start_time=self.start_time, + carrier_freq=carrier_freqs[0], + phase=phases[0], + ) + + return DiscreteSignalSum( + dt=self.dt, + samples=samples, + start_time=self.start_time, + carrier_freq=carrier_freqs, + phase=phases, + )
    + + + +
    +[docs] +class SignalList(SignalCollection): + r"""A list of signals with functionality for simultaneous evaluation. + + The passed list is stored in the ``components`` attribute. + """ + + def __init__(self, signal_list: List[Signal]): + signal_list = [to_SignalSum(signal) for signal in signal_list] + + super().__init__(signal_list) + + # setup complex value and full signal evaluation + if Array.default_backend() == "jax": + self._eval_complex_value = array_funclist_evaluate( + [sig.complex_value for sig in self.components] + ) + self._eval_signals = array_funclist_evaluate(self.components) + else: + self._eval_complex_value = lambda t: [sig.complex_value(t) for sig in self.components] + self._eval_signals = lambda t: [sig(t) for sig in self.components] + +
    +[docs] + def complex_value(self, t: Union[float, np.array, Array]) -> Union[np.array, Array]: + """Vectorized evaluation of complex value of components.""" + return np.moveaxis(self._eval_complex_value(t), 0, -1)
    + + + def __call__(self, t: Union[float, np.array, Array]) -> Union[np.array, Array]: + """Vectorized evaluation of all components.""" + return np.moveaxis(self._eval_signals(t), 0, -1) + +
    +[docs] + def flatten(self) -> "SignalList": + """Return a ``SignalList`` with each component flattened.""" + flattened_list = [] + for sig in self.components: + if isinstance(sig, SignalSum): + flattened_list.append(sig.flatten()) + else: + flattened_list.append(sig) + + return SignalList(flattened_list)
    + + + @property + def drift(self) -> Array: + r"""Return the drift ``Array``\, i.e. return an ``Array`` whose entries are the sum + of the constant parts of the corresponding component of this ``SignalList``\. + """ + + drift_array = [] + for sig_entry in self.components: + val = 0.0 + + if not isinstance(sig_entry, SignalSum): + sig_entry = SignalSum(sig_entry) + + for term in sig_entry: + if term.is_constant: + val += Array(term(0.0)).data + + drift_array.append(val) + + return Array(drift_array)
    + + + +def signal_add(sig1: Signal, sig2: Signal) -> SignalSum: + """Add two signals.""" + + # generic routine + # convert to SignalSum instances + try: + sig1 = to_SignalSum(sig1) + sig2 = to_SignalSum(sig2) + except QiskitError as qe: + raise QiskitError("Only a number or a Signal instance can be added to a Signal.") from qe + + # if both are DiscreteSignalSum objects with compatible structure, append data together + if isinstance(sig1, DiscreteSignalSum) and isinstance(sig2, DiscreteSignalSum): + if ( + sig1.dt == sig2.dt + and sig1.start_time == sig2.start_time + and sig1.duration == sig2.duration + ): + samples = np.append(sig1.samples, sig2.samples, axis=1) + carrier_freq = np.append(sig1.carrier_freq, sig2.carrier_freq) + phase = np.append(sig1.phase, sig2.phase) + return DiscreteSignalSum( + dt=sig1.dt, + samples=samples, + start_time=sig1.start_time, + carrier_freq=carrier_freq, + phase=phase, + ) + + sig_sum = SignalSum(*(sig1.components + sig2.components)) + + return sig_sum + + +def signal_multiply(sig1: Signal, sig2: Signal) -> SignalSum: + r"""Multiply two ``Signal``\s. For a pair of elementary (non-``SignalSum``\) ``Signal``\s, + expands the product of two signals into a ``SignalSum`` via the formula: + + .. math:: + Re[f(t)e^{i(2 \pi \nu t + \phi)}] \times Re[g(t)e^{i(2 \pi \omega t + \psi)}] + = Re[\frac{1}{2} f(t)g(t)e^{i(2\pi (\omega + \nu)t + (\phi + \psi))} ] + + Re[\frac{1}{2} f(t)\overline{g(t)}e^{i(2\pi (\omega - \nu)t + (\phi - \psi))} ] + + If either (or both) of ``sig1`` or ``sig2`` are ``SignalSum``\s, the multiplication is + distributed over addition. + """ + + # convert to SignalSum instances + try: + sig1 = to_SignalSum(sig1) + sig2 = to_SignalSum(sig2) + except QiskitError as qe: + raise QiskitError("Only a number or a Signal instance can multiply a Signal.") from qe + + sig1, sig2 = sort_signals(sig1, sig2) + + # if sig1 contains only a constant and sig2 is a DiscreteSignalSum + if len(sig1) == 1 and sig1[0].is_constant and isinstance(sig2, DiscreteSignalSum): + return DiscreteSignalSum( + dt=sig2.dt, + samples=sig1(0.0) * sig2.samples, + start_time=sig2.start_time, + carrier_freq=sig2.carrier_freq, + phase=sig2.phase, + ) + # if both are DiscreteSignalSum objects with compatible structure, append data together + elif isinstance(sig1, DiscreteSignalSum) and isinstance(sig2, DiscreteSignalSum): + if ( + sig1.dt == sig2.dt + and sig1.start_time == sig2.start_time + and sig1.duration == sig2.duration + ): + # this vectorized operation produces a 2d array whose columns are the products of + # the original columns + new_samples = Array( + 0.5 + * (sig1.samples[:, :, None] * sig2.samples[:, None, :]).reshape( + (sig1.samples.shape[0], sig1.samples.shape[1] * sig2.samples.shape[1]), + order="C", + ) + ) + new_samples_conj = Array( + 0.5 + * (sig1.samples[:, :, None] * sig2.samples[:, None, :].conj()).reshape( + (sig1.samples.shape[0], sig1.samples.shape[1] * sig2.samples.shape[1]), + order="C", + ) + ) + samples = np.append(new_samples, new_samples_conj, axis=1) + + new_freqs = sig1.carrier_freq + sig2.carrier_freq + new_freqs_conj = sig1.carrier_freq - sig2.carrier_freq + freqs = np.append(Array(new_freqs), Array(new_freqs_conj)) + + new_phases = sig1.phase + sig2.phase + new_phases_conj = sig1.phase - sig2.phase + phases = np.append(Array(new_phases), Array(new_phases_conj)) + + return DiscreteSignalSum( + dt=sig1.dt, + samples=samples, + start_time=sig1.start_time, + carrier_freq=freqs, + phase=phases, + ) + + # initialize to empty sum + product = SignalSum() + + # loop through every pair of components and multiply + for comp1, comp2 in itertools.product(sig1.components, sig2.components): + product += base_signal_multiply(comp1, comp2) + + return product + + +def base_signal_multiply(sig1: Signal, sig2: Signal) -> Signal: + r"""Utility function for multiplying two elementary (non ``SignalSum``\) signals. + This function assumes ``sig1`` and ``sig2`` are legitimate instances of ``Signal`` + subclasses. + + Special cases: + + - Multiplication of two constant ``Signal``\s returns a constant ``Signal``\. + - Multiplication of a constant ``Signal`` and a ``DiscreteSignal`` returns + a ``DiscreteSignal``\. + - If two ``DiscreteSignal``\s have compatible parameters, the resulting signals are + ``DiscreteSignal``\, with the multiplication being implemented by array multiplication of + the samples. + - Lastly, if no special rules apply, the two ``Signal``\s are multiplied generically via + multiplication of the envelopes as functions. + + When a sum with two signals is produced, the carrier frequency (phase) of each component are, + respectively, the sum and difference of the two frequencies (phases). For special cases + involving constant ``Signal``\s and a non-constant ``Signal``, the carrier frequency and phase + are preserved as that of the non-constant piece. + + Args: + sig1: First signal. + sig2: Second signal. + + Returns: + SignalSum: Representing the RHS of the formula when two Signals are multiplied. + """ + + # ensure signals are ordered from most to least specialized + sig1, sig2 = sort_signals(sig1, sig2) + + if sig1.is_constant and sig2.is_constant: + return Signal(sig1(0.0) * sig2(0.0)) + elif sig1.is_constant and type(sig2) is DiscreteSignal: + # multiply the samples by the constant + return DiscreteSignal( + dt=sig2.dt, + samples=sig1(0.0) * sig2.samples, + start_time=sig2.start_time, + carrier_freq=sig2.carrier_freq, + phase=sig2.phase, + ) + elif sig1.is_constant and type(sig2) is Signal: + const = sig1(0.0) + + def new_env(t): + return const * sig2.envelope(t) + + return Signal(envelope=new_env, carrier_freq=sig2.carrier_freq, phase=sig2.phase) + elif type(sig1) is DiscreteSignal and type(sig2) is DiscreteSignal: + # verify compatible parameters before applying special rule + if ( + sig1.start_time == sig2.start_time + and sig1.dt == sig2.dt + and len(sig1.samples) == len(sig2.samples) + ): + pwc1 = DiscreteSignal( + dt=sig2.dt, + samples=0.5 * sig1.samples * sig2.samples, + start_time=sig2.start_time, + carrier_freq=sig1.carrier_freq + sig2.carrier_freq, + phase=sig1.phase + sig2.phase, + ) + pwc2 = DiscreteSignal( + dt=sig2.dt, + samples=0.5 * sig1.samples * np.conjugate(sig2.samples), + start_time=sig2.start_time, + carrier_freq=sig1.carrier_freq - sig2.carrier_freq, + phase=sig1.phase - sig2.phase, + ) + return pwc1 + pwc2 + + # if no special cases apply, implement generic rule + def new_env1(t): + return 0.5 * sig1.envelope(t) * sig2.envelope(t) + + def new_env2(t): + return 0.5 * sig1.envelope(t) * np.conjugate(sig2.envelope(t)) + + prod1 = Signal( + envelope=new_env1, + carrier_freq=sig1.carrier_freq + sig2.carrier_freq, + phase=sig1.phase + sig2.phase, + ) + prod2 = Signal( + envelope=new_env2, + carrier_freq=sig1.carrier_freq - sig2.carrier_freq, + phase=sig1.phase - sig2.phase, + ) + return prod1 + prod2 + + +def sort_signals(sig1: Signal, sig2: Signal) -> Tuple[Signal, Signal]: + r"""Utility function for ordering a pair of ``Signal``\s according to the partial order: + ``sig1 <= sig2`` if and only if: + - ``type(sig1)`` precedes ``type(sig2)`` in the list + ``[constant, DiscreteSignal, Signal, SignalSum, DiscreteSignalSum]``\. + """ + if sig1.is_constant: + pass + elif sig2.is_constant: + sig1, sig2 = sig2, sig1 + elif isinstance(sig1, DiscreteSignal) and not isinstance(sig1, DiscreteSignalSum): + pass + elif isinstance(sig2, DiscreteSignal) and not isinstance(sig2, DiscreteSignalSum): + sig2, sig1 = sig1, sig2 + elif isinstance(sig1, Signal) and not isinstance(sig1, SignalSum): + pass + elif isinstance(sig2, Signal) and not isinstance(sig2, SignalSum): + sig2, sig1 = sig1, sig2 + elif isinstance(sig1, SignalSum) and not isinstance(sig1, DiscreteSignalSum): + pass + elif isinstance(sig2, SignalSum) and not isinstance(sig2, DiscreteSignalSum): + sig2, sig1 = sig1, sig2 + elif isinstance(sig1, DiscreteSignalSum): + pass + elif isinstance(sig2, DiscreteSignalSum): + sig2, sig1 = sig1, sig2 + + return sig1, sig2 + + +def to_SignalSum(sig: Union[int, float, complex, Array, Signal]) -> SignalSum: + r"""Convert the input to a SignalSum according to: + + - If it is already a ``SignalSum``\, do nothing. + - If it is a Signal but not a ``SignalSum``\, wrap in a ``SignalSum``\. + - If it is a number, wrap in constant ``Signal`` in a ``SignalSum``\. + - Otherwise, raise an error. + + Args: + sig: A SignalSum compatible input. + + Returns: + SignalSum + + Raises: + QiskitError: If the input type is incompatible with SignalSum. + """ + + if isinstance(sig, (int, float, complex)) or (isinstance(sig, Array) and sig.ndim == 0): + return SignalSum(Signal(sig)) + elif isinstance(sig, DiscreteSignal) and not isinstance(sig, DiscreteSignalSum): + if Array(sig.samples.data).shape == (0,): + new_samples = Array([sig.samples.data]) + else: + new_samples = Array([sig.samples.data]).transpose(1, 0) + return DiscreteSignalSum( + dt=sig.dt, + samples=new_samples, + start_time=sig.start_time, + carrier_freq=Array([sig.carrier_freq.data]), + phase=Array([sig.phase.data]), + ) + elif isinstance(sig, Signal) and not isinstance(sig, SignalSum): + return SignalSum(sig) + elif isinstance(sig, SignalSum): + return sig + + raise QiskitError("Input type incompatible with SignalSum.") + + +def array_funclist_evaluate(func_list: List[Callable]) -> Callable: + """Utility for evaluating a list of functions in a way that respects Arrays. + Currently relevant for JAX evaluation. + """ + + def eval_func(t): + return Array([Array(func(t)).data for func in func_list]) + + return eval_func +
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    Source code for qiskit_dynamics.signals.transfer_functions

    +# -*- coding: utf-8 -*-
    +
    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Module for transformations between signals.
    +"""
    +
    +from abc import ABC, abstractmethod
    +from typing import Callable, Union, List
    +import numpy as np
    +
    +from qiskit import QiskitError
    +from qiskit_dynamics.array import Array
    +
    +from .signals import Signal, DiscreteSignal
    +
    +
    +class BaseTransferFunction(ABC):
    +    """Base class for transforming signals."""
    +
    +    @property
    +    @abstractmethod
    +    def n_inputs(self):
    +        """Number of input signals to the transfer function."""
    +        pass
    +
    +    def __call__(self, *args, **kwargs) -> Union[Signal, List[Signal]]:
    +        """
    +        Apply the transfer function to the input signals.
    +
    +        Args:
    +            *args: The signals to which the transfer function will be applied.
    +            **kwargs: Key word arguments to control the transfer functions.
    +
    +        Returns:
    +            Signal: The transformed signal.
    +
    +        Raises:
    +            QiskitError: if the number of args is not correct.
    +        """
    +
    +        if len(args) != self.n_inputs:
    +            raise QiskitError(
    +                f"""{self.__class__.__name__} expected {len(args)}
    +                input signals but {self.n_inputs} were given."""
    +            )
    +
    +        return self._apply(*args, **kwargs)
    +
    +    @abstractmethod
    +    def _apply(self, *args, **kwargs) -> Union[Signal, List[Signal]]:
    +        """
    +        Applies a transformation on a signal, such as a convolution,
    +        low pass filter, etc.
    +
    +        Args:
    +            *args: The signals to which the transfer function will be applied.
    +            **kwargs: Key word arguments to control the transfer functions.
    +
    +        Returns:
    +            Signal: The transformed signal.
    +        """
    +        pass
    +
    +
    +
    +[docs] +class Convolution(BaseTransferFunction): + """Applies a convolution as a sum + + (f*g)(n) = sum_k f(k)g(n-k) + + The implementation is quadratic in the number of samples in the signal. + """ + + def __init__(self, func: Callable): + """ + Args: + func: The convolution function specified in time. + This function will be normalized to one before doing + the convolution. To scale signals multiply them by a float. + """ + self._func = func + + @property + def n_inputs(self): + return 1 + + # pylint: disable=arguments-differ + def _apply(self, signal: Signal) -> Signal: + """ + Applies a transformation on a signal, such as a convolution, + low pass filter, etc. Once a convolution is applied the signal + can longer have a carrier as the carrier is part of the signal + value and gets convolved. + + Args: + signal: A signal or list of signals to which the + transfer function will be applied. + + Returns: + signal: The transformed signal or list of signals. + + Raises: + QiskitError: if the signal is not pwc. + """ + if isinstance(signal, DiscreteSignal): + # Perform a discrete time convolution. + dt = signal.dt + func_samples = Array([self._func(dt * i) for i in range(signal.duration)]) + func_samples = func_samples / sum(func_samples) + sig_samples = signal(dt * np.arange(signal.duration)) + + convoluted_samples = list(np.convolve(func_samples, sig_samples)) + + return DiscreteSignal(dt, convoluted_samples, carrier_freq=0.0, phase=0.0) + else: + raise QiskitError("Transfer function not defined on input.")
    + + + +class FFTConvolution(BaseTransferFunction): + """ + Applies a convolution by moving into the fourier domain. + """ + + def __init__(self, func: Callable): + self._func = func + + @property + def n_inputs(self): + return 1 + + # pylint: disable=arguments-differ + def _apply(self, signal: Signal) -> Signal: + raise NotImplementedError + + +class Sampler(BaseTransferFunction): + """ + Re sample a signal by wrapping DiscreteSignal.from_Signal. + """ + + def __init__(self, dt: float, n_samples: int, start_time: float = 0): + """ + Args: + dt: The new sample period. + n_samples: number of samples to resample with. + start_time: start time from which to resample. + """ + self._dt = dt + self._n_samples = n_samples + self._start_time = start_time + + @property + def n_inputs(self): + """Number of input signals to the transfer function.""" + return 1 + + # pylint: disable=arguments-differ + def _apply(self, signal: Signal) -> Signal: + """Apply the transfer function to the signal.""" + return DiscreteSignal.from_Signal( + signal, dt=self._dt, n_samples=self._n_samples, start_time=self._start_time + ) + + +
    +[docs] +class IQMixer(BaseTransferFunction): + """ + Implements an IQ Mixer. The IQ mixer takes as input three signals: + - in-phase signal: I cos(w_if t + phi_I) + - quadrature: Q cos(w_if t + phi_Q) + - local oscillator: K cos(w_lo t) + + In this implementation the local oscillator is specified by its frequency + w_lo and, without loss of generality we assume K = 1. Furthermore, we + require that the carrier frequency of the I and Q be identical. + + The output RF signal is defined by + + s_rf = I [cos(wp t + phi_I) + cos(wm t + phi_I)]/2 + + Q [cos(wp t + phi_Q - pi/2) + cos(wm t + phi_Q + pi/2)]/2 + + where wp = w_lo + w_if and wp = w_lo - w_if. + + The output of this transfer function will produce a piece-wise constant + that does not have a carrier frequency or phase. All information is in the + samples. Mixer imperfections are not included. + """ + + def __init__(self, lo: float): + """ + Args: + lo: The carrier of the IQ mixer. + """ + self._lo = lo + + @property + def n_inputs(self): + return 2 + + # pylint: disable=arguments-differ + def _apply(self, si: Signal, sq: Signal) -> Signal: + """ + Args: + si: In phase signal + sq: Quadrature signal. + + Returns: + The up-converted signal. + + Raises: + QiskitError: if the carriers frequencies of I and Q differ. + """ + + # Check compatibility of the input signals + if si.carrier_freq != sq.carrier_freq: + raise QiskitError("IQ mixer requires the same sideband frequencies for I and Q.") + + phi_i, phi_q = si.phase, sq.phase + wp, wm = self._lo + si.carrier_freq, self._lo - si.carrier_freq + wp *= 2 * np.pi + wm *= 2 * np.pi + + def mixer_func(t): + """Function of the IQ mixer.""" + osc_i = np.cos(wp * t + phi_i) + np.cos(wm * t + phi_i) + osc_q = np.cos(wp * t + phi_q - np.pi / 2) + np.cos(wm * t + phi_q + np.pi / 2) + return si.envelope(t) * osc_i / 2 + sq.envelope(t) * osc_q / 2 + + return Signal(mixer_func, carrier_freq=0, phase=0)
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    Source code for qiskit_dynamics.solvers.perturbative_solvers.dyson_solver

    +# -*- coding: utf-8 -*-
    +
    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2022.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Dyson series based solver.
    +"""
    +
    +from typing import Optional, List, Union
    +
    +from scipy.integrate._ivp.ivp import OdeResult
    +
    +from multiset import Multiset
    +
    +from qiskit.quantum_info import Operator
    +
    +from qiskit_dynamics import Signal, RotatingFrame
    +from qiskit_dynamics.array import Array
    +
    +from .expansion_model import ExpansionModel
    +from .perturbative_solver import _PerturbativeSolver, _perturbative_solve, _perturbative_solve_jax
    +
    +
    +
    +[docs] +class DysonSolver(_PerturbativeSolver): + r"""Solver for linear matrix differential equations based on the Dyson series. + + This class implements the Dyson-series based solver presented in + [:footcite:`puzzuoli_sensitivity_2022`], which is a variant of the *Dysolve* algorithm + originally introduced in [:footcite:p:`shillito_fast_2020`]. + This solver applies to linear matrix differential equations with generators of the form: + + .. math:: + + G(t) = G_0 + \sum_{j=1}^s \textnormal{Re}[f_j(t) e^{i 2 \pi \nu_j t}]G_j, + + and solves the LMDE in the rotating frame of :math:`G_0`, which is assumed to be + anti-Hermitian. I.e. it solves the LMDE with generator: + + .. math:: + + \tilde{G}(t) = \sum_{j=1}^s \textnormal{Re}[f_j(t) e^{i 2 \pi \nu_j t}]\tilde{G}_j(t), + + with :math:`\tilde{G}_i(t) = e^{-t G_0} G_i e^{tG_0}`. The solver is *fixed-step*, + with step size :math:`\Delta t` being defined at instantiation, + and solves over each step by computing a truncated Dyson series. See the + :ref:`Time-dependent perturbation theory and multi-variable + series expansions review <perturbation review>` for a description of the Dyson series. + + At instantiation, the following parameters, which define the structure of the Dyson series + used, are fixed: + + - The step size :math:`\Delta t`, + - The operator structure :math:`G_0`, :math:`G_i`, + - The reference frequencies :math:`\nu_j`, + - Approximation schemes for the envelopes :math:`f_j` over each time step (see below), and + - The Dyson series terms to keep in the truncation. + + A 'compilation' or 'pre-computation' step computing the truncated expansion occurs + at instantiation. Once instantiated, the LMDE can be solved repeatedly for different lists of + envelopes :math:`f_1(t), \dots, f_s(t)` by calling the :meth:`solve` method with the + initial time ``t0`` and number of time-steps ``n_steps`` of size :math:`\Delta t`. + The list of envelopes are specified as :class:`~qiskit_dynamics.signals.Signal` objects, + whose carrier frequencies are automatically shifted to the reference frequencies :math:`\nu_j`, + with the frequency difference, and any phase, being absorbed into the envelope. + + More explicitly, the process of solving over an interval :math:`[t_0, t_0 + \Delta t]` + is as follows. After shifting the carrier frequencies, the resulting envelopes are approximated + using a discrete Chebyshev transform, whose orders for each signal is given by + ``chebyshev_orders``. That is, for :math:`t \in [t_0, t_0 + \Delta t]`, each envelope is + approximated as: + + .. math:: + + f_j(t) \approx \sum_{m=0}^{d_j} f_{j,m}T_m(t-t_0) + + where :math:`T_m(\cdot)` are the Chebyshev polynomials over the interval, + :math:`f_{j,m}` are the approximation coefficients attained via Discrete Chebyshev Transform, + and :math:`d_j` is the order of approximation used for the given envelope. + Using: + + .. math:: + + \textnormal{Re}[f_{j,m}T_m(t-t_0)e^{i2 \pi \nu_j t}] = + \textnormal{Re}[f_{j,m}e^{i 2 \pi \nu_j t_0}] \cos(2 \pi \nu_j (t-t_0))T_m(t-t_0) \\ + + \textnormal{Im}[f_{j,m}e^{i 2 \pi \nu_j t_0}] \sin(-2 \pi \nu_j (t-t_0))T_m(t-t_0) + + The generator is approximately decomposed as + + .. math:: + + \tilde{G}(t) \approx \sum_{j=1}^s \sum_{m=0}^{d_j} + \textnormal{Re}[f_{j,m}e^{i 2 \pi \nu_j t_0}] + \cos(2 \pi \nu_j (t-t_0))T_m(t-t_0) \tilde{G}_j \\ + + \sum_{j=1}^s \sum_{m=0}^{d_j} + \textnormal{Im}[f_{j,m}e^{i 2 \pi \nu_j t_0}] + \sin(- 2 \pi \nu_j (t-t_0))T_m(t-t_0) \tilde{G}_j + + The multivariable Dyson series is then computed relative to the + above decomposition, with the variables being the + :math:`\textnormal{Re}[f_{j,m}e^{i 2 \pi \nu_j t_0}]` and + :math:`\textnormal{Im}[f_{j,m}e^{i 2 \pi \nu_j t_0}]`, and the operators being + :math:`\cos(2 \pi \nu_j (t-t_0))T_m(t-t_0) G_j` and + :math:`\sin(- 2 \pi \nu_j (t-t_0))T_m(t-t_0) G_j`. As shown in + [:footcite:`puzzuoli_sensitivity_2022`, :footcite:p:`shillito_fast_2020`], + the multivariable Dyson series for intervals of length :math:`\Delta t` + with different starting times are related via a simple frame change, and as such + these need only be computed once, and this makes up the 'pre-computation' step of this + object. + + The optional argument ``include_imag`` can be used to control, on a signal by signal basis, + whether or not the imaginary terms + + .. math:: + + \textnormal{Im}[f_{j,m}e^{i 2 \pi \nu_j t_0}] + \sin(- 2 \pi \nu_j (t-t_0))T_m(t-t_0) \tilde{G}_j + + are included in the scheme. In generality they are required, but in special cases they are not + necessary, such as when :math:`\nu_j = 0`, or if :math:`f_j(t)`, including phase, is purely + real. By default all such terms are included. + + .. footbibliography:: + """ + + def __init__( + self, + operators: List[Operator], + rotating_frame: Union[Array, Operator, RotatingFrame, None], + dt: float, + carrier_freqs: Array, + chebyshev_orders: List[int], + expansion_order: Optional[int] = None, + expansion_labels: Optional[List[Multiset]] = None, + integration_method: Optional[str] = None, + include_imag: Optional[List[bool]] = None, + **kwargs, + ): + r"""Initialize. + + Args: + operators: List of constant operators specifying the operators with signal coefficients. + rotating_frame: Rotating frame to setup the solver in. + Must be Hermitian or anti-Hermitian. + dt: Fixed step size to compile to. + carrier_freqs: Carrier frequencies of the signals in the generator decomposition. + chebyshev_orders: Approximation degrees for each signal over the interval [0, dt]. + expansion_order: Order of perturbation terms to compute up to. Specifying this + argument results in computation of all terms up to the given order. + Can be used in conjunction with ``expansion_terms``. + expansion_labels: Specific perturbation terms to compute. If both ``expansion_order`` + and ``expansion_terms`` are specified, then all terms up to + ``expansion_order`` are computed, along with the additional terms + specified in ``expansion_terms``. Labels are specified either as + ``Multiset`` or as valid arguments to the ``Multiset`` constructor. + This function further requires that ``Multiset``\s consist only of + non-negative integers. + integration_method: ODE solver method to use when computing perturbation terms. + include_imag: List of bools determining whether to keep imaginary components in + the signal approximation. Defaults to True for all signals. + kwargs: Additional arguments to pass to the solver when computing perturbation terms. + """ + model = ExpansionModel( + operators=operators, + rotating_frame=rotating_frame, + dt=dt, + carrier_freqs=carrier_freqs, + chebyshev_orders=chebyshev_orders, + expansion_method="dyson", + expansion_order=expansion_order, + expansion_labels=expansion_labels, + integration_method=integration_method, + include_imag=include_imag, + **kwargs, + ) + super().__init__(model=model) + + def _solve(self, t0: float, n_steps: int, y0: Array, signals: List[Signal]) -> OdeResult: + ys = None + if Array.default_backend() == "jax": + single_step = lambda x: self.model.evaluate(x).data + ys = [y0, _perturbative_solve_jax(single_step, self.model, signals, y0, t0, n_steps)] + else: + single_step = lambda coeffs, y: self.model.evaluate(coeffs) @ y + ys = [y0, _perturbative_solve(single_step, self.model, signals, y0, t0, n_steps)] + + return OdeResult(t=[t0, t0 + n_steps * self.model.dt], y=ys)
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    Source code for qiskit_dynamics.solvers.perturbative_solvers.magnus_solver

    +# -*- coding: utf-8 -*-
    +
    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2022.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Magnus expansion-based solver.
    +"""
    +
    +from typing import Optional, List, Union
    +
    +from scipy.linalg import expm
    +from scipy.integrate._ivp.ivp import OdeResult
    +
    +from multiset import Multiset
    +
    +from qiskit.quantum_info import Operator
    +
    +from qiskit_dynamics import Signal, RotatingFrame
    +from qiskit_dynamics.array import Array
    +
    +from .expansion_model import ExpansionModel
    +from .perturbative_solver import _PerturbativeSolver, _perturbative_solve, _perturbative_solve_jax
    +
    +try:
    +    from jax.scipy.linalg import expm as jexpm
    +except ImportError:
    +    pass
    +
    +
    +
    +[docs] +class MagnusSolver(_PerturbativeSolver): + """Solver for linear matrix differential equations based on the Magnus expansion. + + This class implements the Magnus expansion-based solver presented in + [:footcite:`puzzuoli_sensitivity_2022`], which is a Magnus expansion variant of the + *Dysolve* algorithm originally introduced in [:footcite:p:`shillito_fast_2020`]. Its + setup and behaviour are the same as as the :class:`~qiskit_dynamics.solvers.DysonSolver` + class, with the sole exception being that it uses a truncated Magnus expansion + and matrix exponentiation to solve over a single time step. See the + :ref:`Time-dependent perturbation theory and multi-variable + series expansions review <perturbation review>` for a description of the Magnus expansion, + and the documentation for :class:`~qiskit_dynamics.solvers.DysonSolver` for more detailed + behaviour of this class. + """ + + def __init__( + self, + operators: List[Operator], + rotating_frame: Union[Array, Operator, RotatingFrame, None], + dt: float, + carrier_freqs: Array, + chebyshev_orders: List[int], + expansion_order: Optional[int] = None, + expansion_labels: Optional[List[Multiset]] = None, + integration_method: Optional[str] = None, + include_imag: Optional[List[bool]] = None, + **kwargs, + ): + r"""Initialize. + + Args: + operators: List of constant operators specifying the operators with signal coefficients. + rotating_frame: Rotating frame to setup the solver in. + Must be Hermitian or anti-Hermitian. + dt: Fixed step size to compile to. + carrier_freqs: Carrier frequencies of the signals in the generator decomposition. + chebyshev_orders: Approximation degrees for each signal over the interval [0, dt]. + expansion_order: Order of perturbation terms to compute up to. Specifying this + argument results in computation of all terms up to the given order. + Can be used in conjunction with ``expansion_terms``. + expansion_labels: Specific perturbation terms to compute. If both ``expansion_order`` + and ``expansion_terms`` are specified, then all terms up to + ``expansion_order`` are computed, along with the additional terms + specified in ``expansion_terms``. Labels are specified either as + ``Multiset`` or as valid arguments to the ``Multiset`` constructor. + This function further requires that ``Multiset``\s consist only of + non-negative integers. + integration_method: ODE solver method to use when computing perturbation terms. + include_imag: List of bools determining whether to keep imaginary components in + the signal approximation. Defaults to True for all signals. + kwargs: Additional arguments to pass to the solver when computing perturbation terms. + """ + model = ExpansionModel( + operators=operators, + rotating_frame=rotating_frame, + dt=dt, + carrier_freqs=carrier_freqs, + chebyshev_orders=chebyshev_orders, + expansion_method="magnus", + expansion_order=expansion_order, + expansion_labels=expansion_labels, + integration_method=integration_method, + include_imag=include_imag, + **kwargs, + ) + super().__init__(model=model) + + def _solve(self, t0: float, n_steps: int, y0: Array, signals: List[Signal]) -> OdeResult: + ys = None + if Array.default_backend() == "jax": + single_step = lambda x: self.model.Udt @ jexpm(self.model.evaluate(x).data) + ys = [y0, _perturbative_solve_jax(single_step, self.model, signals, y0, t0, n_steps)] + else: + single_step = lambda coeffs, y: self.model.Udt @ expm(self.model.evaluate(coeffs)) @ y + ys = [y0, _perturbative_solve(single_step, self.model, signals, y0, t0, n_steps)] + + return OdeResult(t=[t0, t0 + n_steps * self.model.dt], y=ys)
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/solvers/perturbative_solvers/perturbative_solver.html b/stable/0.4/_modules/qiskit_dynamics/solvers/perturbative_solvers/perturbative_solver.html new file mode 100644 index 000000000..125f05c3d --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/solvers/perturbative_solvers/perturbative_solver.html @@ -0,0 +1,565 @@ + + + + + + + + qiskit_dynamics.solvers.perturbative_solvers.perturbative_solver - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    Source code for qiskit_dynamics.solvers.perturbative_solvers.perturbative_solver

    +# -*- coding: utf-8 -*-
    +
    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2022.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +"""
    +Perturbative solver base class.
    +"""
    +
    +from abc import ABC, abstractmethod
    +from typing import Callable, List, Union
    +
    +import numpy as np
    +from scipy.integrate._ivp.ivp import OdeResult
    +
    +from qiskit import QiskitError
    +
    +from qiskit_dynamics import Signal
    +from qiskit_dynamics.signals import SignalList
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.dispatch.dispatch import Dispatch
    +
    +from .expansion_model import ExpansionModel
    +from ..solver_utils import setup_args_lists
    +
    +try:
    +    import jax.numpy as jnp
    +    from jax import vmap
    +    from jax.lax import associative_scan
    +except ImportError:
    +    pass
    +
    +
    +class _PerturbativeSolver(ABC):
    +    """Abstract base class for perturbation-based solvers."""
    +
    +    @abstractmethod
    +    def __init__(self, model: ExpansionModel):
    +        r"""Initialize.
    +
    +        Args:
    +            model: ExpansionModel defining solver behaviour.
    +        """
    +        self._model = model
    +
    +    @property
    +    def model(self) -> ExpansionModel:
    +        """Model object storing expansion details."""
    +        return self._model
    +
    +    def solve(
    +        self,
    +        t0: Union[float, List[float]],
    +        n_steps: Union[int, List[int]],
    +        y0: Union[Array, List[Array]],
    +        signals: Union[List[Signal], List[List[Signal]]],
    +    ) -> Union[OdeResult, List[OdeResult]]:
    +        """Solve given an initial time, number of steps, signals, and initial state.
    +
    +        Note that this method can be used to solve a list of simulations at once, by specifying
    +        one or more of the arguments ``t0``, ``n_steps``, ``y0``, or ``signals`` as a list of
    +        valid inputs. For this mode of operation, all of these arguments must be either lists of
    +        the same length, or a single valid input, which will be used repeatedly.
    +
    +        Args:
    +            t0: Initial time.
    +            n_steps: Number of time steps to solve for.
    +            y0: Initial state at time ``t0``.
    +            signals: List of signals.
    +
    +        Returns:
    +            OdeResult: Results object, or list of results objects.
    +
    +        Raises:
    +            QiskitError: If improperly formatted arguments.
    +        """
    +
    +        # validate and setup list of simulations
    +        [t0_list, n_steps_list, y0_list, signals_list], multiple_sims = setup_args_lists(
    +            args_list=[t0, n_steps, y0, signals],
    +            args_names=["t0", "n_steps", "y0", "signals"],
    +            args_to_list=[
    +                lambda x: _scalar_to_list(x, "t0"),
    +                lambda x: _scalar_to_list(x, "n_steps"),
    +                _y0_to_list,
    +                _signals_to_list,
    +            ],
    +        )
    +
    +        all_results = []
    +        for args in zip(t0_list, n_steps_list, y0_list, signals_list):
    +            if len(args[-1]) != len(self.model.operators):
    +                raise QiskitError("Signals must be the same length as the operators in the model.")
    +            all_results.append(
    +                self._solve(t0=args[0], n_steps=args[1], y0=args[2], signals=args[3])
    +            )
    +
    +        if multiple_sims is False:
    +            return all_results[0]
    +
    +        return all_results
    +
    +    @abstractmethod
    +    def _solve(self, t0: float, n_steps: int, y0: Array, signals: List[Signal]) -> OdeResult:
    +        """Solve once for a list of signals, initial state, initial time, and number of steps.
    +
    +        Args:
    +            t0: Initial time.
    +            n_steps: Number of time steps to solve for.
    +            y0: Initial state at time t0.
    +            signals: List of signals.
    +
    +        Returns:
    +            OdeResult: Results object.
    +        """
    +        pass
    +
    +
    +def _perturbative_solve(
    +    single_step: Callable,
    +    model: "ExpansionModel",
    +    signals: List[Signal],
    +    y0: np.ndarray,
    +    t0: float,
    +    n_steps: int,
    +) -> np.ndarray:
    +    """Standard python logic version of perturbative solving routine."""
    +    U0 = model.rotating_frame.state_out_of_frame(t0, np.eye(model.Udt.shape[0], dtype=complex))
    +    Uf = model.rotating_frame.state_into_frame(
    +        t0 + n_steps * model.dt, np.eye(U0.shape[0], dtype=complex)
    +    )
    +
    +    sig_cheb_coeffs = model.approximate_signals(signals, t0, n_steps)
    +
    +    y = U0 @ y0
    +    for k in range(n_steps):
    +        y = single_step(sig_cheb_coeffs[:, k], y)
    +
    +    return Uf @ y
    +
    +
    +def _perturbative_solve_jax(
    +    single_step: Callable,
    +    model: "ExpansionModel",
    +    signals: List[Signal],
    +    y0: np.ndarray,
    +    t0: float,
    +    n_steps: int,
    +) -> np.ndarray:
    +    """JAX version of _perturbative_solve."""
    +    U0 = model.rotating_frame.state_out_of_frame(
    +        t0, jnp.eye(model.Udt.shape[0], dtype=complex)
    +    ).data
    +    Uf = model.rotating_frame.state_into_frame(
    +        t0 + n_steps * model.dt, jnp.eye(U0.shape[0], dtype=complex)
    +    ).data
    +
    +    sig_cheb_coeffs = model.approximate_signals(signals, t0, n_steps).data
    +
    +    y = U0 @ y0
    +
    +    step_propagators = vmap(single_step)(jnp.flip(sig_cheb_coeffs.transpose(), axis=0))
    +    y = associative_scan(jnp.matmul, step_propagators, axis=0)[-1] @ y
    +
    +    return Uf @ y
    +
    +
    +def _scalar_to_list(x, name):
    +    """Check if x is a scalar or a list of scalars, and convert to a list in either case."""
    +    was_list = False
    +    x_ndim = _nested_ndim(x)
    +    if x_ndim > 1:
    +        raise QiskitError(f"{name} must be either 0d or 1d.")
    +
    +    if x_ndim == 1:
    +        was_list = True
    +    else:
    +        x = [x]
    +
    +    return x, was_list
    +
    +
    +def _y0_to_list(y0):
    +    """Check if y0 is a single array or list of arrays, and return as a list in either case."""
    +    was_list = False
    +    if not isinstance(y0, list):
    +        y0 = [y0]
    +    else:
    +        was_list = True
    +
    +    return y0, was_list
    +
    +
    +def _signals_to_list(signals):
    +    """Check if signals is a single signal specification or a list of
    +    such specifications, and return as a list in either case.
    +    """
    +    was_list = False
    +    if signals is None:
    +        signals = [signals]
    +    elif isinstance(signals, list) and isinstance(signals[0], (list, SignalList)):
    +        # multiple lists
    +        was_list = True
    +    elif isinstance(signals, SignalList) or (
    +        isinstance(signals, list) and not isinstance(signals[0], (list, SignalList))
    +    ):
    +        # single signals list
    +        signals = [signals]
    +    else:
    +        raise QiskitError("Signals specified in invalid format.")
    +
    +    return signals, was_list
    +
    +
    +def _nested_ndim(x):
    +    """Determine the 'ndim' of x, which could be composed of nested lists and array types."""
    +    if isinstance(x, (list, tuple)):
    +        return 1 + _nested_ndim(x[0])
    +    elif issubclass(type(x), Dispatch.REGISTERED_TYPES) or isinstance(x, Array):
    +        return x.ndim
    +
    +    # assume scalar
    +    return 0
    +
    +
    +
    +
    + +
    +
    + + Made with Sphinx and @pradyunsg's + + Furo +
    + Last updated on 2024/03/18
    +
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_modules/qiskit_dynamics/solvers/solver_classes.html b/stable/0.4/_modules/qiskit_dynamics/solvers/solver_classes.html new file mode 100644 index 000000000..6a3bfabe0 --- /dev/null +++ b/stable/0.4/_modules/qiskit_dynamics/solvers/solver_classes.html @@ -0,0 +1,1248 @@ + + + + + + + + qiskit_dynamics.solvers.solver_classes - Qiskit Dynamics 0.4.5 documentation + + + + + + + + + + + + + + + + + + + + + Contents + + + + + + + + Menu + + + + + + + + + + + Expand + + + + + + + + + + + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    Source code for qiskit_dynamics.solvers.solver_classes

    +# -*- coding: utf-8 -*-
    +
    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2021.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name
    +
    +r"""
    +Solver classes.
    +"""
    +
    +
    +from typing import Optional, Union, Tuple, Any, Type, List, Callable
    +
    +import numpy as np
    +
    +from scipy.integrate._ivp.ivp import OdeResult  # pylint: disable=unused-import
    +
    +from qiskit import QiskitError
    +from qiskit.pulse import Schedule, ScheduleBlock
    +from qiskit.pulse.transforms import block_to_schedule
    +
    +from qiskit.circuit import Gate, QuantumCircuit
    +from qiskit.quantum_info.operators.base_operator import BaseOperator
    +from qiskit.quantum_info.operators.channel.quantum_channel import QuantumChannel
    +from qiskit.quantum_info.states.quantum_state import QuantumState
    +from qiskit.quantum_info import SuperOp, Operator, DensityMatrix
    +
    +from qiskit_dynamics.models import (
    +    HamiltonianModel,
    +    LindbladModel,
    +    RotatingFrame,
    +    rotating_wave_approximation,
    +)
    +from qiskit_dynamics.signals import Signal, DiscreteSignal, SignalList
    +from qiskit_dynamics.pulse import InstructionToSignals
    +from qiskit_dynamics.array import Array
    +from qiskit_dynamics.dispatch.dispatch import Dispatch
    +
    +from .solver_functions import solve_lmde, _is_diffrax_method
    +from .solver_utils import (
    +    is_lindblad_model_vectorized,
    +    is_lindblad_model_not_vectorized,
    +    setup_args_lists,
    +)
    +
    +
    +try:
    +    from jax import core, jit
    +    import jax.numpy as jnp
    +except ImportError:
    +    pass
    +
    +
    +
    +[docs] +class Solver: + r"""Solver class for simulating both Hamiltonian and Lindblad dynamics, with high + level type-handling of input states. + + If only Hamiltonian information is provided, this class will internally construct + a :class:`.HamiltonianModel` instance, and simulate the model + using the Schrodinger equation :math:`\dot{y}(t) = -iH(t)y(t)` + (see the :meth:`.Solver.solve` method documentation for details + on how different initial state types are handled). + :class:`.HamiltonianModel` represents a decomposition of the Hamiltonian of the form: + + .. math:: + + H(t) = H_0 + \sum_i s_i(t) H_i, + + where :math:`H_0` is the static component, the :math:`H_i` are the + time-dependent components of the Hamiltonian, and the :math:`s_i(t)` are the + time-dependent signals, specifiable as either :class:`.Signal` + objects, or constructed from Qiskit Pulse schedules if :class:`.Solver` + is configured for Pulse simulation (see below). + + If dissipators are specified as part of the model, then a + :class:`.LindbladModel` is constructed, and simulations are performed + by solving the Lindblad equation: + + .. math:: + + \dot{y}(t) = -i[H(t), y(t)] + \mathcal{D}_0(y(t)) + \mathcal{D}(t)(y(t)), + + where :math:`H(t)` is the Hamiltonian part, specified as above, and :math:`\mathcal{D}_0` + and :math:`\mathcal{D}(t)` are the static and time-dependent portions of the dissipator, + given by: + + .. math:: + + \mathcal{D}_0(y(t)) = \sum_j N_j y(t) N_j^\dagger + - \frac{1}{2} \{N_j^\dagger N_j, y(t)\}, + + and + + .. math:: + + \mathcal{D}(t)(y(t)) = \sum_j \gamma_j(t) L_j y(t) L_j^\dagger + - \frac{1}{2} \{L_j^\dagger L_j, y(t)\}, + + with :math:`N_j` the static dissipators, :math:`L_j` the time-dependent dissipator + operators, and :math:`\gamma_j(t)` the time-dependent signals + specifiable as either :class:`.Signal` + objects, or constructed from Qiskit Pulse schedules if :class:`.Solver` + is configured for Pulse simulation (see below). + + Transformations on the model can be specified via the optional arguments: + + * ``rotating_frame``: Transforms the model into a rotating frame. Note that the + operator specifying the frame will be substracted from the ``static_hamiltonian``. + If supplied as a 1d array, ``rotating_frame`` is interpreted as the diagonal + elements of a diagonal matrix. Given a frame operator :math:`F = -i H_0`, + for the Schrodinger equation entering the rotating frame of :math:`F`, corresponds + to transforming the solution as :math:`y(t) \mapsto exp(-tF)y(t)`, and for the + Lindblad equation it corresponds to transforming the solution as + :math:`y(t) \mapsto exp(-tF)y(t)exp(tF)`. + See :class:`.RotatingFrame` for more details. + * ``in_frame_basis``: Whether to represent the model in the basis in which the frame + operator is diagonal, henceforth called the "frame basis". + If ``rotating_frame`` is ``None`` or was supplied as a 1d array, + this kwarg has no effect. If ``rotating_frame`` was specified as a 2d array, + the frame basis is the diagonalizing basis supplied by ``np.linalg.eigh``. + If ``in_frame_basis==True``, this objects behaves as if all + operators were supplied in the frame basis: calls to ``solve`` will assume the initial + state is supplied in the frame basis, and the results will be returned in the frame basis. + If ``in_frame_basis==False``, the system will still be solved in the frame basis for + efficiency, however the initial state (and final output states) will automatically be + transformed into (and, respectively, out of) the frame basis. + * ``rwa_cutoff_freq`` and ``rwa_carrier_freqs``: Performs a rotating wave approximation (RWA) + on the model with cutoff frequency ``rwa_cutoff_freq``, assuming the time-dependent + coefficients of the model have carrier frequencies specified by ``rwa_carrier_freqs``. + If ``dissipator_operators is None``, ``rwa_carrier_freqs`` must be a list of floats + of length equal to ``hamiltonian_operators``, and if ``dissipator_operators is not None``, + ``rwa_carrier_freqs`` must be a ``tuple`` of lists of floats, with the first entry + the list of carrier frequencies for ``hamiltonian_operators``, and the second + entry the list of carrier frequencies for ``dissipator_operators``. + See :func:`.rotating_wave_approximation` for details on + the mathematical approximation. + + .. note:: + When using the ``rwa_cutoff_freq`` optional argument, + :class:`.Solver` cannot be instantiated within + a JAX-transformable function. However, after construction, instances can + still be used within JAX-transformable functions regardless of whether an + ``rwa_cutoff_freq`` is set. + + :class:`.Solver` can be configured to simulate Qiskit Pulse schedules + by setting all of the following parameters, which determine how Pulse schedules are + interpreted: + + * ``hamiltonian_channels``: List of channels in string format corresponding to the + time-dependent coefficients of ``hamiltonian_operators``. + * ``dissipator_channels``: List of channels in string format corresponding to time-dependent + coefficients of ``dissipator_operators``. + * ``channel_carrier_freqs``: Dictionary mapping channel names to frequencies. A frequency + must be specified for every channel appearing in ``hamiltonian_channels`` and + ``dissipator_channels``. When simulating ``schedule``\s, these frequencies are + interpreted as the analog carrier frequencies associated with the channel; deviations from + these frequencies due to ``SetFrequency`` or ``ShiftFrequency`` instructions are + implemented by digitally modulating the samples for the channel envelope. + If an ``rwa_cutoff_freq`` is specified, and no ``rwa_carrier_freqs`` is specified, these + frequencies will be used for the RWA. + * ``dt``: The envelope sample width. + + If configured to simulate Pulse schedules while ``Array.default_backend() == 'jax'``, + calling :meth:`.Solver.solve` will automatically compile + simulation runs when calling with a JAX-based solver method. + + The evolution given by the model can be simulated by calling :meth:`.Solver.solve`, which + calls :func:`.solve_lmde`, and does various automatic + type handling operations for :mod:`qiskit.quantum_info` state and super operator types. + """ + + def __init__( + self, + static_hamiltonian: Optional[Array] = None, + hamiltonian_operators: Optional[Array] = None, + static_dissipators: Optional[Array] = None, + dissipator_operators: Optional[Array] = None, + hamiltonian_channels: Optional[List[str]] = None, + dissipator_channels: Optional[List[str]] = None, + channel_carrier_freqs: Optional[dict] = None, + dt: Optional[float] = None, + rotating_frame: Optional[Union[Array, RotatingFrame]] = None, + in_frame_basis: bool = False, + evaluation_mode: str = "dense", + rwa_cutoff_freq: Optional[float] = None, + rwa_carrier_freqs: Optional[Union[Array, Tuple[Array, Array]]] = None, + validate: bool = True, + ): + """Initialize solver with model information. + + Args: + static_hamiltonian: Constant Hamiltonian term. If a ``rotating_frame`` + is specified, the ``frame_operator`` will be subtracted from + the static_hamiltonian. + hamiltonian_operators: Hamiltonian operators. + static_dissipators: Constant dissipation operators. + dissipator_operators: Dissipation operators with time-dependent coefficients. + hamiltonian_channels: List of channel names in pulse schedules corresponding to + Hamiltonian operators. + dissipator_channels: List of channel names in pulse schedules corresponding to + dissipator operators. + channel_carrier_freqs: Dictionary mapping channel names to floats which represent + the carrier frequency of the pulse channel with the + corresponding name. + dt: Sample rate for simulating pulse schedules. + rotating_frame: Rotating frame to transform the model into. Rotating frames which + are diagonal can be supplied as a 1d array of the diagonal elements, + to explicitly indicate that they are diagonal. + in_frame_basis: Whether to represent the model in the basis in which the rotating + frame operator is diagonalized. See class documentation for a more + detailed explanation on how this argument affects object behaviour. + evaluation_mode: Method for model evaluation. See documentation for + ``HamiltonianModel.evaluation_mode`` or + ``LindbladModel.evaluation_mode``. + (if dissipators in model) for valid modes. + rwa_cutoff_freq: Rotating wave approximation cutoff frequency. If ``None``, no + approximation is made. + rwa_carrier_freqs: Carrier frequencies to use for rotating wave approximation. + If no time dependent coefficients in model leave as ``None``, + if no time-dependent dissipators specify as a list of frequencies + for each Hamiltonian operator, and if time-dependent dissipators + present specify as a tuple of lists of frequencies, one for + Hamiltonian operators and one for dissipators. + validate: Whether or not to validate Hamiltonian operators as being Hermitian. + + Raises: + QiskitError: If arguments concerning pulse-schedule interpretation are insufficiently + specified. + """ + + # set pulse specific information if specified + self._hamiltonian_channels = None + self._dissipator_channels = None + self._all_channels = None + self._channel_carrier_freqs = None + self._dt = None + self._schedule_converter = None + + if any([dt, channel_carrier_freqs, hamiltonian_channels, dissipator_channels]): + all_channels = [] + + if hamiltonian_channels is not None: + hamiltonian_channels = [chan.lower() for chan in hamiltonian_channels] + if hamiltonian_operators is None or len(hamiltonian_operators) != len( + hamiltonian_channels + ): + raise QiskitError( + """hamiltonian_channels must have same length as hamiltonian_operators""" + ) + for chan in hamiltonian_channels: + if chan not in all_channels: + all_channels.append(chan) + + self._hamiltonian_channels = hamiltonian_channels + + if dissipator_channels is not None: + dissipator_channels = [chan.lower() for chan in dissipator_channels] + for chan in dissipator_channels: + if chan not in all_channels: + all_channels.append(chan) + if dissipator_operators is None or len(dissipator_operators) != len( + dissipator_channels + ): + raise QiskitError( + """dissipator_channels must have same length as dissipator_operators""" + ) + + self._dissipator_channels = dissipator_channels + self._all_channels = all_channels + + if channel_carrier_freqs is None: + channel_carrier_freqs = {} + else: + channel_carrier_freqs = { + key.lower(): val for key, val in channel_carrier_freqs.items() + } + + for chan in all_channels: + if chan not in channel_carrier_freqs: + raise QiskitError( + f"""Channel '{chan}' does not have carrier frequency specified in + channel_carrier_freqs.""" + ) + + if len(channel_carrier_freqs) == 0: + channel_carrier_freqs = None + self._channel_carrier_freqs = channel_carrier_freqs + + if dt is not None: + self._dt = dt + + self._schedule_converter = InstructionToSignals( + dt=self._dt, carriers=self._channel_carrier_freqs, channels=self._all_channels + ) + else: + raise QiskitError("dt must be specified if channel information is provided.") + + # setup model + model = None + if static_dissipators is None and dissipator_operators is None: + model = HamiltonianModel( + static_operator=static_hamiltonian, + operators=hamiltonian_operators, + rotating_frame=rotating_frame, + in_frame_basis=in_frame_basis, + evaluation_mode=evaluation_mode, + validate=validate, + ) + else: + model = LindbladModel( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=hamiltonian_operators, + static_dissipators=static_dissipators, + dissipator_operators=dissipator_operators, + rotating_frame=rotating_frame, + in_frame_basis=in_frame_basis, + evaluation_mode=evaluation_mode, + validate=validate, + ) + + self._rwa_signal_map = None + self._model = model + if rwa_cutoff_freq: + # if rwa_carrier_freqs is None, take from channel_carrier_freqs or set all to 0. + if rwa_carrier_freqs is None: + if self._channel_carrier_freqs is not None: + if self._hamiltonian_channels is not None: + rwa_carrier_freqs = [ + self._channel_carrier_freqs[c] for c in self._hamiltonian_channels + ] + + if self._dissipator_channels is not None: + rwa_carrier_freqs = ( + rwa_carrier_freqs, + [self._channel_carrier_freqs[c] for c in self._dissipator_channels], + ) + else: + rwa_carrier_freqs = [] + if hamiltonian_operators is not None: + rwa_carrier_freqs = [0.0] * len(hamiltonian_operators) + + if dissipator_operators is not None: + rwa_carrier_freqs = (rwa_carrier_freqs, [0.0] * len(dissipator_operators)) + + if isinstance(rwa_carrier_freqs, tuple): + rwa_ham_sigs = None + rwa_lindblad_sigs = None + if rwa_carrier_freqs[0]: + rwa_ham_sigs = [Signal(1.0, carrier_freq=freq) for freq in rwa_carrier_freqs[0]] + if rwa_carrier_freqs[1]: + rwa_lindblad_sigs = [ + Signal(1.0, carrier_freq=freq) for freq in rwa_carrier_freqs[1] + ] + + self._model.signals = (rwa_ham_sigs, rwa_lindblad_sigs) + else: + rwa_sigs = [Signal(1.0, carrier_freq=freq) for freq in rwa_carrier_freqs] + + if isinstance(model, LindbladModel): + rwa_sigs = (rwa_sigs, None) + + self._model.signals = rwa_sigs + + self._model, rwa_signal_map = rotating_wave_approximation( + self._model, rwa_cutoff_freq, return_signal_map=True + ) + self._rwa_signal_map = rwa_signal_map + + # clear signals + self._set_new_signals(None) + + @property + def model(self) -> Union[HamiltonianModel, LindbladModel]: + """The model of the system, either a Hamiltonian or Lindblad model.""" + return self._model + +
    +[docs] + def solve( + self, + t_span: Array, + y0: Union[Array, QuantumState, BaseOperator], + signals: Optional[ + Union[ + List[Union[Schedule, ScheduleBlock]], + List[Signal], + Tuple[List[Signal], List[Signal]], + ] + ] = None, + convert_results: bool = True, + **kwargs, + ) -> Union[OdeResult, List[OdeResult]]: + r"""Solve a dynamical problem, or a set of dynamical problems. + + Calls :func:`.solve_lmde`, and returns an ``OdeResult`` + object in the style of ``scipy.integrate.solve_ivp``, with results + formatted to be the same types as the input. See Additional Information + for special handling of various input types, and for specifying multiple + simulations at once. + + Args: + t_span: Time interval to integrate over. + y0: Initial state. + signals: Specification of time-dependent coefficients to simulate, either in + Signal format or as Qiskit Pulse Pulse schedules. + If specifying in Signal format, if ``dissipator_operators is None``, + specify as a list of signals for the Hamiltonian component, otherwise + specify as a tuple of two lists, one for Hamiltonian components, and + one for the ``dissipator_operators`` coefficients. + convert_results: If ``True``, convert returned solver state results to the same class + as y0. If ``False``, states will be returned in the native array type + used by the specified solver method. + **kwargs: Keyword args passed to :func:`.solve_lmde`. + + Returns: + OdeResult: object with formatted output types. + + Raises: + QiskitError: Initial state ``y0`` is of invalid shape. If ``signals`` specifies + ``Schedule`` simulation but ``Solver`` hasn't been configured to + simulate pulse schedules. + + Additional Information: + + The behaviour of this method is impacted by the input type of ``y0`` + and the internal model, summarized in the following table: + + .. list-table:: Type-based behaviour + :widths: 10 10 10 70 + :header-rows: 1 + + * - ``y0`` type + - Model type + - ``yf`` type + - Description + * - ``Array``, ``np.ndarray``, ``Operator`` + - Any + - Same as ``y0`` + - Solves either the Schrodinger equation or Lindblad equation + with initial state ``y0`` as specified. + * - ``Statevector`` + - ``HamiltonianModel`` + - ``Statevector`` + - Solves the Schrodinger equation with initial state ``y0``. + * - ``DensityMatrix`` + - ``HamiltonianModel`` + - ``DensityMatrix`` + - Solves the Schrodinger equation with initial state the identity matrix to compute + the unitary, then conjugates ``y0`` with the result to solve for the density matrix. + * - ``Statevector``, ``DensityMatrix`` + - ``LindbladModel`` + - ``DensityMatrix`` + - Solve the Lindblad equation with initial state ``y0``, converting to a + ``DensityMatrix`` first if ``y0`` is a ``Statevector``. + * - ``QuantumChannel`` + - ``HamiltonianModel`` + - ``SuperOp`` + - Converts ``y0`` to a ``SuperOp`` representation, then solves the Schrodinger + equation with initial state the identity matrix to compute the unitary and + composes with ``y0``. + * - ``QuantumChannel`` + - ``LindbladModel`` + - ``SuperOp`` + - Solves the vectorized Lindblad equation with initial state ``y0``. + ``evaluation_mode`` must be set to a vectorized option. + + In some cases (e.g. if using JAX), wrapping the returned states in the type + given in the ``yf`` type column above may be undesirable. Setting + ``convert_results=False`` prevents this wrapping, while still allowing + usage of the automatic type-handling for the input state. + + In addition to the above, this method can be used to specify multiple simulations + simultaneously. This can be done by specifying one or more of the arguments + ``t_span``, ``y0``, or ``signals`` as a list of valid inputs. + For this mode of operation, all of these arguments must be either lists of the same + length, or a single valid input, which will be used repeatedly. + + For example the following code runs three simulations, returning results in a list: + + .. code-block:: python + + t_span = [span1, span2, span3] + y0 = [state1, state2, state3] + signals = [signals1, signals2, signals3] + + results = solver.solve(t_span=t_span, y0=y0, signals=signals) + + The following code block runs three simulations, for different sets of signals, + repeatedly using the same ``t_span`` and ``y0``: + + .. code-block:: python + + t_span = [t0, tf] + y0 = state1 + signals = [signals1, signals2, signal3] + + results = solver.solve(t_span=t_span, y0=y0, signals=signals) + """ + + # convert any ScheduleBlocks to Schedules + if isinstance(signals, ScheduleBlock): + signals = block_to_schedule(signals) + elif isinstance(signals, list): + signals = [block_to_schedule(x) if isinstance(x, ScheduleBlock) else x for x in signals] + + # validate and setup list of simulations + [t_span_list, y0_list, signals_list], multiple_sims = setup_args_lists( + args_list=[t_span, y0, signals], + args_names=["t_span", "y0", "signals"], + args_to_list=[t_span_to_list, _y0_to_list, _signals_to_list], + ) + + all_results = None + method = kwargs.get("method", "") + if ( + Array.default_backend() == "jax" + and (method == "jax_odeint" or _is_diffrax_method(method)) + and all(isinstance(x, Schedule) for x in signals_list) + # check if jit transformation is already performed. + and not (isinstance(jnp.array(0), core.Tracer)) + ): + all_results = self._solve_schedule_list_jax( + t_span_list=t_span_list, + y0_list=y0_list, + schedule_list=signals_list, + convert_results=convert_results, + **kwargs, + ) + else: + all_results = self._solve_list( + t_span_list=t_span_list, + y0_list=y0_list, + signals_list=signals_list, + convert_results=convert_results, + **kwargs, + ) + + # ensure model signals are empty + self._set_new_signals(None) + + if multiple_sims is False: + return all_results[0] + + return all_results
    + + + def _solve_list( + self, + t_span_list: List[Array], + y0_list: List[Union[Array, QuantumState, BaseOperator]], + signals_list: Optional[ + Union[List[Schedule], List[List[Signal]], List[Tuple[List[Signal], List[Signal]]]] + ] = None, + convert_results: bool = True, + **kwargs, + ) -> List[OdeResult]: + """Run a list of simulations.""" + + all_results = [] + for t_span, y0, signals in zip(t_span_list, y0_list, signals_list): + if isinstance(signals, Schedule): + signals = self._schedule_to_signals(signals) + + self._set_new_signals(signals) + + # setup initial state + y0, y0_input, y0_cls, state_type_wrapper = validate_and_format_initial_state( + y0, self.model + ) + + results = solve_lmde(generator=self.model, t_span=t_span, y0=y0, **kwargs) + results.y = format_final_states(results.y, self.model, y0_input, y0_cls) + + if y0_cls is not None and convert_results: + results.y = [state_type_wrapper(yi) for yi in results.y] + + all_results.append(results) + + self._set_new_signals(None) + + return all_results + + def _solve_schedule_list_jax( + self, + t_span_list: List[Array], + y0_list: List[Union[Array, QuantumState, BaseOperator]], + schedule_list: List[Schedule], + convert_results: bool = True, + **kwargs, + ) -> List[OdeResult]: + """Run a list of schedule simulations utilizing JAX compilation. + The jitting strategy is to define a function whose inputs are t_span, y0 as an array, the + samples for all channels in a single large array, and other initial state information. + To avoid recompilation for schedules with a different number of samples, i.e. a different + duration, all schedules are padded to be the length of the schedule with the max duration. + """ + + # determine fixed array shape for containing all samples + max_duration = 0 + for idx, sched in enumerate(schedule_list): + max_duration = max(sched.duration, max_duration) + all_samples_shape = (len(self._all_channels), max_duration) + + # define sim function to jit + def sim_function(t_span, y0, all_samples, y0_input, y0_cls): + # store signals to ensure purity + model_sigs = self.model.signals + + # re-construct signals from the samples + signals = [] + for idx, samples in enumerate(all_samples): + carrier_freq = self._channel_carrier_freqs[self._all_channels[idx]] + signals.append( + DiscreteSignal(dt=self._dt, samples=samples, carrier_freq=carrier_freq) + ) + + # map signals to correct structure for model + signals = organize_signals_to_channels( + signals, + self._all_channels, + self.model.__class__, + self._hamiltonian_channels, + self._dissipator_channels, + ) + + self._set_new_signals(signals) + + results = solve_lmde(generator=self.model, t_span=t_span, y0=y0, **kwargs) + results.y = format_final_states(results.y, self.model, y0_input, y0_cls) + + # reset signals to ensure purity + self.model.signals = model_sigs + + return Array(results.t).data, Array(results.y).data + + jit_sim_function = jit(sim_function, static_argnums=(4,)) + + # run simulations + all_results = [] + for t_span, y0, sched in zip(t_span_list, y0_list, schedule_list): + # setup initial state + y0, y0_input, y0_cls, state_type_wrapper = validate_and_format_initial_state( + y0, self.model + ) + + # setup array of all samples + all_signals = self._schedule_converter.get_signals(sched) + + all_samples = np.zeros(all_samples_shape, dtype=complex) + for idx, sig in enumerate(all_signals): + all_samples[idx, 0 : len(sig.samples)] = np.array(sig.samples) + + results_t, results_y = jit_sim_function( + Array(t_span).data, Array(y0).data, all_samples, Array(y0_input).data, y0_cls + ) + results = OdeResult(t=results_t, y=Array(results_y, backend="jax", dtype=complex)) + + if y0_cls is not None and convert_results: + results.y = [state_type_wrapper(yi) for yi in results.y] + + all_results.append(results) + + return all_results + + def _set_new_signals(self, signals): + """Helper function for setting new signals in self.model.""" + if signals is not None: + # if Lindblad model and signals are given as a list set as Hamiltonian part of signals + if isinstance(self.model, LindbladModel) and isinstance(signals, (list, SignalList)): + signals = (signals, None) + + if self._rwa_signal_map: + signals = self._rwa_signal_map(signals) + self.model.signals = signals + else: + if isinstance(self.model, LindbladModel): + self.model.signals = (None, None) + else: + self.model.signals = None + + def _schedule_to_signals(self, schedule: Schedule): + """Convert a schedule into the signal format required by the model.""" + if self._schedule_converter is None: + raise QiskitError("Solver instance not configured for pulse Schedule simulation.") + + return organize_signals_to_channels( + self._schedule_converter.get_signals(schedule), + self._all_channels, + self.model.__class__, + self._hamiltonian_channels, + self._dissipator_channels, + )
    + + + +def initial_state_converter(obj: Any) -> Tuple[Array, Type, Callable]: + """Convert initial state object to an Array, the type of the initial input, and return + function for constructing a state of the same type. + + Args: + obj: An initial state. + + Returns: + tuple: (Array, Type, Callable) + """ + # pylint: disable=invalid-name + y0_cls = None + if isinstance(obj, Array): + y0, y0_cls, wrapper = obj, None, lambda x: x + if isinstance(obj, QuantumState): + y0, y0_cls = Array(obj.data), obj.__class__ + wrapper = lambda x: y0_cls(np.array(x), dims=obj.dims()) + elif isinstance(obj, QuantumChannel): + y0, y0_cls = Array(SuperOp(obj).data), SuperOp + wrapper = lambda x: SuperOp( + np.array(x), input_dims=obj.input_dims(), output_dims=obj.output_dims() + ) + elif isinstance(obj, (BaseOperator, Gate, QuantumCircuit)): + y0, y0_cls = Array(Operator(obj.data)), Operator + wrapper = lambda x: Operator( + np.array(x), input_dims=obj.input_dims(), output_dims=obj.output_dims() + ) + else: + y0, y0_cls, wrapper = Array(obj), None, lambda x: x + + return y0, y0_cls, wrapper + + +def validate_and_format_initial_state(y0: any, model: Union[HamiltonianModel, LindbladModel]): + """Format initial state for simulation. This function encodes the logic of how + simulations are run based on initial state type. + + Args: + y0: The user-specified input state. + model: The model contained in the solver. + + Returns: + Tuple containing the input state to pass to the solver, the user-specified input + as an array, the class of the user specified input, and a function for converting + the output states to the right class. + + Raises: + QiskitError: Initial state ``y0`` is of invalid shape relative to the model. + """ + + if isinstance(y0, QuantumState) and isinstance(model, LindbladModel): + y0 = DensityMatrix(y0) + + y0, y0_cls, wrapper = initial_state_converter(y0) + + y0_input = y0 + + # validate types + if (y0_cls is SuperOp) and is_lindblad_model_not_vectorized(model): + raise QiskitError( + """Simulating SuperOp for a LindbladModel requires setting + vectorized evaluation. Set LindbladModel.evaluation_mode to a vectorized option. + """ + ) + + # if Simulating density matrix or SuperOp with a HamiltonianModel, simulate the unitary + if y0_cls in [DensityMatrix, SuperOp] and isinstance(model, HamiltonianModel): + y0 = np.eye(model.dim, dtype=complex) + # if LindbladModel is vectorized and simulating a density matrix, flatten + elif ( + (y0_cls is DensityMatrix) + and isinstance(model, LindbladModel) + and "vectorized" in model.evaluation_mode + ): + y0 = y0.flatten(order="F") + + # validate y0 shape before passing to solve_lmde + if isinstance(model, HamiltonianModel) and (y0.shape[0] != model.dim or y0.ndim > 2): + raise QiskitError("""Shape mismatch for initial state y0 and HamiltonianModel.""") + if is_lindblad_model_vectorized(model) and (y0.shape[0] != model.dim**2 or y0.ndim > 2): + raise QiskitError( + """Shape mismatch for initial state y0 and LindbladModel + in vectorized evaluation mode.""" + ) + if is_lindblad_model_not_vectorized(model) and y0.shape[-2:] != ( + model.dim, + model.dim, + ): + raise QiskitError("""Shape mismatch for initial state y0 and LindbladModel.""") + + return y0, y0_input, y0_cls, wrapper + + +def format_final_states(y, model, y0_input, y0_cls): + """Format final states for a single simulation.""" + + y = Array(y) + + if y0_cls is DensityMatrix and isinstance(model, HamiltonianModel): + # conjugate by unitary + return y @ y0_input @ y.conj().transpose((0, 2, 1)) + elif y0_cls is SuperOp and isinstance(model, HamiltonianModel): + # convert to SuperOp and compose + return ( + np.einsum("nka,nlb->nklab", y.conj(), y).reshape( + y.shape[0], y.shape[1] ** 2, y.shape[1] ** 2 + ) + @ y0_input + ) + elif (y0_cls is DensityMatrix) and is_lindblad_model_vectorized(model): + return y.reshape((len(y),) + y0_input.shape, order="F") + + return y + + +def t_span_to_list(t_span): + """Check if t_span is validly specified as a single interval or a list of intervals, + and return as a list in either case.""" + was_list = False + t_span_ndim = _nested_ndim(t_span) + if t_span_ndim > 2: + raise QiskitError("t_span must be either 1d or 2d.") + if t_span_ndim == 1: + t_span = [t_span] + else: + was_list = True + + return t_span, was_list + + +def _y0_to_list(y0): + """Check if y0 is validly specified as a single initial state or a list of initial states, + and return as a list in either case.""" + was_list = False + if not isinstance(y0, list): + y0 = [y0] + else: + was_list = True + + return y0, was_list + + +def _signals_to_list(signals): + """Check if signals is validly specified as a single signal specification or a list of + such specifications, and return as a list in either case.""" + was_list = False + if signals is None: + signals = [signals] + elif isinstance(signals, tuple): + # single Lindblad + signals = [signals] + elif isinstance(signals, list) and isinstance(signals[0], tuple): + # multiple lindblad + was_list = True + elif isinstance(signals, Schedule): + # pulse simulation + signals = [signals] + elif isinstance(signals, list) and isinstance(signals[0], Schedule): + # multiple pulse simulation + was_list = True + elif isinstance(signals, list) and isinstance(signals[0], (list, SignalList)): + # multiple Hamiltonian signals lists + was_list = True + elif isinstance(signals, SignalList) or ( + isinstance(signals, list) and not isinstance(signals[0], (list, SignalList)) + ): + # single Hamiltonian signals list + signals = [signals] + else: + raise QiskitError("Signals specified in invalid format.") + + return signals, was_list + + +def organize_signals_to_channels( + all_signals, all_channels, model_class, hamiltonian_channels, dissipator_channels +): + """Restructures a list of signals with order corresponding to all_channels, into the correctly + formatted data structure to pass into model.signals, according to the ordering specified + by hamiltonian_channels and dissipator_channels. + """ + + if model_class == HamiltonianModel: + if hamiltonian_channels is not None: + return [all_signals[all_channels.index(chan)] for chan in hamiltonian_channels] + else: + return None + else: + hamiltonian_signals = None + dissipator_signals = None + if hamiltonian_channels is not None: + hamiltonian_signals = [ + all_signals[all_channels.index(chan)] for chan in hamiltonian_channels + ] + if dissipator_channels is not None: + dissipator_signals = [ + all_signals[all_channels.index(chan)] for chan in dissipator_channels + ] + return (hamiltonian_signals, dissipator_signals) + + +def _nested_ndim(x): + """Determine the 'ndim' of x, which could be composed of nested lists and array types.""" + if isinstance(x, (list, tuple)): + return 1 + _nested_ndim(x[0]) + elif issubclass(type(x), Dispatch.REGISTERED_TYPES) or isinstance(x, Array): + return x.ndim + + # assume scalar + return 0 +
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    Source code for qiskit_dynamics.solvers.solver_functions

    +# -*- coding: utf-8 -*-
    +
    +# This code is part of Qiskit.
    +#
    +# (C) Copyright IBM 2020.
    +#
    +# This code is licensed under the Apache License, Version 2.0. You may
    +# obtain a copy of this license in the LICENSE.txt file in the root directory
    +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
    +#
    +# Any modifications or derivative works of this code must retain this
    +# copyright notice, and modified files need to carry a notice indicating
    +# that they have been altered from the originals.
    +# pylint: disable=invalid-name,no-member,attribute-defined-outside-init
    +
    +r"""
    +Solver functions.
    +"""
    +
    +from typing import Optional, Union, Callable, Tuple, List, TypeVar
    +from warnings import warn
    +
    +from scipy.integrate import OdeSolver
    +
    +from scipy.integrate._ivp.ivp import OdeResult  # pylint: disable=unused-import
    +
    +from qiskit import QiskitError
    +from qiskit_dynamics.array import Array
    +
    +from qiskit_dynamics.models import (
    +    BaseGeneratorModel,
    +    GeneratorModel,
    +    LindbladModel,
    +)
    +from qiskit_dynamics.models.hamiltonian_model import HamiltonianModel
    +
    +from .solver_utils import is_lindblad_model_not_vectorized
    +from .fixed_step_solvers import (
    +    RK4_solver,
    +    jax_RK4_solver,
    +    scipy_expm_solver,
    +    lanczos_diag_solver,
    +    jax_lanczos_diag_solver,
    +    jax_expm_solver,
    +    jax_RK4_parallel_solver,
    +    jax_expm_parallel_solver,
    +)
    +from .scipy_solve_ivp import scipy_solve_ivp, SOLVE_IVP_METHODS
    +from .jax_odeint import jax_odeint
    +from .diffrax_solver import diffrax_solver
    +
    +ODE_METHODS = (
    +    ["RK45", "RK23", "BDF", "DOP853", "Radau", "LSODA"]  # scipy solvers
    +    + ["RK4"]  # fixed step solvers
    +    + ["jax_odeint", "jax_RK4"]  # jax solvers
    +)
    +LMDE_METHODS = [
    +    "scipy_expm",
    +    "lanczos_diag",
    +    "jax_lanczos_diag",
    +    "jax_expm",
    +    "jax_expm_parallel",
    +    "jax_RK4_parallel",
    +]
    +
    +# diffrax solver type placeholder
    +DiffraxAbstractSolver = TypeVar("AbstractSolver")
    +
    +
    +def _is_jax_method(method: any) -> bool:
    +    """Check if method is a jax solver method."""
    +    if method in [
    +        "jax_odeint",
    +        "jax_RK4",
    +        "jax_expm",
    +        "jax_expm_parallel",
    +        "jax_RK4_parallel",
    +        "jax_lanczos_diag",
    +    ]:
    +        return True
    +
    +    # only other jax methods are diffrax methods
    +    return _is_diffrax_method(method)
    +
    +
    +def _is_diffrax_method(method: any) -> bool:
    +    """Check if method is a diffrax method."""
    +    try:
    +        from diffrax.solver import AbstractSolver
    +
    +        return isinstance(method, AbstractSolver)
    +    except ImportError:
    +        return False
    +
    +
    +def _lanczos_validation(
    +    rhs: Union[Callable, BaseGeneratorModel],
    +    t_span: Array,
    +    y0: Array,
    +    k_dim: int,
    +):
    +    """Validation checks to run lanczos based solvers."""
    +    if isinstance(rhs, BaseGeneratorModel):
    +        if not isinstance(rhs, HamiltonianModel):
    +            raise QiskitError(
    +                """Lanczos solver can only be used for HamiltonianModel or function-based
    +                    anti-Hermitian generators."""
    +            )
    +        if "sparse" not in rhs.evaluation_mode:
    +            warn(
    +                """lanczos_diag should be used with a generator in sparse mode
    +                for better performance.""",
    +                category=Warning,
    +                stacklevel=2,
    +            )
    +
    +    dim = rhs(t_span[0]).shape[0]
    +    if k_dim > dim:
    +        raise QiskitError("k_dim can be no larger than the dimension of the generator.")
    +
    +    if y0.ndim not in [1, 2]:
    +        raise QiskitError("y0 must be 1d or 2d.")
    +
    +
    +
    +[docs] +def solve_ode( + rhs: Union[Callable, BaseGeneratorModel], + t_span: Array, + y0: Array, + method: Optional[Union[str, OdeSolver, DiffraxAbstractSolver]] = "DOP853", + t_eval: Optional[Union[Tuple, List, Array]] = None, + **kwargs, +): + r"""General interface for solving Ordinary Differential Equations (ODEs). + + ODEs are differential equations of the form + + .. math:: + + \dot{y}(t) = f(t, y(t)), + + where :math:`f` is a callable function and the state :math:`y(t)` is an + arbitrarily-shaped complex :class:`Array`. + + The ``method`` argument exposes a variety of underlying ODE solvers. Optional + arguments for any of the solver routines can be passed via ``kwargs``. + Available methods are: + + - ``scipy.integrate.solve_ivp`` - supports methods + ``['RK45', 'RK23', 'BDF', 'DOP853', 'Radau', 'LSODA']`` or by passing a valid + ``scipy`` :class:`OdeSolver` instance. + - ``'RK4'``: A fixed-step 4th order Runge-Kutta solver. + Requires additional kwarg ``max_dt``, indicating the maximum step + size to take. This solver will break integration periods into even + sub-intervals no larger than ``max_dt``, and step over each sub-interval + using the standard 4th order Runge-Kutta integration rule. + - ``'jax_RK4'``: JAX backend implementation of ``'RK4'`` method. + - ``'jax_odeint'``: Calls ``jax.experimental.ode.odeint`` variable step solver. + - ``diffrax.diffeqsolve`` - a JAX solver function, called by passing ``method`` + as a valid ``diffrax.solver.AbstractSolver`` instance. Requires the ``diffrax`` library. + + Results are returned as a :class:`OdeResult` object. + + Args: + rhs: RHS function :math:`f(t, y)`. + t_span: ``Tuple`` or ``list`` of initial and final time. + y0: State at initial time. + method: Solving method to use. + t_eval: Times at which to return the solution. Must lie within ``t_span``. If unspecified, + the solution will be returned at the points in ``t_span``. + **kwargs: Additional arguments to pass to the solver. + + Returns: + OdeResult: Results object. + + Raises: + QiskitError: If specified method does not exist. + """ + + if method not in ODE_METHODS and not ( + (isinstance(method, type) and (issubclass(method, OdeSolver))) or _is_diffrax_method(method) + ): + raise QiskitError("Method " + str(method) + " not supported by solve_ode.") + + y0 = Array(y0) + + if isinstance(rhs, BaseGeneratorModel): + _, solver_rhs, y0, model_in_frame_basis = setup_generator_model_rhs_y0_in_frame_basis( + rhs, y0 + ) + else: + solver_rhs = rhs + + # solve the problem using specified method + if method in SOLVE_IVP_METHODS or (isinstance(method, type) and issubclass(method, OdeSolver)): + results = scipy_solve_ivp(solver_rhs, t_span, y0, method, t_eval=t_eval, **kwargs) + elif isinstance(method, str) and method == "RK4": + results = RK4_solver(solver_rhs, t_span, y0, t_eval=t_eval, **kwargs) + elif isinstance(method, str) and method == "jax_RK4": + results = jax_RK4_solver(solver_rhs, t_span, y0, t_eval=t_eval, **kwargs) + elif isinstance(method, str) and method == "jax_odeint": + results = jax_odeint(solver_rhs, t_span, y0, t_eval=t_eval, **kwargs) + elif _is_diffrax_method(method): + results = diffrax_solver(solver_rhs, t_span, y0, method=method, t_eval=t_eval, **kwargs) + + # convert results out of frame basis if necessary + if isinstance(rhs, BaseGeneratorModel): + if not model_in_frame_basis: + results.y = results_y_out_of_frame_basis(rhs, Array(results.y), y0.ndim) + + # convert model back to original basis + rhs.in_frame_basis = model_in_frame_basis + + return results
    + + + +
    +[docs] +def solve_lmde( + generator: Union[Callable, BaseGeneratorModel], + t_span: Array, + y0: Array, + method: Optional[Union[str, OdeSolver, DiffraxAbstractSolver]] = "DOP853", + t_eval: Optional[Union[Tuple, List, Array]] = None, + **kwargs, +): + r"""General interface for solving Linear Matrix Differential Equations (LMDEs) + in standard form. + + LMDEs in standard form are differential equations of the form: + + .. math:: + + \dot{y}(t) = G(t)y(t). + + where :math:`G(t)` is a square matrix valued-function called the *generator*, and :math:`y(t)` + is an :class:`Array` of appropriate shape. + + Thus function accepts :math:`G(t)` as a ``qiskit_dynamics`` model class, or as an arbitrary + callable. + + .. note:: + + Not all model classes are by-default in standard form. E.g. + :class:`~qiskit_dynamics.models.LindbladModel` represents an LMDE which is not typically + written in standard form. As such, using LMDE-specific methods with this generator requires + setting a vectorized evaluation mode. + + The ``method`` argument exposes solvers specialized to both LMDEs, as well as general ODE + solvers. If the method is not specific to LMDEs, the problem will be passed to + :meth:`~qiskit_dynamics.solve_ode` by automatically setting up the RHS function :math:`f(t, y) = + G(t)y`. + + Optional arguments for any of the solver routines can be passed via ``kwargs``. Available + LMDE-specific methods are: + + - ``'scipy_expm'``: A fixed-step matrix-exponential solver using ``scipy.linalg.expm``. Requires + additional kwarg ``max_dt`` indicating the maximum step size to take. This solver will break + integration periods into even sub-intervals no larger than ``max_dt`` and solve over each + sub-interval. The optional kwarg ``magnus_order`` controls the integration rule: if + ``magnus_order==1``, the generator is sampled at the interval midpoint and exponentiated, and + if ``magnus_order==2`` or ``magnus_order==3``, higher-order exponentiation rules are adopted + from :footcite:`blanes_magnus_2009`. The ``magnus_order`` parameter defaults to ``1``. + - ``'lanczos_diag'``: A fixed-step matrix-exponential solver, similar to ``'scipy_expm'`` but + restricted to anti-Hermitian generators. The matrix exponential is performed by diagonalizing + an approximate projection of the generator to a small subspace (the Krylov Subspace), obtained + via the Lanczos algorithm, and then exponentiating the eigenvalues. Requires additional kwargs + ``max_dt`` and ``k_dim`` indicating the maximum step size to take and Krylov subspace + dimension, respectively. ``k_dim`` acts as an adjustable accuracy parameter and can be no + larger than the dimension of the generator. The method is recommended for sparse systems with + large dimension. + - ``'jax_lanczos_diag'``: JAX implementation of ``'lanczos_diag'``, with the same arguments and + behaviour. Note that this method contains calls to ``jax.numpy.eigh``, which may have limited + validity when automatically differentiated. + - ``'jax_expm'``: JAX-implemented version of ``'scipy_expm'``, with the same arguments and + behaviour. Note that this method cannot be used for a model in sparse evaluation mode. + - ``'jax_expm_parallel'``: Same as ``'jax_expm'``, however all loops are implemented using + parallel operations. I.e. all matrix-exponentials for taking a single step are computed in + parallel using ``jax.vmap``, and are subsequently multiplied together in parallel using + ``jax.lax.associative_scan``. This method is only recommended for use with GPU execution. Note + that this method cannot be used for a model in sparse evaluation mode. + - ``'jax_RK4_parallel'``: 4th order Runge-Kutta fixed step solver. Under the assumption of the + structure of an LMDE, utilizes the same parallelization approach as ``'jax_expm_parallel'``, + however the single step rule is the standard 4th order Runge-Kutta rule, rather than + matrix-exponentiation. Requires and utilizes the ``max_dt`` kwarg in the same manner as + ``method='scipy_expm'``. This method is only recommended for use with GPU execution. + + Results are returned as a :class:`OdeResult` object. + + Args: + generator: Representation of generator function :math:`G(t)`. + t_span: ``Tuple`` or `list` of initial and final time. + y0: State at initial time. + method: Solving method to use. + t_eval: Times at which to return the solution. Must lie within ``t_span``. If unspecified, + the solution will be returned at the points in ``t_span``. + **kwargs: Additional arguments to pass to the solver. + + Returns: + OdeResult: Results object. + + Raises: + QiskitError: If specified method does not exist, + if dimension of ``y0`` is incompatible with generator dimension, or if an + LMDE-specific method is passed with a LindbladModel. + Additional Information: + While all :class:`~qiskit_dynamics.models.BaseGeneratorModel` subclasses represent LMDEs, + they are not all in standard form by defualt. Using an LMDE-specific models like + :class:`~qiskit_dynamics.models.LindbladModel` requires first setting a vectorized + evaluation mode. + """ + + # delegate to solve_ode if necessary + if ( + method in ODE_METHODS + or (isinstance(method, type) and (issubclass(method, OdeSolver))) + or _is_diffrax_method(method) + ): + if isinstance(generator, BaseGeneratorModel): + rhs = generator + else: + # treat generator as a function + def rhs(t, y): + return generator(t) @ y + + return solve_ode(rhs, t_span, y0, method=method, t_eval=t_eval, **kwargs) + + # raise error if neither an ODE_METHOD or an LMDE_METHOD + if method not in LMDE_METHODS: + raise QiskitError(f"Method {method} not supported by solve_lmde.") + + # lmde-specific methods can't be used with LindbladModel unless vectorized + if is_lindblad_model_not_vectorized(generator): + raise QiskitError( + """LMDE-specific methods with LindbladModel requires setting a + vectorized evaluation mode.""" + ) + + y0 = Array(y0) + + # setup generator and rhs functions to pass to numerical methods + if isinstance(generator, BaseGeneratorModel): + solver_generator, _, y0, model_in_frame_basis = setup_generator_model_rhs_y0_in_frame_basis( + generator, y0 + ) + else: + solver_generator = generator + + if method == "scipy_expm": + results = scipy_expm_solver(solver_generator, t_span, y0, t_eval=t_eval, **kwargs) + elif "lanczos_diag" in method: + _lanczos_validation(generator, t_span, y0, kwargs["k_dim"]) + if method == "lanczos_diag": + results = lanczos_diag_solver(solver_generator, t_span, y0, t_eval=t_eval, **kwargs) + elif method == "jax_lanczos_diag": + results = jax_lanczos_diag_solver(solver_generator, t_span, y0, t_eval=t_eval, **kwargs) + elif method == "jax_expm": + if isinstance(generator, BaseGeneratorModel) and "sparse" in generator.evaluation_mode: + raise QiskitError("jax_expm cannot be used with a generator in sparse mode.") + results = jax_expm_solver(solver_generator, t_span, y0, t_eval=t_eval, **kwargs) + elif method == "jax_expm_parallel": + results = jax_expm_parallel_solver(solver_generator, t_span, y0, t_eval=t_eval, **kwargs) + elif method == "jax_RK4_parallel": + results = jax_RK4_parallel_solver(solver_generator, t_span, y0, t_eval=t_eval, **kwargs) + + # convert results to correct basis if necessary + if isinstance(generator, BaseGeneratorModel): + if not model_in_frame_basis: + results.y = results_y_out_of_frame_basis(generator, Array(results.y), y0.ndim) + + generator.in_frame_basis = model_in_frame_basis + + return results
    + + + +def setup_generator_model_rhs_y0_in_frame_basis( + generator_model: BaseGeneratorModel, y0: Array +) -> Tuple[Callable, Callable, Array]: + """Helper function for setting up a subclass of + :class:`~qiskit_dynamics.models.BaseGeneratorModel` to be solved in the frame basis. + + Note: this function modifies ``generator_model`` to function in the frame basis. + + Args: + generator_model: Subclass of :class:`~qiskit_dynamics.models.BaseGeneratorModel`. + y0: Initial state. + + Returns: + Callable for generator in frame basis, callable for RHS in frame basis, y0 + in frame basis, and boolean indicating whether model was already specified in frame basis. + """ + + model_in_frame_basis = generator_model.in_frame_basis + + # if model not specified in frame basis, transform initial state into frame basis + if not model_in_frame_basis: + if ( + isinstance(generator_model, LindbladModel) + and "vectorized" in generator_model.evaluation_mode + ): + if generator_model.rotating_frame.frame_basis is not None: + y0 = generator_model.rotating_frame.vectorized_frame_basis_adjoint @ y0 + elif isinstance(generator_model, LindbladModel): + y0 = generator_model.rotating_frame.operator_into_frame_basis(y0) + elif isinstance(generator_model, GeneratorModel): + y0 = generator_model.rotating_frame.state_into_frame_basis(y0) + + # set model to operator in frame basis + generator_model.in_frame_basis = True + + # define rhs functions in frame basis + def generator(t): + return generator_model(t) + + def rhs(t, y): + return generator_model(t, y) + + return generator, rhs, y0, model_in_frame_basis + + +def results_y_out_of_frame_basis( + generator_model: BaseGeneratorModel, results_y: Array, y0_ndim: int +) -> Array: + """Convert the results of a simulation for :class:`~qiskit_dynamics.models.BaseGeneratorModel` + out of the frame basis. + + Args: + generator_model: Subclass of :class:`~qiskit_dynamics.models.BaseGeneratorModel`. + results_y: Array whose first index corresponds to the evaluation points of the state + for the results of ``solve_lmde`` or ``solve_ode``. + y0_ndim: Number of dimensions of initial state. + + Returns: + Callable for generator in frame basis, Callable for RHS in frame basis, and y0 + transformed to frame basis. + """ + # for left multiplication cases, if number of input dimensions is 1 + # vectorized basis transformation requires transposing before and after + if y0_ndim == 1: + results_y = results_y.T + + if ( + isinstance(generator_model, LindbladModel) + and "vectorized" in generator_model.evaluation_mode + ): + if generator_model.rotating_frame.frame_basis is not None: + results_y = generator_model.rotating_frame.vectorized_frame_basis @ results_y + elif isinstance(generator_model, LindbladModel): + results_y = generator_model.rotating_frame.operator_out_of_frame_basis(results_y) + else: + results_y = generator_model.rotating_frame.state_out_of_frame_basis(results_y) + + if y0_ndim == 1: + results_y = results_y.T + + return results_y +
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    + + + + + + + + + + + \ No newline at end of file diff --git a/stable/0.4/_sources/apidocs/array.rst.txt b/stable/0.4/_sources/apidocs/array.rst.txt new file mode 100644 index 000000000..ce8720f6c --- /dev/null +++ b/stable/0.4/_sources/apidocs/array.rst.txt @@ -0,0 +1,6 @@ +.. _qiskit_dynamics-array: + +.. automodule:: qiskit_dynamics.array + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/stable/0.4/_sources/apidocs/backend.rst.txt b/stable/0.4/_sources/apidocs/backend.rst.txt new file mode 100644 index 000000000..e69b81f46 --- /dev/null +++ b/stable/0.4/_sources/apidocs/backend.rst.txt @@ -0,0 +1,6 @@ +.. _qiskit_dynamics-backend: + +.. automodule:: qiskit_dynamics.backend + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/stable/0.4/_sources/apidocs/dispatch.rst.txt b/stable/0.4/_sources/apidocs/dispatch.rst.txt new file mode 100644 index 000000000..6b8e1e4cf --- /dev/null +++ b/stable/0.4/_sources/apidocs/dispatch.rst.txt @@ -0,0 +1,6 @@ +.. _qiskit_dynamics-dispatch: + +.. automodule:: qiskit_dynamics.dispatch + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/stable/0.4/_sources/apidocs/index.rst.txt b/stable/0.4/_sources/apidocs/index.rst.txt new file mode 100644 index 000000000..3d28fd3ac --- /dev/null +++ b/stable/0.4/_sources/apidocs/index.rst.txt @@ -0,0 +1,19 @@ +.. _qiskit-dynamics: + +.. module:: qiskit_dynamics + +============================= +Qiskit Dynamics API Reference +============================= + +.. toctree:: + :maxdepth: 2 + + solvers + backend + models + signals + pulse + perturbation + array + dispatch diff --git a/stable/0.4/_sources/apidocs/models.rst.txt b/stable/0.4/_sources/apidocs/models.rst.txt new file mode 100644 index 000000000..89e780254 --- /dev/null +++ b/stable/0.4/_sources/apidocs/models.rst.txt @@ -0,0 +1,6 @@ +.. _qiskit_dynamics-models: + +.. automodule:: qiskit_dynamics.models + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/stable/0.4/_sources/apidocs/perturbation.rst.txt b/stable/0.4/_sources/apidocs/perturbation.rst.txt new file mode 100644 index 000000000..8e68731d1 --- /dev/null +++ b/stable/0.4/_sources/apidocs/perturbation.rst.txt @@ -0,0 +1,6 @@ +.. _qiskit_dynamics-perturbation: + +.. automodule:: qiskit_dynamics.perturbation + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/stable/0.4/_sources/apidocs/pulse.rst.txt b/stable/0.4/_sources/apidocs/pulse.rst.txt new file mode 100644 index 000000000..610e4810c --- /dev/null +++ b/stable/0.4/_sources/apidocs/pulse.rst.txt @@ -0,0 +1,6 @@ +.. _qiskit_dynamics-pulse: + +.. automodule:: qiskit_dynamics.pulse + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/stable/0.4/_sources/apidocs/signals.rst.txt b/stable/0.4/_sources/apidocs/signals.rst.txt new file mode 100644 index 000000000..4e63527ae --- /dev/null +++ b/stable/0.4/_sources/apidocs/signals.rst.txt @@ -0,0 +1,6 @@ +.. _qiskit_dynamics-signals: + +.. automodule:: qiskit_dynamics.signals + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/stable/0.4/_sources/apidocs/solvers.rst.txt b/stable/0.4/_sources/apidocs/solvers.rst.txt new file mode 100644 index 000000000..825ed8cc7 --- /dev/null +++ b/stable/0.4/_sources/apidocs/solvers.rst.txt @@ -0,0 +1,6 @@ +.. _qiskit_dynamics-solvers: + +.. automodule:: qiskit_dynamics.solvers + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/stable/0.4/_sources/discussions/dyson_magnus.rst.txt b/stable/0.4/_sources/discussions/dyson_magnus.rst.txt new file mode 100644 index 000000000..dc04b4214 --- /dev/null +++ b/stable/0.4/_sources/discussions/dyson_magnus.rst.txt @@ -0,0 +1,214 @@ +.. _perturbation review: + +Time-dependent perturbation theory and multi-variable series expansions review +============================================================================== + +The :mod:`.perturbation` module contains functionality for +numerically computing perturbation theory expansions used in the study of the +dynamics of quantum systems. Following :footcite:`puzzuoli_sensitivity_2022`, +this discussion reviews key concepts required +to understand and utilize the module, including the Dyson series and Magnus expansion, +their generalization to a multi-variable setting, and the notation used to represent +multi-variable power series in terms of multisets. + + +The Dyson series and Magnus expansion +------------------------------------- + +The Dyson series :footcite:`dyson_radiation_1949` and Magnus expansion +:footcite:`magnus_exponential_1954,blanes_magnus_2009` +are time-dependent perturbation theory expansions for solutions of linear matrix differential +equations (LMDEs). For an LMDE + +.. math:: + + \dot{U}(t) = G(t)U(t) + +with :math:`U(0) = I` the identity matrix, the Dyson series directly expands the solution: + +.. math:: + + U(t) &= I + \sum_{k=1}^\infty D_k(t)\textnormal{, with} \\ + D_k(t) &= \int_0^t dt_1 \dots \int_0^{t_{k-1}} dt_k G(t_1) \dots G(t_k). + +The Magnus expansion alternatively seeks to construct a time-averaged generator, i.e. an operator +:math:`\Omega(t)` for which + +.. math:: + + U(t) = \exp(\Omega(t)). + +The Magnus expansion provides +a series expansion, which, under certain conditions :footcite:`blanes_magnus_2009`, +converges to :math:`\Omega(t)`: + +.. math:: + + \Omega(t) = \sum_{k=1}^\infty \Omega_k(t), + +where explicit expressions for the :math:`\Omega_k(t)` are given in the literature +:footcite:`blanes_magnus_2009`. + + +Generalizing to the multi-variable case +--------------------------------------- + +In applications, these expansions are often used in a *multi-variable* setting, in which +the generator :math:`G(t)` depends on several variables :math:`c_0, \dots, c_{r-1}`, +and the Dyson series or Magnus expansion are used to understand how the evolution changes +under perturbations to several of these parameters simultaneously. For working with +these expansions algorithmically it is necessary to formalize +the expression of these expansions in the multi-variable setting. + +Mathematically, we explicitly write the generator as a function of these variables +:math:`G(t, c_0, \dots, c_{r-1})`, and expand :math:`G` in a +multi-variable power series in the variables :math:`c_i`: + +.. math:: + + G(t, c_0, \dots, c_{r-1}) = + G_\emptyset(t) + + \sum_{k=1}^\infty \sum_{0 \leq i_1 \leq \dots \leq i_k \leq r-1} + c_{i_1} \dots c_{i_k} G_{i_1, \dots, i_k}(t). + +For physical applications we take the existence of such a power series for granted: +up to constant factors, the coefficients :math:`G_{i_1, \dots, i_k}(t)` are the partial +derivatives of :math:`G` with respect to the variables :math:`c_i`. Commonly, :math:`G` +depends linearly on the variables, e.g. when representing couplings between quantum systems. + +Before defining the multi-variable Dyson series and Magnus expansions, we transform +the generator into the *toggling frame* of :math:`G_\emptyset(t)` +:footcite:`evans_timedependent_1967,haeberlen_1968`. Denoting + +.. math:: + + V(t) = \mathcal{T}\exp\left(\int_{t_0}^t ds G_\emptyset(s)\right), + +the generator :math:`G` in the toggling frame of :math:`G_\emptyset(t)`, +the unperturbed generator, is given by: + +.. math:: + + \tilde{G}(t, c_0, \dots, c_{r-1}) &= + \sum_{k=1}^\infty \sum_{0 \leq i_1 \leq \dots \leq i_k \leq r-1} + c_{i_1} \dots c_{i_k} \tilde{G}_{i_1, \dots, i_k}(t)\textnormal{, with} \\ + \tilde{G}_{i_1, \dots, i_k}(t) &= V^{-1}(t) G_{i_1, \dots, i_k}(t)V(t) + +Denoting :math:`U(t, c_0, \dots, c_{r-1})` as the solution of the LMDE with +generator :math:`\tilde{G}`, note that + +.. math:: + + U(t, c_0, \dots, c_{r-1}) = + V(t)\mathcal{T}\exp\left(\int_{t_0}^t ds \tilde{G}(s, c_0, \dots, c_{r-1})\right), + +and hence solution for :math:`G` and :math:`\tilde{G}` are simply related by :math:`V(t)`. + +Using this, :footcite:`puzzuoli_sensitivity_2022` defines the multi-variable Dyson series +for the generator :math:`\tilde{G}(t, c_0, \dots, c_{r-1})` as: + +.. math:: + + U(t, c_0, \dots, c_{r-1}) = I + + \sum_{k=1}^\infty \sum_{0 \leq i_1 \leq \dots \leq i_k \leq r-1} + c_{i_1} \dots c_{i_k} \mathcal{D}_{i_1, \dots, i_k}(t), + +where the :math:`\mathcal{D}_{i_1, \dots, i_k}(t)` are defined implicitly by the above +equation, and are called the *multi-variable Dyson series terms*. Similarly the +multi-variable Magnus expansion for :math:`\tilde{G}` is given as: + +.. math:: + + \Omega(t, c_0, \dots, c_{r-1}) = + \sum_{k=1}^\infty \sum_{0 \leq i_1 \leq \dots \leq i_k \leq r-1} + c_{i_1} \dots c_{i_k} \mathcal{O}_{i_1, \dots, i_k}(t), + +with the :math:`\mathcal{O}_{i_1, \dots, i_k}(t)` again defined implicitly, and called the +*multi-variable Magnus expansion terms*. + + +Computing multi-variable Dyson series and Magnus expansion terms +---------------------------------------------------------------- + +Given a power series decomposition of the generator as above, +the function :func:`.solve_lmde_perturbation` computes, +in the toggling frame of the unperturbed generator, either multi-variable +Dyson series or Magnus expansion terms via the algorithms in +:footcite:`puzzuoli_sensitivity_2022`. It can also be used to compute Dyson-like terms via +the algorithm in :footcite:`haas_engineering_2019`. In the presentation here and elsewhere, +the expansions are phrased as infinite series, but of course in practice truncated +versions must be specified and computed. + +Utilizing this function, and working with the other objects in the module, requires +understanding the notation and data structures used to represent power series. + +.. _multiset power series: + +Multiset power series notation +------------------------------ + +Following :footcite:`puzzuoli_sensitivity_2022`, the :mod:`.perturbation` +module utilizes a *multiset* notation to more compactly represent and work with power series. + +Consider the power series expansion above for the generator :math:`G(t, c_0, \dots, c_{r-1})`. +Structurally, each term in the power series is labelled by the number of times each +variable :math:`c_0, \dots, c_{r-1}` appears in the product :math:`c_{i_1} \dots c_{i_k}`. +Equivalently, each term may be indexed by the number of times each variable label +:math:`0, \dots, r-1` appears. The data structure used to represent these labels in this +module is that of a *multiset*, i.e. a "set with repeated entries". Denoting multisets +with round brackets, e.g. :math:`I = (i_1, \dots, i_k)`, we define + +.. math:: + + c_I = c_{i_1} \times \dots \times c_{i_k}. + +and similarly denote :math:`G_I = G_{i_1, \dots, i_k}`. This notation is chosen due to +the simple relationship between algebraic operations and multiset operations. E.g., +for two multisets :math:`I, J`, it holds that: + +.. math:: + + c_{I + J} = c_I \times c_J, + +where :math:`I + J` denotes the multiset whose object counts are the sum of both :math:`I` and +:math:`J`. + +Some example usages of this notation are: + + - :math:`c_{(0, 1)} = c_0 c_1`, + - :math:`c_{(1, 1)} = c_1^2`, and + - :math:`c_{(1, 2, 2, 3)} = c_1 c_2^2 c_3`. + +Finally, we denote the set of multisets of size $k$ with elements in :math:`\{0, \dots, r-1\}` +as :math:`\mathcal{I}_k(r)`. Combining everything, the power series for :math:`G` may be +rewritten as: + +.. math:: + + G(t, c_0, \dots, c_{r-1}) = G_\emptyset(t) + + \sum_{k=1}^\infty \sum_{I \in \mathcal{I}_k(r)} c_I G_I(t). + +Similarly, the multi-variable Dyson series is written as: + +.. math:: + + U(t, c_0, \dots, c_{r-1}) = + I + \sum_{k=1}^\infty \sum_{I \in \mathcal{I}_k(r)} c_I \mathcal{D}_I(t), + +and the multi-variable Magnus expansion as: + +.. math:: + + \Omega(t, c_0, \dots, c_{r-1}) = + \sum_{k=1}^\infty \sum_{I \in \mathcal{I}_k(r)} c_I \mathcal{O}_I(t). + +In the module, multisets are represented using the ``Multiset`` object in the +`multiset package `_. Arguments to functions +which must specify a multiset or a list of multisets accept either ``Multiset`` instances +directly, or a valid argument to the constructor to ``Multiset``, with the restriction that +the multiset entries must be non-negative integers. + + + + +.. footbibliography:: diff --git a/stable/0.4/_sources/discussions/index.rst.txt b/stable/0.4/_sources/discussions/index.rst.txt new file mode 100644 index 000000000..cab84b9b9 --- /dev/null +++ b/stable/0.4/_sources/discussions/index.rst.txt @@ -0,0 +1,16 @@ +#################### +Dynamics Discussions +#################### + +Discussions about topics and concepts related to the package. + +.. toctree:: + :maxdepth: 1 + + dyson_magnus.rst + + +.. Hiding - Indices and tables + :ref:`genindex` + :ref:`modindex` + :ref:`search` diff --git a/stable/0.4/_sources/index.rst.txt b/stable/0.4/_sources/index.rst.txt new file mode 100644 index 000000000..b9cb37812 --- /dev/null +++ b/stable/0.4/_sources/index.rst.txt @@ -0,0 +1,38 @@ +############################# +Qiskit Dynamics documentation +############################# + +Qiskit Dynamics is an open-source project for building, transforming, and solving +models of quantum systems in Qiskit. + +The goal of Qiskit Dynamics is to provide access to different numerical +methods, and to automate common processes typically performed by hand, +e.g. entering rotating frames, or doing the rotating wave approximation. + +Qiskit Dynamics can be configured to use either +`NumPy `_ or `JAX `_ +as the backend for array operations. `NumPy `_ is the default, +and `JAX `_ is an optional dependency, which enables +just-in-time compilation, automatic differentiation, and GPU execution of Qiskit Dynamics code. + +.. warning:: + + This package is still in the early stages of development and it is very likely + that there will be breaking API changes in future releases. + If you encounter any bugs please open an issue on + `Github `_ + + +.. toctree:: + :maxdepth: 1 + + Tutorials + User Guide + API References + Discussions + Release Notes + +.. Hiding - Indices and tables + :ref:`genindex` + :ref:`modindex` + :ref:`search` diff --git a/stable/0.4/_sources/release_notes.rst.txt b/stable/0.4/_sources/release_notes.rst.txt new file mode 100644 index 000000000..7e2951be4 --- /dev/null +++ b/stable/0.4/_sources/release_notes.rst.txt @@ -0,0 +1 @@ +.. release-notes:: Release Notes \ No newline at end of file diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.array.Array.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.array.Array.rst.txt new file mode 100644 index 000000000..32f385906 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.array.Array.rst.txt @@ -0,0 +1,24 @@ +Array +===== + +.. currentmodule:: qiskit_dynamics.array + +.. autoclass:: Array + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: Array.available_backends + .. automethod:: Array.default_backend + .. automethod:: Array.set_default_backend + + + + .. rubric:: Attributes + + .. autoattribute:: backend + .. autoattribute:: data diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.array.wrap.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.array.wrap.rst.txt new file mode 100644 index 000000000..1c6997cf6 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.array.wrap.rst.txt @@ -0,0 +1,6 @@ +qiskit\_dynamics.array.wrap +=========================== + +.. currentmodule:: qiskit_dynamics.array + +.. autofunction:: wrap \ No newline at end of file diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.backend.DynamicsBackend.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.backend.DynamicsBackend.rst.txt new file mode 100644 index 000000000..9cffa12bc --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.backend.DynamicsBackend.rst.txt @@ -0,0 +1,48 @@ +DynamicsBackend +=============== + +.. currentmodule:: qiskit_dynamics.backend + +.. autoclass:: DynamicsBackend + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: DynamicsBackend.acquire_channel + .. automethod:: DynamicsBackend.configuration + .. automethod:: DynamicsBackend.control_channel + .. automethod:: DynamicsBackend.defaults + .. automethod:: DynamicsBackend.drive_channel + .. automethod:: DynamicsBackend.from_backend + .. automethod:: DynamicsBackend.measure_channel + .. automethod:: DynamicsBackend.qubit_properties + .. automethod:: DynamicsBackend.run + .. automethod:: DynamicsBackend.set_options + + + + .. rubric:: Attributes + + .. autoattribute:: coupling_map + .. autoattribute:: dt + .. autoattribute:: dtm + .. autoattribute:: instruction_durations + .. autoattribute:: instruction_schedule_map + .. autoattribute:: instructions + .. autoattribute:: max_circuits + .. autoattribute:: meas_map + .. autoattribute:: num_qubits + .. autoattribute:: operation_names + .. autoattribute:: operations + .. autoattribute:: options + .. autoattribute:: provider + .. autoattribute:: target + .. autoattribute:: version + .. autoattribute:: name + .. autoattribute:: description + .. autoattribute:: online_date + .. autoattribute:: backend_version diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.backend.default_experiment_result_function.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.backend.default_experiment_result_function.rst.txt new file mode 100644 index 000000000..50ee9984d --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.backend.default_experiment_result_function.rst.txt @@ -0,0 +1,6 @@ +qiskit\_dynamics.backend.default\_experiment\_result\_function +============================================================== + +.. currentmodule:: qiskit_dynamics.backend + +.. autofunction:: default_experiment_result_function \ No newline at end of file diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.backend.parse_backend_hamiltonian_dict.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.backend.parse_backend_hamiltonian_dict.rst.txt new file mode 100644 index 000000000..b610dc14a --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.backend.parse_backend_hamiltonian_dict.rst.txt @@ -0,0 +1,6 @@ +qiskit\_dynamics.backend.parse\_backend\_hamiltonian\_dict +========================================================== + +.. currentmodule:: qiskit_dynamics.backend + +.. autofunction:: parse_backend_hamiltonian_dict \ No newline at end of file diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.dispatch.asarray.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.dispatch.asarray.rst.txt new file mode 100644 index 000000000..00335bdb2 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.dispatch.asarray.rst.txt @@ -0,0 +1,6 @@ +qiskit\_dynamics.dispatch.asarray +================================= + +.. currentmodule:: qiskit_dynamics.dispatch + +.. autofunction:: asarray \ No newline at end of file diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.dispatch.requires_backend.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.dispatch.requires_backend.rst.txt new file mode 100644 index 000000000..626835186 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.dispatch.requires_backend.rst.txt @@ -0,0 +1,6 @@ +qiskit\_dynamics.dispatch.requires\_backend +=========================================== + +.. currentmodule:: qiskit_dynamics.dispatch + +.. autofunction:: requires_backend \ No newline at end of file diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.models.GeneratorModel.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.models.GeneratorModel.rst.txt new file mode 100644 index 000000000..21963c0c2 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.models.GeneratorModel.rst.txt @@ -0,0 +1,29 @@ +GeneratorModel +============== + +.. currentmodule:: qiskit_dynamics.models + +.. autoclass:: GeneratorModel + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: GeneratorModel.copy + .. automethod:: GeneratorModel.evaluate + .. automethod:: GeneratorModel.evaluate_rhs + + + + .. rubric:: Attributes + + .. autoattribute:: dim + .. autoattribute:: evaluation_mode + .. autoattribute:: in_frame_basis + .. autoattribute:: operators + .. autoattribute:: rotating_frame + .. autoattribute:: signals + .. autoattribute:: static_operator diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.models.HamiltonianModel.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.models.HamiltonianModel.rst.txt new file mode 100644 index 000000000..4af473eeb --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.models.HamiltonianModel.rst.txt @@ -0,0 +1,29 @@ +HamiltonianModel +================ + +.. currentmodule:: qiskit_dynamics.models + +.. autoclass:: HamiltonianModel + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: HamiltonianModel.copy + .. automethod:: HamiltonianModel.evaluate + .. automethod:: HamiltonianModel.evaluate_rhs + + + + .. rubric:: Attributes + + .. autoattribute:: dim + .. autoattribute:: evaluation_mode + .. autoattribute:: in_frame_basis + .. autoattribute:: operators + .. autoattribute:: rotating_frame + .. autoattribute:: signals + .. autoattribute:: static_operator diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.models.LindbladModel.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.models.LindbladModel.rst.txt new file mode 100644 index 000000000..e066e3715 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.models.LindbladModel.rst.txt @@ -0,0 +1,33 @@ +LindbladModel +============= + +.. currentmodule:: qiskit_dynamics.models + +.. autoclass:: LindbladModel + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: LindbladModel.copy + .. automethod:: LindbladModel.evaluate + .. automethod:: LindbladModel.evaluate_hamiltonian + .. automethod:: LindbladModel.evaluate_rhs + .. automethod:: LindbladModel.from_hamiltonian + + + + .. rubric:: Attributes + + .. autoattribute:: dim + .. autoattribute:: dissipator_operators + .. autoattribute:: evaluation_mode + .. autoattribute:: hamiltonian_operators + .. autoattribute:: in_frame_basis + .. autoattribute:: rotating_frame + .. autoattribute:: signals + .. autoattribute:: static_dissipators + .. autoattribute:: static_hamiltonian diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.models.RotatingFrame.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.models.RotatingFrame.rst.txt new file mode 100644 index 000000000..fb5c77ac6 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.models.RotatingFrame.rst.txt @@ -0,0 +1,37 @@ +RotatingFrame +============= + +.. currentmodule:: qiskit_dynamics.models + +.. autoclass:: RotatingFrame + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: RotatingFrame.generator_into_frame + .. automethod:: RotatingFrame.generator_out_of_frame + .. automethod:: RotatingFrame.operator_into_frame + .. automethod:: RotatingFrame.operator_into_frame_basis + .. automethod:: RotatingFrame.operator_out_of_frame + .. automethod:: RotatingFrame.operator_out_of_frame_basis + .. automethod:: RotatingFrame.state_into_frame + .. automethod:: RotatingFrame.state_into_frame_basis + .. automethod:: RotatingFrame.state_out_of_frame + .. automethod:: RotatingFrame.state_out_of_frame_basis + .. automethod:: RotatingFrame.vectorized_map_into_frame + + + + .. rubric:: Attributes + + .. autoattribute:: dim + .. autoattribute:: frame_basis + .. autoattribute:: frame_basis_adjoint + .. autoattribute:: frame_diag + .. autoattribute:: frame_operator + .. autoattribute:: vectorized_frame_basis + .. autoattribute:: vectorized_frame_basis_adjoint diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.models.rotating_wave_approximation.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.models.rotating_wave_approximation.rst.txt new file mode 100644 index 000000000..db16e1e14 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.models.rotating_wave_approximation.rst.txt @@ -0,0 +1,6 @@ +qiskit\_dynamics.models.rotating\_wave\_approximation +===================================================== + +.. currentmodule:: qiskit_dynamics.models + +.. autofunction:: rotating_wave_approximation \ No newline at end of file diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.ArrayPolynomial.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.ArrayPolynomial.rst.txt new file mode 100644 index 000000000..f642c82b3 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.ArrayPolynomial.rst.txt @@ -0,0 +1,33 @@ +ArrayPolynomial +=============== + +.. currentmodule:: qiskit_dynamics.perturbation + +.. autoclass:: ArrayPolynomial + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: ArrayPolynomial.add + .. automethod:: ArrayPolynomial.compute_monomials + .. automethod:: ArrayPolynomial.conj + .. automethod:: ArrayPolynomial.matmul + .. automethod:: ArrayPolynomial.mul + .. automethod:: ArrayPolynomial.sum + .. automethod:: ArrayPolynomial.trace + .. automethod:: ArrayPolynomial.transpose + + + + .. rubric:: Attributes + + .. autoattribute:: array_coefficients + .. autoattribute:: constant_term + .. autoattribute:: monomial_labels + .. autoattribute:: ndim + .. autoattribute:: real + .. autoattribute:: shape diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.DysonLikeData.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.DysonLikeData.rst.txt new file mode 100644 index 000000000..9d3cb1839 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.DysonLikeData.rst.txt @@ -0,0 +1,23 @@ +DysonLikeData +============= + +.. currentmodule:: qiskit_dynamics.perturbation + +.. autoclass:: DysonLikeData + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: DysonLikeData.get_item + + + + .. rubric:: Attributes + + .. autoattribute:: metadata + .. autoattribute:: data + .. autoattribute:: labels diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.PowerSeriesData.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.PowerSeriesData.rst.txt new file mode 100644 index 000000000..e2cf91248 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.PowerSeriesData.rst.txt @@ -0,0 +1,23 @@ +PowerSeriesData +=============== + +.. currentmodule:: qiskit_dynamics.perturbation + +.. autoclass:: PowerSeriesData + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: PowerSeriesData.get_item + + + + .. rubric:: Attributes + + .. autoattribute:: metadata + .. autoattribute:: data + .. autoattribute:: labels diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.solve_lmde_perturbation.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.solve_lmde_perturbation.rst.txt new file mode 100644 index 000000000..74384835e --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.perturbation.solve_lmde_perturbation.rst.txt @@ -0,0 +1,6 @@ +qiskit\_dynamics.perturbation.solve\_lmde\_perturbation +======================================================= + +.. currentmodule:: qiskit_dynamics.perturbation + +.. autofunction:: solve_lmde_perturbation \ No newline at end of file diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.pulse.InstructionToSignals.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.pulse.InstructionToSignals.rst.txt new file mode 100644 index 000000000..5491826c4 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.pulse.InstructionToSignals.rst.txt @@ -0,0 +1,18 @@ +InstructionToSignals +==================== + +.. currentmodule:: qiskit_dynamics.pulse + +.. autoclass:: InstructionToSignals + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: InstructionToSignals.get_awg_signals + .. automethod:: InstructionToSignals.get_signals + + diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.signals.Convolution.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.Convolution.rst.txt new file mode 100644 index 000000000..a8b19d81c --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.Convolution.rst.txt @@ -0,0 +1,16 @@ +Convolution +=========== + +.. currentmodule:: qiskit_dynamics.signals + +.. autoclass:: Convolution + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + + + .. rubric:: Attributes + + .. autoattribute:: n_inputs diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.signals.DiscreteSignal.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.DiscreteSignal.rst.txt new file mode 100644 index 000000000..eaf05964b --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.DiscreteSignal.rst.txt @@ -0,0 +1,33 @@ +DiscreteSignal +============== + +.. currentmodule:: qiskit_dynamics.signals + +.. autoclass:: DiscreteSignal + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: DiscreteSignal.add_samples + .. automethod:: DiscreteSignal.complex_value + .. automethod:: DiscreteSignal.conjugate + .. automethod:: DiscreteSignal.draw + .. automethod:: DiscreteSignal.envelope + .. automethod:: DiscreteSignal.from_Signal + + + + .. rubric:: Attributes + + .. autoattribute:: carrier_freq + .. autoattribute:: dt + .. autoattribute:: duration + .. autoattribute:: is_constant + .. autoattribute:: name + .. autoattribute:: phase + .. autoattribute:: samples + .. autoattribute:: start_time diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.signals.DiscreteSignalSum.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.DiscreteSignalSum.rst.txt new file mode 100644 index 000000000..fd50a83f2 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.DiscreteSignalSum.rst.txt @@ -0,0 +1,36 @@ +DiscreteSignalSum +================= + +.. currentmodule:: qiskit_dynamics.signals + +.. autoclass:: DiscreteSignalSum + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: DiscreteSignalSum.add_samples + .. automethod:: DiscreteSignalSum.complex_value + .. automethod:: DiscreteSignalSum.conjugate + .. automethod:: DiscreteSignalSum.draw + .. automethod:: DiscreteSignalSum.envelope + .. automethod:: DiscreteSignalSum.flatten + .. automethod:: DiscreteSignalSum.from_Signal + .. automethod:: DiscreteSignalSum.from_SignalSum + + + + .. rubric:: Attributes + + .. autoattribute:: carrier_freq + .. autoattribute:: components + .. autoattribute:: dt + .. autoattribute:: duration + .. autoattribute:: is_constant + .. autoattribute:: name + .. autoattribute:: phase + .. autoattribute:: samples + .. autoattribute:: start_time diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.signals.IQMixer.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.IQMixer.rst.txt new file mode 100644 index 000000000..c34e86f6b --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.IQMixer.rst.txt @@ -0,0 +1,16 @@ +IQMixer +======= + +.. currentmodule:: qiskit_dynamics.signals + +.. autoclass:: IQMixer + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + + + .. rubric:: Attributes + + .. autoattribute:: n_inputs diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.signals.Signal.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.Signal.rst.txt new file mode 100644 index 000000000..13cde4098 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.Signal.rst.txt @@ -0,0 +1,27 @@ +Signal +====== + +.. currentmodule:: qiskit_dynamics.signals + +.. autoclass:: Signal + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: Signal.complex_value + .. automethod:: Signal.conjugate + .. automethod:: Signal.draw + .. automethod:: Signal.envelope + + + + .. rubric:: Attributes + + .. autoattribute:: carrier_freq + .. autoattribute:: is_constant + .. autoattribute:: name + .. autoattribute:: phase diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.signals.SignalList.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.SignalList.rst.txt new file mode 100644 index 000000000..2ffcc0eb6 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.SignalList.rst.txt @@ -0,0 +1,24 @@ +SignalList +========== + +.. currentmodule:: qiskit_dynamics.signals + +.. autoclass:: SignalList + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: SignalList.complex_value + .. automethod:: SignalList.conjugate + .. automethod:: SignalList.flatten + + + + .. rubric:: Attributes + + .. autoattribute:: components + .. autoattribute:: drift diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.signals.SignalSum.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.SignalSum.rst.txt new file mode 100644 index 000000000..5b1af525e --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.signals.SignalSum.rst.txt @@ -0,0 +1,29 @@ +SignalSum +========= + +.. currentmodule:: qiskit_dynamics.signals + +.. autoclass:: SignalSum + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: SignalSum.complex_value + .. automethod:: SignalSum.conjugate + .. automethod:: SignalSum.draw + .. automethod:: SignalSum.envelope + .. automethod:: SignalSum.flatten + + + + .. rubric:: Attributes + + .. autoattribute:: carrier_freq + .. autoattribute:: components + .. autoattribute:: is_constant + .. autoattribute:: name + .. autoattribute:: phase diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.DysonSolver.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.DysonSolver.rst.txt new file mode 100644 index 000000000..b2b47d70e --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.DysonSolver.rst.txt @@ -0,0 +1,21 @@ +DysonSolver +=========== + +.. currentmodule:: qiskit_dynamics.solvers + +.. autoclass:: DysonSolver + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: DysonSolver.solve + + + + .. rubric:: Attributes + + .. autoattribute:: model diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.MagnusSolver.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.MagnusSolver.rst.txt new file mode 100644 index 000000000..07338c02f --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.MagnusSolver.rst.txt @@ -0,0 +1,21 @@ +MagnusSolver +============ + +.. currentmodule:: qiskit_dynamics.solvers + +.. autoclass:: MagnusSolver + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: MagnusSolver.solve + + + + .. rubric:: Attributes + + .. autoattribute:: model diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.Solver.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.Solver.rst.txt new file mode 100644 index 000000000..30ff33f4a --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.Solver.rst.txt @@ -0,0 +1,21 @@ +Solver +====== + +.. currentmodule:: qiskit_dynamics.solvers + +.. autoclass:: Solver + :no-members: + :show-inheritance: + :no-inherited-members: + :no-special-members: + + .. rubric:: Methods + + + .. automethod:: Solver.solve + + + + .. rubric:: Attributes + + .. autoattribute:: model diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.solve_lmde.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.solve_lmde.rst.txt new file mode 100644 index 000000000..0314bcb27 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.solve_lmde.rst.txt @@ -0,0 +1,6 @@ +qiskit\_dynamics.solvers.solve\_lmde +==================================== + +.. currentmodule:: qiskit_dynamics.solvers + +.. autofunction:: solve_lmde \ No newline at end of file diff --git a/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.solve_ode.rst.txt b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.solve_ode.rst.txt new file mode 100644 index 000000000..28ed3e608 --- /dev/null +++ b/stable/0.4/_sources/stubs/qiskit_dynamics.solvers.solve_ode.rst.txt @@ -0,0 +1,6 @@ +qiskit\_dynamics.solvers.solve\_ode +=================================== + +.. currentmodule:: qiskit_dynamics.solvers + +.. autofunction:: solve_ode \ No newline at end of file diff --git a/stable/0.4/_sources/tutorials/Lindblad_dynamics_simulation.rst.txt b/stable/0.4/_sources/tutorials/Lindblad_dynamics_simulation.rst.txt new file mode 100644 index 000000000..1d17caf88 --- /dev/null +++ b/stable/0.4/_sources/tutorials/Lindblad_dynamics_simulation.rst.txt @@ -0,0 +1,275 @@ +Solving the Lindblad dynamics of a qubit chain +============================================== + +In this tutorial we walk through an example of solving the time +evolution of the density matrix of coupled qubits using +``qiskit_dynamics``. The model that we solve consists of a +time-independent Hamiltonian for qubits interacting with their nearest +neighbors along a ring. In addition, energy relaxation terms acting on +each qubit are modeled by using a non-Markovian master equation in +Lindblad form. We will discuss the system’s steady state as a function +of the model parameters. + +In the sections below we define a model, solve the dynamics and plot +some observables using the following steps: + +1. Define the number of qubits and precompute some matrix operators. +2. Define all relevant parameters and setup a :class:`Solver` instance with the model of the system, + consisting of the Hamiltonian and the jump operators of the Lindblad dissipator. +3. Define the initial state and other parameters for the initial value problem, + and evolve the system state. +4. Define observables and calculate their values as a function of time. +5. Plot some observables and discuss the results. + +The model that we solve describes the time evolution of :math:`N` qubits +with coherent dynamics dictated by a given Hamiltonian, and the +environment modeled as a memory-less (Markovian) bath. Together, the +density matrix evolves according to the Lindblad master equation, + +.. math:: \partial_t\rho = -\frac{i}{\hbar} \left[H,\rho\right] + \mathcal{D}[\rho]. + +The Hamiltonian is composed of a sum of single-qubit terms and two-qubit +interactions, + +.. math:: H = H_0 + H_I. + +We take the qubits to have identical parameters, with a diagonal term of +frequency :math:`\nu_z` and a transverse term of amplitude +:math:`\nu_x`. The single-qubit part of the Hamiltonian is + +.. math:: H_0 = \frac{1}{2}\sum_i^N \left[2 \pi \nu_z {Z}_i + 2 \pi \nu_x {X}_i\right], + +where :math:`\{X_i,Y_i,Z_i\}` are the Pauli matrices for qubit :math:`i` +(also written as :math:`\sigma_i^a` with :math:`a\in\{x,y,z\}`). + +We set the interactions between nearest-neighbor qubits to be of +“flip-flop” type, also called “XY” coupling. We consider periodic +boundary conditions, such that the last qubit is connected to the first +qubit as well, with + +.. math:: H_I = \frac{1}{2} \sum_{\langle i,j\rangle}2 \pi J \left[{X_i X_j} + {Y_i Y_j}\right] + +In ``qiskit``, each qubit’s ground state is by convention the state +:math:`|0\rangle` which is the eigenstate of :math:`Z` with eigenvalue 1 +(the state that is known also as “up”). Therefore the action of energy +relaxation terms describing damping into the environment tend to bring +qubits to this state, as generated by the Lindblad dissipator + +.. math:: \mathcal{D}[\rho] = \sum_i \Gamma\left(\sigma_i^+ \rho\sigma_i^- - \frac{1}{2} \{\sigma_i^- \sigma_i^+,\rho\}\right), + +with :math:`\sigma_i^{\pm}= \frac{1}{2}\left(X_i\pm i Y_i\right)`. + +1. Prepare the single-qubit operators +------------------------------------- + +In ``qiskit-dynamics``, dynamical simulations are defined using the +operators that act on the states appearing in the differential +equations. We start by creating the single-qubit operators that act on +each qubit in the simulation, and are represented as matrices in the +Hilbert space of :math:`N` qubits. Using ``qiskit`` library routines, it +is easy to create :math:`N`-qubit operators that are products of basic +single-qubit operators, by using labels (descriptive strings), and the +callable syntax of ``Pauli`` classes to indicate a qubit number, as +below. + +Below, we first set the number of qubits :math:`N` to be simulated, and +then prepare and store the single-qubit Pauli operators that will be +used in the rest of this tutorial. + +.. jupyter-execute:: + :hide-code: + + import warnings + warnings.filterwarnings('ignore', message='', category=Warning, module='', lineno=0, append=False) + + +.. jupyter-execute:: + + import numpy as np + from qiskit.quantum_info import Operator, Pauli + + N = 6 + + x_ops = [] + y_ops = [] + z_ops = [] + qubits = range(N) + zeros = Operator(np.zeros((2 ** N, 2 ** N))) + + for i in qubits: + X = zeros + Pauli('X')(i) + x_ops.append(X) + + Y = zeros + Pauli('Y')(i) + y_ops.append(Y) + + Z = zeros + Pauli('Z')(i) + z_ops.append(Z) + + +2. Setup the solver +------------------- + +In this section we setup a :class:`Solver` class that stores and manipulates +the model to be solved. In the following, we will set :math:`\hbar=1` +and set the driving amplitude to be :math:`\nu_x \equiv 1`. This sets the +time units, with the other frequency +parameters scaled accordingly. Below, we first set a few values for +these free parameters, and then create the Hamiltonian matrix and the +list of dissipator operators. We build the full Hamiltonian matrix by +summing all single-qubit and two-qubit terms. Since there are no +time-dependent terms, and we do not plan to take partial derivatives of +parameters, we do not use the :class:`Signal` class in this tutorial. See the other tutorials for various +generalizations of this approach supported with ``qiskit-dynamics``. + +.. jupyter-execute:: + + from qiskit_dynamics import Solver, Signal + + nu_z = 4. + nu_x = 1. + J = 4. + Gamma = 4. + + H = zeros + for i in qubits: + X = x_ops[i] + Z = z_ops[i] + H += .5 * 2 * np.pi * nu_x * X + H += .5 * 2 * np.pi * nu_z * Z + + if N > 1: + j = i + 1 if i < (N - 1) else 0 # Nearest neighbors, with periodic boundary conditions + op = zeros + Pauli('XX')(i, j) + H += .5 * 2 * np.pi * J * op + + op = zeros + Pauli('YY')(i, j) + H += .5 * 2 * np.pi * J * op + + L_ops = [] + L_sig = [] + for i in qubits: + X = x_ops[i] + Y = y_ops[i] + L_ops.append(np.sqrt(Gamma) * 0.5 * (X + 1j * Y)) + + solver = Solver(static_hamiltonian=H, static_dissipators=L_ops) + + +3. Define the simulation parameters and solve the dynamics +---------------------------------------------------------- + +We now define the initial state for the simulation, the time span to +simulate for, and the intermediate times for which the solution is +requested. + +.. jupyter-execute:: + + from qiskit.quantum_info import DensityMatrix + + t_final = 8. / Gamma + tau = .01 + + # A density matrix with all qubits in ground state + y0 = DensityMatrix.from_label('0' * N) + + n_steps = int(np.ceil(t_final / tau)) + 1 + t_eval = np.linspace(0., t_final, n_steps) + + sol = solver.solve(t_span=[0., t_final], y0=y0, t_eval=t_eval) + + +4. Define the observables and calculate their values +---------------------------------------------------- + +Below we calculate single-qubit Pauli expectation values for each qubit +as a function of time (which define also the Bloch vector), + +.. math:: \langle\sigma_i^a(t)\rangle, + +and also the mean components of the collective Bloch vector over all +qubits, at each evaluation time, + +.. math:: \frac{1}{N}\sum_i\langle\sigma_i^a(t)\rangle. + +Since both the model and the initial state as defined above are +translation invariant (all qubits have identical parameters, and there +is no boundary), we expect the solution to remain translation invariant +as well. Hence the mean Bloch vector should be equal to any qubit’s +Bloch vector, and observing that this equality holds is a simple and +useful verification of the numerical solution that will be added in the +next section. + +.. jupyter-execute:: + + n_times = len(sol.y) + x_data = np.zeros((N, n_times)) + y_data = np.zeros((N, n_times)) + z_data = np.zeros((N, n_times)) + x_mean = np.zeros((n_times,)) + y_mean = np.zeros((n_times,)) + z_mean = np.zeros((n_times,)) + + for t_i, sol_t in enumerate(sol.y): + for qubit, obs in enumerate(x_ops): + x_data[qubit, t_i] = sol_t.expectation_value(obs).real + x_mean[t_i] = np.mean(x_data[:, t_i]) + + for qubit, obs in enumerate(y_ops): + y_data[qubit, t_i] = sol_t.expectation_value(obs).real + y_mean[t_i] = np.mean(y_data[:, t_i]) + + for qubit, obs in enumerate(z_ops): + z_data[qubit, t_i] = sol_t.expectation_value(obs).real + z_mean[t_i] = np.mean(z_data[:, t_i]) + + +5. Plot some observables and discuss the results +------------------------------------------------ + +Finally, let’s plot some of the results of our dynamical simulation, +using the single-qubit observables calculated as a function of time. We +plot both the time evolution of the collective Bloch vector, and the +Bloch vector at the final time, depicted in 3D within the Bloch sphere. +We also print a warning if the Bloch vector at the final time is not +translation invariant according to a simplified random check of two +values (taken up to a small numerical precision). + +Looking at the figures below, we see that for the above parameters the +steady state is nearly pure, with a large ground state component and a +small tilt along the negative :math:`x` axis. The direction and +magnitude of the collective Bloch vector is determined by a nontrivial +competition between the single-site terms, the qubit interactions, and +the damping. To test this statement, if you go back and vary the +interaction strength :math:`J`, you can see that the steady state may +change significantly. For example for :math:`J=1` the collective Bloch +vector will significantly tilt along :math:`+x`, while for :math:`J=3` it +will significantly shorten (the steady state becomes a mixed state), +becoming tilted along :math:`-y`. This complex dependence of the +Bloch vector on the parameters can be systematically analyzed - we encourage you to try +it! + +.. jupyter-execute:: + + from qiskit.visualization import plot_bloch_vector + import matplotlib.pyplot as plt + %matplotlib inline + + fontsize = 16 + + _, ax = plt.subplots(figsize = (10, 6)) + plt.rcParams.update({'font.size': fontsize}) + plt.plot(t_eval, x_mean, label = '$ N^{-1}\sum_i \\langle X_i \\rangle$') + plt.plot(t_eval, y_mean, label = '$ N^{-1}\sum_i \\langle Y_i \\rangle$') + plt.plot(t_eval, z_mean, label = '$ N^{-1}\sum_i \\langle Z_i \\rangle$') + plt.legend(fontsize = fontsize) + ax.set_xlabel('$t$', fontsize = fontsize) + ax.set_title('Mean Bloch vector vs. $t$', fontsize = fontsize) + + display(plot_bloch_vector([x_mean[-1], y_mean[-1], z_mean[-1]], + f'Mean Bloch vector at $t = {t_eval[-1]}$')) + + if N > 1 and ((abs(x_mean[-1]) > 1e-5 and abs(x_data[0, -1] / x_mean[-1] - 1) > 1e-5 or + (abs(z_mean[-1]) > 1e-5 and abs(z_data[1, -1] / z_mean[-1] - 1) > 1e-5))): + print("The solution at the final time appears to break translation invariance. " + "The precision of the simulation should be examined.") diff --git a/stable/0.4/_sources/tutorials/Rabi_oscillations.rst.txt b/stable/0.4/_sources/tutorials/Rabi_oscillations.rst.txt new file mode 100644 index 000000000..6346b444e --- /dev/null +++ b/stable/0.4/_sources/tutorials/Rabi_oscillations.rst.txt @@ -0,0 +1,205 @@ +Simulating Rabi oscillations with noise and decoherence +======================================================= + +In this tutorial we walk through an example of solving using +``qiskit_dynamics`` the time evolution of a qubit being driven close to +resonance. The model that we solve consists of a single qubit perturbed +by a sinusoidal drive. In addition, will consider energy relaxation and +decoherence terms modeled by using a Lindblad master equation. + +In the sections below we define a model, solve the dynamics and plot the +qubit oscillations using the following steps: + +1. Setup a :class:`.Solver` with the Hamiltonian model +2. Define the initial state and simulation times, and evolve the system state. +3. Plot the qubit state as a function of time and discuss the results. +4. Solve again the the model with jump operators for the Lindblad dissipator, and plot the results. + +In the first step below, we model the time evolution of a qubit’s state +taken as a two-level system, using the Schrödinger equation with a +Hamiltonian containing a diagonal term of frequency :math:`\nu_z` and a +transverse term of amplitude :math:`\nu_x` and harmonic driving +frequency :math:`\nu_d` (see how the Hamiltonians are derived on +`Qiskit Textbook page on Introduction to Transmon Physics +`_), + +.. math:: H = \frac{1}{2} \times 2 \pi \nu_z {Z} + 2 \pi \nu_x \cos(2 \pi \nu_d t){X}, + +where :math:`\{X,Y,Z\}` are the Pauli matrices (also written as +:math:`\sigma^a` with :math:`a\in\{x,y,z\}`). + +1. Setup the solver with the Hamiltonian model +---------------------------------------------- + +In the following, we will set :math:`\hbar=1` and fix some arbitrary +time units, with all frequency parameters scaled accordingly. Below, we +first set a few values for these frequency parameters, and then setup the +:class:`.Solver` class instance that stores and manipulates the model to be +solved, using matrices and :class:`.Signal` instances. For the +time-independent :math:`z` term we set the signal to a constant, while +for the trasverse driving term we setup a harmonic signal. + +.. jupyter-execute:: + :hide-code: + + import warnings + warnings.filterwarnings('ignore', message='', category=Warning, module='', lineno=0, append=False) + + +.. jupyter-execute:: + + import numpy as np + from qiskit.quantum_info import Operator + from qiskit_dynamics import Solver, Signal + + + nu_z = 10. + nu_x = 1. + nu_d = 9.98 # Almost on resonance with the Hamiltonian's energy levels difference, nu_z + + X = Operator.from_label('X') + Y = Operator.from_label('Y') + Z = Operator.from_label('Z') + s_p = 0.5 * (X + 1j * Y) + + solver = Solver( + static_hamiltonian=.5 * 2 * np.pi * nu_z * Z, + hamiltonian_operators=[2 * np.pi * nu_x * X], + ) + +2. Solve the system +------------------- + +We now define the initial state for the simulation, the time span to +simulate for, and the intermediate times for which the solution is +requested, and solve the evolution. + +.. jupyter-execute:: + + from qiskit.quantum_info.states import Statevector + from qiskit.quantum_info import DensityMatrix + + t_final = .5 / nu_x + tau = .005 + + y0 = Statevector([1., 0.]) + + n_steps = int(np.ceil(t_final / tau)) + 1 + t_eval = np.linspace(0., t_final, n_steps) + signals = [Signal(envelope=1., carrier_freq=nu_d)] + + sol = solver.solve(t_span=[0., t_final], y0=y0, signals=signals, t_eval=t_eval) + +3. Plot the qubit state +----------------------- + +Below we define a local function that calculates the qubit’s Pauli +expectation values as a function of time (which define also the Bloch +vector), + +.. math:: \langle X(t)\rangle, \langle Y(t)\rangle, \langle Z(t)\rangle. + +The same function plots both these three curves, and the Bloch vector at +the final time, depicted in 3D on the Bloch sphere. We will reuse this +function in the next section. + +We see that for the parameters we have defined, the qubit has completed +almost exactly a :math:`\pi`-rotation of the qubit Bloch vector about +the :math:`x` axis, from the ground to the excited state (with many +intermediate rotations of its transverse component, whose amplitude +increases and decreases). This mechanism of Rabi oscillations is the +basis for the single-qubit gates used to manipulate quantum devices - in +particular this is a realization of the :math:`X` gate. + +.. jupyter-execute:: + + from qiskit.visualization import plot_bloch_vector + import matplotlib.pyplot as plt + %matplotlib inline + + fontsize = 16 + + def plot_qubit_dynamics(sol, t_eval, X, Y, Z): + n_times = len(sol.y) + x_data = np.zeros((n_times,)) + y_data = np.zeros((n_times,)) + z_data = np.zeros((n_times,)) + + for t_i, sol_t in enumerate(sol.y): + x_data[t_i] = sol_t.expectation_value(X).real + y_data[t_i] = sol_t.expectation_value(Y).real + z_data[t_i] = sol_t.expectation_value(Z).real + + _, ax = plt.subplots(figsize = (10, 6)) + plt.rcParams.update({'font.size': fontsize}) + plt.plot(t_eval, x_data, label = '$\\langle X \\rangle$') + plt.plot(t_eval, y_data, label = '$\\langle Y \\rangle$') + plt.plot(t_eval, z_data, label = '$\\langle Z \\rangle$') + plt.legend(fontsize = fontsize) + ax.set_xlabel('$t$', fontsize = fontsize) + ax.set_title('Bloch vector vs. $t$', fontsize = fontsize) + plt.show() + + display(plot_bloch_vector([x_data[-1], y_data[-1], z_data[-1]], + f'Bloch vector at $t = {t_eval[-1]}$')) + + plot_qubit_dynamics(sol, t_eval, X, Y, Z) + +4. Redefine the model with damping and decoherence +-------------------------------------------------- + +Now we add to our simulation an environment modeled as a memory-less +(Markovian) bath, solving the Lindblad master equation with the same +Hamiltonian as before, but accounting also for energy relaxation and +decoherence terms. We simulate the dynamics to times longer than the +typical relaxation times :math:`T_1=1/\Gamma_1` and +:math:`T_{\phi}=1/\Gamma_2`. The qubit’s state has to be described using +a density matrix, now evolving according to the Lindblad master +equation, + +.. math:: \partial_t\rho = -\frac{i}{\hbar} \left[H,\rho\right] + \mathcal{D}[\rho]. + +We take the Lindblad dissipator to consist of two terms, + +.. math:: \mathcal{D}[\rho] = \mathcal{D}_1[\rho] + \mathcal{D}_2[\rho]. + +The action of energy relaxation terms describing damping into the +environment with rate :math:`\Gamma_1` are generated by + +.. math:: \mathcal{D}_1[\rho] = \Gamma_1\left(\sigma^+ \rho\sigma^- - \frac{1}{2} \{\sigma^- \sigma^+,\rho\}\right), + +with :math:`\sigma^{\pm}= \frac{1}{2}\left(X\pm i Y\right)`. + +The second dissipator describes (“pure”) dephasing with rate +:math:`\Gamma_2`, and reads + +.. math:: \mathcal{D}_2[\rho] = \Gamma_2\left(Z \rho Z - \rho\right). + +We use the function defined above for calculating the Bloch vector +components, which can be done since in ``qiskit`` and in +``qiskit-dynamics`` the syntax of many functions is identical for both +state vectors and density matrices. The shrinking of the qubit’s state +within the Bloch sphere due to the incoherent evolution can be clearly +seen in the plots below. + +.. jupyter-execute:: + + Gamma_1 = .8 + Gamma_2 = .2 + + t_final = 5.5 / max(Gamma_1, Gamma_2) + + y0 = DensityMatrix.from_label('0') + solver = Solver( + static_hamiltonian=.5 * 2 * np.pi * nu_z * Z, + hamiltonian_operators=[.5 * 2 * np.pi * nu_x * X], + static_dissipators=[np.sqrt(Gamma_1) * s_p, np.sqrt(Gamma_2) * Z] + ) + + n_steps = int(np.ceil(t_final / tau)) + 1 + t_eval = np.linspace(0., t_final, n_steps) + signals = [Signal(envelope=1., carrier_freq=nu_d)] + + sol = solver.solve(t_span=[0., t_final], y0=y0, signals=signals, t_eval=t_eval) + + plot_qubit_dynamics(sol, t_eval, X, Y, Z) diff --git a/stable/0.4/_sources/tutorials/dynamics_backend.rst.txt b/stable/0.4/_sources/tutorials/dynamics_backend.rst.txt new file mode 100644 index 000000000..f178c35c1 --- /dev/null +++ b/stable/0.4/_sources/tutorials/dynamics_backend.rst.txt @@ -0,0 +1,500 @@ +.. Substitution to reduce text length. +.. |CRHamitonian| replace:: :class:`~qiskit_experiments.library.characterization.CrossResonanceHamiltonian` + +.. _dynamics backend: + +Simulating backends at the pulse-level with :class:`.DynamicsBackend` +===================================================================== + +In this tutorial we walk through how to use the :class:`.DynamicsBackend` class as a Qiskit +Dynamics-backed, pulse-level simulator of a real backend. In particular, we demonstrate how to +configure a :class:`.DynamicsBackend` to simulate pulse schedules, circuits whose gates have pulse +definitions, and calibration and characterization experiments from Qiskit Experiments. + +The sections of this tutorial are as follows: + +1. Configure Dynamics to use JAX. +2. Instantiating a minimally-configured :class:`.DynamicsBackend` with a 2 qubit model. +3. Simulating pulse schedules on the :class:`.DynamicsBackend`. +4. Simulating circuits at the pulse level using the :class:`.DynamicsBackend`. +5. Simulating single-qubit calibration processes via Qiskit Experiments. +6. Simulating 2 qubit interaction characterization via the |CRHamitonian| experiment. + +1. Configure Dynamics to use JAX +-------------------------------- + +Note that the :class:`.DynamicsBackend` internally performs just-in-time compilation automatically +when configured to use JAX. See the :ref:`User Guide entry on using JAX with Dynamics ` for more information. + +.. jupyter-execute:: + :hide-code: + + import warnings + warnings.filterwarnings('ignore', message='', category=Warning, module='', lineno=0, append=False) + +.. jupyter-execute:: + + # Configure to use JAX internally + import jax + jax.config.update("jax_enable_x64", True) + jax.config.update("jax_platform_name", "cpu") + from qiskit_dynamics.array import Array + Array.set_default_backend("jax") + +2. Instantiating a minimally-configured :class:`.DynamicsBackend` with a 2 qubit model +-------------------------------------------------------------------------------------- + +To create the :class:`.DynamicsBackend`, first specify a :class:`.Solver` instance using the model +details. Note that the choice of model depends on the type of device you wish to simulate. Here, we +will use a :math:`2` qubit fixed-frequency transmon model with fixed coupling, with the following +Hamiltonian (see the `Qiskit Textbook page on Circuit Quantum Electrodynamics +`_ for details on how transmon +Hamiltonians are derived): + +.. math:: + + H(t) = 2 \pi \nu_0 &N_0 + \pi \alpha_0 N_0 (N_0 - I) + 2 \pi \nu_1 N_1 + + \pi \alpha_1 N_1(N_1 - I) + 2 \pi J (a_0 + a_0^\dagger)(a_1 + a_1^\dagger) \\ + & + 2 \pi r_0 s_0(t)(a_0 + a_0^\dagger) + 2 \pi r_1 s_1(t)(a_1 + a_1^\dagger), + +where + +- :math:`\nu_0` and :math:`\nu_1` are the qubit frequencies, +- :math:`\alpha_0` and :math:`\alpha_1` are the qubit anharmonicities, +- :math:`J` is the coupling strength, +- :math:`r_0` and :math:`r_1` are the Rabi strengths, and :math:`s_0(t)` and :math:`s_1(t)` are the + drive signals, +- :math:`a_j` and :math:`a_j^\dagger` are the lowering and raising operators for qubit :math:`j`, + and +- :math:`N_0` and :math:`N_1` are the number operators for qubits :math:`0` and :math:`1` + respectively. + +.. jupyter-execute:: + + import numpy as np + + dim = 3 + + v0 = 4.86e9 + anharm0 = -0.32e9 + r0 = 0.22e9 + + v1 = 4.97e9 + anharm1 = -0.32e9 + r1 = 0.26e9 + + J = 0.002e9 + + a = np.diag(np.sqrt(np.arange(1, dim)), 1) + adag = np.diag(np.sqrt(np.arange(1, dim)), -1) + N = np.diag(np.arange(dim)) + + ident = np.eye(dim, dtype=complex) + full_ident = np.eye(dim**2, dtype=complex) + + N0 = np.kron(ident, N) + N1 = np.kron(N, ident) + + a0 = np.kron(ident, a) + a1 = np.kron(a, ident) + + a0dag = np.kron(ident, adag) + a1dag = np.kron(adag, ident) + + + static_ham0 = 2 * np.pi * v0 * N0 + np.pi * anharm0 * N0 * (N0 - full_ident) + static_ham1 = 2 * np.pi * v1 * N1 + np.pi * anharm1 * N1 * (N1 - full_ident) + + static_ham_full = static_ham0 + static_ham1 + 2 * np.pi * J * ((a0 + a0dag) @ (a1 + a1dag)) + + drive_op0 = 2 * np.pi * r0 * (a0 + a0dag) + drive_op1 = 2 * np.pi * r1 * (a1 + a1dag) + +Construct the :class:`.Solver` using the model details, including parameters necessary for pulse +simulation. See the :class:`.Solver` documentation, as well as the :ref:`tutorial example ` for more details. Here, we choose to perform the simulation in the rotating frame of the +static Hamiltonian, which provides performance improvements (see the user guide entry on +:ref:`configuring simulations for performance `). Note that the measurement +outcomes of :meth:`.DynamicsBackend.run` are independent of the choice of rotating frame in the +:class:`.Solver`, and as such we are free to choose the rotating frame that provides the best +performance. + +.. jupyter-execute:: + + from qiskit_dynamics import Solver + + # build solver + dt = 1/4.5e9 + + solver = Solver( + static_hamiltonian=static_ham_full, + hamiltonian_operators=[drive_op0, drive_op1, drive_op0, drive_op1], + rotating_frame=static_ham_full, + hamiltonian_channels=["d0", "d1", "u0", "u1"], + channel_carrier_freqs={"d0": v0, "d1": v1, "u0": v1, "u1": v0}, + dt=dt, + ) + +Next, instantiate the :class:`.DynamicsBackend`. The ``solver`` is used for simulation, +``subsystem_dims`` indicates how the full system decomposes for measurement data computation, and +``solver_options`` are consistent options used by :meth:`.Solver.solve` when simulating the +differential equation. The full list of allowable ``solver_options`` are the arguments to +:func:`.solve_ode`. + +Note that, to enable the internal automatic jit-compilation, we choose a JAX integration method. +Furthermore, note that in the solver options we set the max step size to the pulse sample width +``dt`` via the ``"hmax"`` argument for the method ``"jax_odeint"``. This is important for preventing +variable step solvers from accidentally stepping over pulses in schedules with long idle times. + +.. jupyter-execute:: + + from qiskit_dynamics import DynamicsBackend + + # Consistent solver option to use throughout notebook + solver_options = {"method": "jax_odeint", "atol": 1e-6, "rtol": 1e-8, "hmax": dt} + + backend = DynamicsBackend( + solver=solver, + subsystem_dims=[dim, dim], # for computing measurement data + solver_options=solver_options, # to be used every time run is called + ) + +Alternatively to the above, the :meth:`.DynamicsBackend.from_backend` method can be used to build +the :class:`.DynamicsBackend` from an existing backend. The above model, which was built manually, +was taken from qubits :math:`0` and :math:`1` of ``almaden``. + +3. Simulating pulse schedules on the :class:`.DynamicsBackend` +-------------------------------------------------------------- + +With the above backend, we can already simulate a list of pulse schedules. The code below generates +a list of schedules specifying experiments on qubit :math:`0`. The schedule is chosen to demonstrate +that the usual instructions work on the :class:`.DynamicsBackend`. + +.. note:: + + In the following constructed schedule, measurement is performed with an + :class:`~qiskit.pulse.instructions.Acquire` instruction of duration ``1``. Measurements in + :class:`.DynamicsBackend` are computed projectively at the start time of the acquire + instructions, and the effects of measurement stimulus through + :class:`~qiskit.pulse.channels.MeasureChannel`\s are not simulated unless explicitly put into + the model by the user. As such, the lack of :class:`~qiskit.pulse.channels.MeasureChannel` + stimulus, and the duration of the :class:`~qiskit.pulse.instructions.Acquire` instruction has no + impact on the returned results. + + +.. jupyter-execute:: + + %%time + + from qiskit import pulse + + sigma = 128 + num_samples = 256 + + schedules = [] + + for amp in np.linspace(0., 1., 10): + gauss = pulse.library.Gaussian( + num_samples, amp, sigma, name="Parametric Gauss" + ) + + with pulse.build() as schedule: + with pulse.align_sequential(): + pulse.play(gauss, pulse.DriveChannel(0)) + pulse.shift_phase(0.5, pulse.DriveChannel(0)) + pulse.shift_frequency(0.1, pulse.DriveChannel(0)) + pulse.play(gauss, pulse.DriveChannel(0)) + pulse.acquire(duration=1, qubit_or_channel=0, register=pulse.MemorySlot(0)) + + schedules.append(schedule) + + job = backend.run(schedules, shots=100) + result = job.result() + +Visualize one of the schedules. + +.. jupyter-execute:: + + schedules[3].draw() + +Retrieve the counts for one of the experiments as would be done using the results object from a real +backend. + +.. jupyter-execute:: + + result.get_counts(3) + +4. Simulating circuits at the pulse level using the :class:`.DynamicsBackend` +----------------------------------------------------------------------------- + +For the :class:`.DynamicsBackend` to simulate a circuit, each circuit element must have a +corresponding pulse schedule. These schedules can either be specified in the gates themselves, by +attaching calibrations, or by adding instructions to the :class:`~qiskit.transpiler.Target` +contained in the :class:`.DynamicsBackend`. + +4.1 Simulating circuits with attached calibrations +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Build a simple circuit. Here we build one consisting of a single Hadamard gate on qubit :math:`0`, +followed by measurement. + +.. jupyter-execute:: + + from qiskit import QuantumCircuit + + circ = QuantumCircuit(1, 1) + circ.h(0) + circ.measure([0], [0]) + + circ.draw("mpl") + +Next, attach a calibration for the Hadamard gate on qubit :math:`0` to the circuit. Note that here +we are only demonstrating the mechanics of adding a calibration; we have not attempted to calibrate +the schedule to implement the Hadamard gate with high fidelity. + +.. jupyter-execute:: + + with pulse.build() as h_q0: + pulse.play( + pulse.library.Gaussian(duration=256, amp=0.2, sigma=50, name="custom"), + pulse.DriveChannel(0) + ) + + circ.add_calibration("h", qubits=[0], schedule=h_q0) + +Call run on the circuit, and get counts as usual. + +.. jupyter-execute:: + + %time res = backend.run(circ).result() + + res.get_counts(0) + +4.2 Simulating circuits via gate definitions in the backend :class:`~qiskit.transpiler.Target` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Alternatively to the above work flow, add the above schedule as the pulse-level definition of the +Hadamard gate on qubit :math:`0` to `backend.target`, which impacts how jobs are transpiled for the +backend. See the :class:`~qiskit.transpiler.Target` class documentation for further information. + +.. jupyter-execute:: + + from qiskit.circuit.library import HGate + from qiskit.transpiler import InstructionProperties + + backend.target.add_instruction(HGate(), {(0,): InstructionProperties(calibration=h_q0)}) + +Rebuild the same circuit, however this time we do not need to add the calibration for the Hadamard +gate to the circuit object. + +.. jupyter-execute:: + + circ2 = QuantumCircuit(1, 1) + circ2.h(0) + circ2.measure([0], [0]) + + %time result = backend.run(circ2).result() + +.. jupyter-execute:: + + result.get_counts(0) + +5. Simulating single-qubit calibration processes via Qiskit Experiments +----------------------------------------------------------------------- + +Next, we perform rough calibrations for ``X`` and ``SX`` gates on both qubits modeled in the +:class:`.DynamicsBackend`, following the single-qubit calibration tutorial for Qiskit Experiments. + +5.1 Configure the :class:`~qiskit.transpiler.Target` to include single qubit instructions +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +To enable running of the single qubit experiments, we add the following to the ``target``: + +- Qubit frequency properties (needed by experiments like + :class:`~qiskit_experiments.library.calibration.rough_frequency.RoughFrequencyCal`). Note that + setting the qubit frequencies in the ``target`` does not impact the behaviour of the + :class:`.DynamicsBackend` itself. It is purely a data field that does not impact functionality. + Previously set frequency properties, such as ``channel_carrier_freqs`` in the :class:`.Solver`, + will remain unchanged. Here, we set the frequencies to the undressed frequencies in the model. +- ``X`` and ``SX`` gate instructions, which the transpiler needs to check are supported by the + backend. +- Add definitions of ``RZ`` gates as phase shifts. These instructions control the phase of the drive + channels, as well as any control channels acting on a given qubit. +- Add a ``CX`` gate between qubits :math:`(0, 1)` and :math:`(1, 0)`. While this tutorial will not + be utilizing it, this ensures that validation steps checking that the device is fully connected + will pass. + +.. jupyter-execute:: + + from qiskit.circuit.library import XGate, SXGate, RZGate, CXGate + from qiskit.circuit import Parameter + from qiskit.providers.backend import QubitProperties + + target = backend.target + + # qubit properties + target.qubit_properties = [QubitProperties(frequency=v0), QubitProperties(frequency=v1)] + + # add instructions + target.add_instruction(XGate(), properties={(0,): None, (1,): None}) + target.add_instruction(SXGate(), properties={(0,): None, (1,): None}) + + target.add_instruction(CXGate(), properties={(0, 1): None, (1, 0): None}) + + # Add RZ instruction as phase shift for drag cal + phi = Parameter("phi") + with pulse.build() as rz0: + pulse.shift_phase(phi, pulse.DriveChannel(0)) + pulse.shift_phase(phi, pulse.ControlChannel(1)) + + with pulse.build() as rz1: + pulse.shift_phase(phi, pulse.DriveChannel(1)) + pulse.shift_phase(phi, pulse.ControlChannel(0)) + + target.add_instruction( + RZGate(phi), + {(0,): InstructionProperties(calibration=rz0), (1,): InstructionProperties(calibration=rz1)} + ) + +5.2 Prepare :class:`~qiskit_experiments.calibration_management.calibrations.Calibrations` object +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Next, prepare the :class:`~qiskit_experiments.calibration_management.calibrations.Calibrations` +object. Here we use the +:class:`~qiskit_experiments.calibration_management.basis_gate_library.FixedFrequencyTransmon` +template library to initialize our calibrations. + +.. jupyter-execute:: + + import pandas as pd + from qiskit_experiments.calibration_management.calibrations import Calibrations + from qiskit_experiments.calibration_management.basis_gate_library import FixedFrequencyTransmon + + cals = Calibrations(libraries=[FixedFrequencyTransmon(basis_gates=['x', 'sx'])]) + + pd.DataFrame(**cals.parameters_table(qubit_list=[0, ()])) + +5.3 Rough amplitude calibration +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Next, run a rough amplitude calibration for ``X`` and ``SX`` gates for both qubits. First, build the +experiments. + +.. jupyter-execute:: + + from qiskit_experiments.library.calibration import RoughXSXAmplitudeCal + + # rabi experiments for qubit 0 + rabi0 = RoughXSXAmplitudeCal([0], cals, backend=backend, amplitudes=np.linspace(-0.2, 0.2, 27)) + + # rabi experiments for qubit 1 + rabi1 = RoughXSXAmplitudeCal([1], cals, backend=backend, amplitudes=np.linspace(-0.2, 0.2, 27)) + +Run the Rabi experiments. + +.. jupyter-execute:: + + %%time + rabi0_data = rabi0.run().block_for_results() + rabi1_data = rabi1.run().block_for_results() + +Plot the results. + +.. jupyter-execute:: + + rabi0_data.figure(0) + +.. jupyter-execute:: + + rabi1_data.figure(0) + +Observe the updated parameters for qubit 0. + +.. jupyter-execute:: + + pd.DataFrame(**cals.parameters_table(qubit_list=[0, ()], parameters="amp")) + +5.4 Rough Drag parameter calibration +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Run rough Drag parameter calibration for the ``X`` and ``SX`` gates. This follows the same procedure +as above. + +.. jupyter-execute:: + + from qiskit_experiments.library.calibration import RoughDragCal + + cal_drag0 = RoughDragCal([0], cals, backend=backend, betas=np.linspace(-20, 20, 15)) + cal_drag1 = RoughDragCal([1], cals, backend=backend, betas=np.linspace(-20, 20, 15)) + + cal_drag0.set_experiment_options(reps=[3, 5, 7]) + cal_drag1.set_experiment_options(reps=[3, 5, 7]) + + cal_drag0.circuits()[5].draw(output="mpl") + +.. jupyter-execute:: + + %%time + drag0_data = cal_drag0.run().block_for_results() + drag1_data = cal_drag1.run().block_for_results() + +.. jupyter-execute:: + + drag0_data.figure(0) + + +.. jupyter-execute:: + + drag1_data.figure(0) + +The updated calibrations object: + +.. jupyter-execute:: + + pd.DataFrame(**cals.parameters_table(qubit_list=[0, ()], parameters="amp")) + +6. Simulating 2 qubit interaction characterization via the |CRHamitonian| experiment +------------------------------------------------------------------------------------ + +Finally, simulate the |CRHamitonian| characterization experiment. + +First, we further configure the backend to run this experiment. This requires defining the control +channel map, which is a dictionary mapping control-target qubit index pairs (given as a tuple) to +the control channel index used to drive the corresponding cross-resonance interaction. This is +required by the experiment to determine which channel to drive for each control-target pair. + +.. jupyter-execute:: + + # set the control channel map + backend.set_options(control_channel_map={(0, 1): 0, (1, 0): 1}) + +Build the characterization experiment object, and update gate definitions in ``target`` with the +values for the single qubit gates calibrated above. + +.. jupyter-execute:: + + from qiskit_experiments.library import CrossResonanceHamiltonian + + cr_ham_experiment = CrossResonanceHamiltonian( + physical_qubits=(0, 1), + durations=np.linspace(1e-7, 1e-6, 17), + backend=backend + ) + + backend.target.update_from_instruction_schedule_map(cals.get_inst_map()) + +.. jupyter-execute:: + + cr_ham_experiment.circuits()[10].draw("mpl") + +Run the simulation. + +.. jupyter-execute:: + + %time data_cr = cr_ham_experiment.run().block_for_results() + + +.. jupyter-execute:: + + data_cr.figure(0) diff --git a/stable/0.4/_sources/tutorials/index.rst.txt b/stable/0.4/_sources/tutorials/index.rst.txt new file mode 100644 index 000000000..6acaf69de --- /dev/null +++ b/stable/0.4/_sources/tutorials/index.rst.txt @@ -0,0 +1,19 @@ +################## +Dynamics Tutorials +################## + + +.. toctree:: + :maxdepth: 1 + + Rabi_oscillations.rst + Lindblad_dynamics_simulation.rst + qiskit_pulse.rst + optimizing_pulse_sequence.rst + dynamics_backend.rst + + +.. Hiding - Indices and tables + :ref:`genindex` + :ref:`modindex` + :ref:`search` diff --git a/stable/0.4/_sources/tutorials/optimizing_pulse_sequence.rst.txt b/stable/0.4/_sources/tutorials/optimizing_pulse_sequence.rst.txt new file mode 100644 index 000000000..bbc25951c --- /dev/null +++ b/stable/0.4/_sources/tutorials/optimizing_pulse_sequence.rst.txt @@ -0,0 +1,391 @@ +.. _optimization tutorial: + +Gradient optimization of a pulse sequence +========================================= + +Here, we walk through an example of optimizing a single-qubit gate using +``qiskit_dynamics``. This tutorial requires JAX - see the user guide +on :ref:`How-to use JAX with qiskit-dynamics `. + +We will optimize an :math:`X`-gate on a model of a qubit system using +the following steps: + +1. Configure ``qiskit-dynamics`` to work with the JAX backend. +2. Setup a :class:`.Solver` instance with the model of the system. +3. Define a pulse sequence parameterization to optimize over. +4. Define a gate fidelity function. +5. Define an objective function for optimization. +6. Use JAX to differentiate the objective, then do the gradient optimization. +7. Repeat the :math:`X`-gate optimization, alternatively using pulse schedules to specify the control sequence. + + +1. Configure to use JAX +----------------------- + +First, set JAX to operate in 64-bit mode, and set JAX as the default +backend using :class:`.Array` for performing array operations. +This is necessary to enable automatic differentiation of the Qiskit Dynamics code +in this tutorial. See the user guide entry on using JAX +for a more detailed explanation of why this step is necessary. + +.. jupyter-execute:: + + import jax + jax.config.update("jax_enable_x64", True) + + # tell JAX we are using CPU + jax.config.update('jax_platform_name', 'cpu') + + from qiskit_dynamics.array import Array + Array.set_default_backend('jax') + + +2. Setup the solver +------------------- + +Here we will setup a :class:`.Solver` with a simple model of a qubit. The +Hamiltonian is: + +.. math:: H(t) = 2 \pi \nu \frac{Z}{2} + 2 \pi r s(t) \frac{X}{2} + +In the above: + +- :math:`\nu` is the qubit frequency, +- :math:`r` is the drive strength, +- :math:`s(t)` is the drive signal which we will optimize, and +- :math:`X` and :math:`Z` are the Pauli X and Z operators. + +We will setup the problem to be in the rotating frame of the drift term. + +Also note: The :class:`.Solver` is initialized *without* signals, as we will +update these and optimize over this later. + +.. jupyter-execute:: + + import numpy as np + from qiskit.quantum_info import Operator + from qiskit_dynamics import Solver + + v = 5. + r = 0.02 + + static_hamiltonian = 2 * np.pi * v * Operator.from_label('Z') / 2 + drive_term = 2 * np.pi * r * Operator.from_label('X') / 2 + + ham_solver = Solver( + hamiltonian_operators=[drive_term], + static_hamiltonian=static_hamiltonian, + rotating_frame=static_hamiltonian, + ) + + +3. Define a pulse sequence parameterization to optimize over +------------------------------------------------------------ + +We will optimize over signals that are: + +- On resonance with piecewise constant envelopes, +- Envelopes bounded between :math:`[-1, 1]`, +- Envelopes are smooth, in the sense that the change between adjacent + samples is small, and +- Envelope starts and ends at :math:`0`. + +In setting up our parameterization, we need t keep in mind that we will +use the BFGS optimization routine, and hence: + +- Optimization parameters must be *unconstrained*. +- Parameterization must be JAX-differentiable. + +We implement a parameterization as follows: + +- Input: Array ``x`` of real values. +- “Normalize” ``x`` by applying a JAX-differentiable function from + :math:`\mathbb{R} \rightarrow [-1, 1]`. +- Pad the normalized ``x`` with a :math:`0.` to start. +- “Smoothen” the above via convolution. +- Construct the signal using the above as the samples for a + piecewise-constant envelope, with carrier frequency on resonance. + +We remark that there are many other parameterizations that may achieve +the same ends, and may have more efficient strategies for achieving a +value of :math:`0` at the beginning and end of the pulse. This is only +meant to demonstrate the need for such an approach, and one simple +example of one. + +.. jupyter-execute:: + + from qiskit_dynamics import DiscreteSignal + from qiskit_dynamics.array import Array + from qiskit_dynamics.signals import Convolution + + # define convolution filter + def gaus(t): + sigma = 15 + _dt = 0.1 + return 2.*_dt/np.sqrt(2.*np.pi*sigma**2)*np.exp(-t**2/(2*sigma**2)) + + convolution = Convolution(gaus) + + # define function mapping parameters to signals + def signal_mapping(params): + samples = Array(params) + + # map samples into [-1, 1] + bounded_samples = np.arctan(samples) / (np.pi / 2) + + # pad with 0 at beginning + padded_samples = np.append(Array([0], dtype=complex), bounded_samples) + + # apply filter + output_signal = convolution(DiscreteSignal(dt=1., samples=padded_samples)) + + # set carrier frequency to v + output_signal.carrier_freq = v + + return output_signal + +Observe, for example, the signal generated when all parameters are +:math:`10^8`: + +.. jupyter-execute:: + + signal = signal_mapping(np.ones(80) * 1e8) + signal.draw(t0=0., tf=signal.duration * signal.dt, n=1000, function='envelope') + + +4. Define gate fidelity +----------------------- + +We will optimize an :math:`X` gate, and define the fidelity of the unitary :math:`U` +implemented by the pulse via the standard fidelity measure: + +.. math:: f(U) = \frac{|\text{Tr}(XU)|^2}{4} + +.. jupyter-execute:: + + X_op = Array(Operator.from_label('X')) + + def fidelity(U): + U = Array(U) + + return np.abs(np.sum(X_op * U))**2 / 4. + +5. Define the objective function +-------------------------------- + +The function we want to optimize consists of: + +- Taking a list of input samples and applying the signal mapping. +- Simulating the Schrodinger equation over the length of the pulse + sequence. +- Computing and return the infidelity (we minimize :math:`1-f(U)`). + +.. jupyter-execute:: + + def objective(params): + + # apply signal mapping and set signals + signal = signal_mapping(params) + + # Simulate + results = ham_solver.solve( + y0=np.eye(2, dtype=complex), + t_span=[0, signal.duration * signal.dt], + signals=[signal], + method='jax_odeint', + atol=1e-8, + rtol=1e-8 + ) + U = results.y[-1] + + # compute and return infidelity + fid = fidelity(U) + return 1. - fid.data + +6. Perform JAX transformations and optimize +------------------------------------------- + +Finally, we gradient optimize the objective: + +- Use ``jax.value_and_grad`` to transform the objective into a function + that computes both the objective and the gradient. +- Use ``jax.jit`` to just-in-time compile the function into optimized + `XLA `__ code. For the initial cost of + performing the compilation, this speeds up each call of the function, + speeding up the optimization. +- Call ``scipy.optimize.minimize`` with the above, with + ``method='BFGS'`` and ``jac=True`` to indicate that the passed + objective also computes the gradient. + +.. jupyter-execute:: + + from jax import jit, value_and_grad + from scipy.optimize import minimize + + jit_grad_obj = jit(value_and_grad(objective)) + + initial_guess = np.random.rand(80) - 0.5 + + opt_results = minimize(fun=jit_grad_obj, x0=initial_guess, jac=True, method='BFGS') + print(opt_results.message) + print('Number of function evaluations: ' + str(opt_results.nfev)) + print('Function value: ' + str(opt_results.fun)) + + +The gate is optimized to an :math:`X` gate, with deviation within the +numerical accuracy of the solver. + +We can draw the optimized signal, which is retrieved by applying the +``signal_mapping`` to the optimized parameters. + +.. jupyter-execute:: + + opt_signal = signal_mapping(opt_results.x) + + opt_signal.draw( + t0=0, + tf=opt_signal.duration * opt_signal.dt, + n=1000, + function='envelope', + title='Optimized envelope' + ) + + +Summing the signal samples yields approximately :math:`\pm 50`, which is +equivalent to what one would expect based on a rotating wave +approximation analysis. + +.. jupyter-execute:: + + opt_signal.samples.sum() + + +7. Repeat the :math:`X`-gate optimization, alternatively using pulse schedules to specify the control sequence. +---------------------------------------------------------------------------------------------------------------- + +Here, we perform the optimization again, however now we specify the parameterized control sequence +to optimize as a pulse schedule. + +We construct a Gaussian square pulse as a :class:`~qiskit.pulse.library.ScalableSymbolicPulse` +instance, parameterized by ``sigma`` and ``width``. Although qiskit pulse provides a +:class:`~qiskit.pulse.library.GaussianSquare`, this class is not JAX compatible. See the user guide +entry on :ref:`JAX-compatible pulse schedules `. + +.. jupyter-execute:: + + import sympy as sym + from qiskit import pulse + + def lifted_gaussian( + t: sym.Symbol, + center, + t_zero, + sigma, + ) -> sym.Expr: + t_shifted = (t - center).expand() + t_offset = (t_zero - center).expand() + + gauss = sym.exp(-((t_shifted / sigma) ** 2) / 2) + offset = sym.exp(-((t_offset / sigma) ** 2) / 2) + + return (gauss - offset) / (1 - offset) + + def gaussian_square_generated_by_pulse(params): + + sigma, width = params + _t, _duration, _amp, _sigma, _width, _angle = sym.symbols( + "t, duration, amp, sigma, width, angle" + ) + _center = _duration / 2 + + _sq_t0 = _center - _width / 2 + _sq_t1 = _center + _width / 2 + + _gaussian_ledge = lifted_gaussian(_t, _sq_t0, -1, _sigma) + _gaussian_redge = lifted_gaussian(_t, _sq_t1, _duration + 1, _sigma) + + envelope_expr = ( + _amp + * sym.exp(sym.I * _angle) + * sym.Piecewise( + (_gaussian_ledge, _t <= _sq_t0), (_gaussian_redge, _t >= _sq_t1), (1, True) + ) + ) + + # we need to set disable_validation True to enable jax-jitting. + pulse.ScalableSymbolicPulse.disable_validation = True + + return pulse.ScalableSymbolicPulse( + pulse_type="GaussianSquare", + duration=230, + amp=1, + angle=0, + parameters={"sigma": sigma, "width": width}, + envelope=envelope_expr, + constraints=sym.And(_sigma > 0, _width >= 0, _duration >= _width), + valid_amp_conditions=sym.Abs(_amp) <= 1.0, + ) + +Next, we construct a pulse schedule using the above parametrized Gaussian square pulse, convert it +to a signal, and simulate the equation over the length of the pulse sequence. + +.. jupyter-execute:: + + from qiskit_dynamics.pulse import InstructionToSignals + + dt = 0.222 + w = 5. + + def objective(params): + + instance = gaussian_square_generated_by_pulse(params) + + with pulse.build() as Xp: + pulse.play(instance, pulse.DriveChannel(0)) + + converter = InstructionToSignals(dt, carriers={"d0": w}) + signal = converter.get_signals(Xp) + + result = ham_solver.solve( + y0=np.eye(2, dtype=complex), + t_span=[0, instance.duration * dt], + signals=[signal], + method='jax_odeint', + atol=1e-8, + rtol=1e-8 + ) + return 1. - fidelity(Array(result[0].y[-1])).data + + +We set the initial values of ``sigma`` and ``width`` for the optimization as +``initial_params = np.array([10, 10])``. + +.. jupyter-execute:: + + initial_params = np.array([10, 10]) + gaussian_square_generated_by_pulse(initial_params).draw() + +.. jupyter-execute:: + + from jax import jit, value_and_grad + from scipy.optimize import minimize + + jit_grad_obj = jit(value_and_grad(objective)) + + initial_params = np.array([10,10]) + + + opt_results = minimize(fun=jit_grad_obj, x0=initial_params, jac=True, method='BFGS') + + print(opt_results.message) + print(f"Optimized Sigma is {opt_results.x[0]} and Width is {opt_results.x[1]}") + print('Number of function evaluations: ' + str(opt_results.nfev)) + print('Function value: ' + str(opt_results.fun)) + + + +We can draw the optimized pulse, whose parameters are retrieved by ``opt_results.x``. + +.. jupyter-execute:: + + gaussian_square_generated_by_pulse(opt_results.x).draw() \ No newline at end of file diff --git a/stable/0.4/_sources/tutorials/qiskit_pulse.rst.txt b/stable/0.4/_sources/tutorials/qiskit_pulse.rst.txt new file mode 100644 index 000000000..2725c5a88 --- /dev/null +++ b/stable/0.4/_sources/tutorials/qiskit_pulse.rst.txt @@ -0,0 +1,175 @@ +Simulating Qiskit Pulse Schedules with Qiskit Dynamics +====================================================== + +This tutorial shows how to use Qiskit Dynamics to simulate a Pulse schedule +with a simple model of a qubit. The +qubit is modeled by the drift hamiltonian + +.. math:: + + H_\text{drift} = \frac{\omega}{2} Z + + +to which we apply the drive + +.. math:: + + H_\text{drive}(t) = \frac{r\,\Omega(t)}{2} X + +Here, :math:`\Omega(t)` is the drive signal which we will create using +Qiskit pulse. The factor :math:`r` is the strength with which the drive +signal drives the qubit. We begin by creating a pulse schedule with a +``sx`` gate followed by a phase shift on the drive so that the following +pulse creates a ``sy`` rotation. Therefore, if the qubit begins in the +ground state we expect that this second pulse will not have any effect +on the qubit. This situation is simulated with the following steps: + +1. Create the pulse schedule +2. Converting pulse schedules to a :class:`.Signal` +3. Create the system model, configured to simulate pulse schedules +4. Simulate the pulse schedule using the model + +1. Create the pulse schedule +---------------------------- + +First, we use the pulse module in Qiskit to create a pulse schedule. + +.. jupyter-execute:: + + import numpy as np + import qiskit.pulse as pulse + + # Strength of the Rabi-rate in GHz. + r = 0.1 + + # Frequency of the qubit transition in GHz. + w = 5. + + # Sample rate of the backend in ns. + dt = 1 / 4.5 + + # Define gaussian envelope function to approximately implement an sx gate. + amp = 1. / 1.75 + sig = 0.6985/r/amp + T = 4*sig + duration = int(T / dt) + beta = 2.0 + + with pulse.build(name="sx-sy schedule") as sxp: + pulse.play(pulse.Drag(duration, amp, sig / dt, beta), pulse.DriveChannel(0)) + pulse.shift_phase(np.pi/2, pulse.DriveChannel(0)) + pulse.play(pulse.Drag(duration, amp, sig / dt, beta), pulse.DriveChannel(0)) + + sxp.draw() + + +2. Convert the pulse schedule to a :class:`.Signal` +--------------------------------------------------- + +Qiskit Dynamics has functionality for converting pulse schedule to instances +of :class:`.Signal`. This is done using the pulse instruction to signal +converter :class:`.InstructionToSignals`. This converter needs to know the +sample rate of the arbitrary waveform generators creating the signals, +i.e. ``dt``, as well as the carrier frequency of the signals, +i.e. ``w``. The plot below shows the envelopes and the signals resulting +from this conversion. The dashed line shows the time at which the +virtual ``Z`` gate is applied. + +.. jupyter-execute:: + + from matplotlib import pyplot as plt + from qiskit_dynamics.pulse import InstructionToSignals + + plt.rcParams["font.size"] = 16 + + converter = InstructionToSignals(dt, carriers={"d0": w}) + + signals = converter.get_signals(sxp) + fig, axs = plt.subplots(1, 2, figsize=(14, 4.5)) + for ax, title in zip(axs, ["envelope", "signal"]): + signals[0].draw(0, 2*T, 2000, title, axis=ax) + ax.set_xlabel("Time (ns)") + ax.set_ylabel("Amplitude") + ax.set_title(title) + ax.vlines(T, ax.get_ylim()[0], ax.get_ylim()[1], "k", linestyle="dashed") + +.. _pulse solver: + +3. Create the system model +-------------------------- + +We now setup a :class:`.Solver` instance with the desired Hamiltonian information, +and configure it to simulate pulse schedules. This requires specifying +which channels act on which operators, channel carrier frequencies, and sample width ``dt``. +Additionally, we setup this solver in the rotating frame and perform the +rotating wave approximation. + +.. jupyter-execute:: + + from qiskit.quantum_info.operators import Operator + from qiskit_dynamics import Solver + + # construct operators + X = Operator.from_label('X') + Z = Operator.from_label('Z') + + drift = 2 * np.pi * w * Z/2 + operators = [2 * np.pi * r * X/2] + + # construct the solver + hamiltonian_solver = Solver( + static_hamiltonian=drift, + hamiltonian_operators=operators, + rotating_frame=drift, + rwa_cutoff_freq=2 * 5.0, + hamiltonian_channels=['d0'], + channel_carrier_freqs={'d0': w}, + dt=dt + ) + +4. Simulate the pulse schedule using the model +---------------------------------------------- + +In the last step we perform the simulation and plot the results. Note that, as we have +configured ``hamiltonian_solver`` to simulate pulse schedules, we pass the schedule ``xp`` +directly to the ``signals`` argument of the ``solve`` method. Equivalently, ``signals`` +generated by ``converter.get_signals`` above can also be passed to the ``signals`` argument +and in this case should produce identical behavior. + +.. jupyter-execute:: + + from qiskit.quantum_info.states import Statevector + + # Start the qubit in its ground state. + y0 = Statevector([1., 0.]) + + %time sol = hamiltonian_solver.solve(t_span=[0., 2*T], y0=y0, signals=sxp, atol=1e-8, rtol=1e-8) + + +.. jupyter-execute:: + + def plot_populations(sol): + pop0 = [psi.probabilities()[0] for psi in sol.y] + pop1 = [psi.probabilities()[1] for psi in sol.y] + + fig = plt.figure(figsize=(8, 5)) + plt.plot(sol.t, pop0, lw=3, label="Population in |0>") + plt.plot(sol.t, pop1, lw=3, label="Population in |1>") + plt.xlabel("Time (ns)") + plt.ylabel("Population") + plt.legend(frameon=False) + plt.ylim([0, 1.05]) + plt.xlim([0, 2*T]) + plt.vlines(T, 0, 1.05, "k", linestyle="dashed") + +The plot below shows the population of the qubit as it evolves during +the pulses. The vertical dashed line shows the time of the virtual Z +rotation which was induced by the ``shift_phase`` instruction in the +pulse schedule. As expected, the first pulse moves the qubit to an +eigenstate of the ``Y`` operator. Therefore, the second pulse, which +drives around the ``Y``-axis due to the phase shift, has hardley any +influence on the populations of the qubit. + +.. jupyter-execute:: + + plot_populations(sol) diff --git a/stable/0.4/_sources/userguide/how_to_configure_simulations.rst.txt b/stable/0.4/_sources/userguide/how_to_configure_simulations.rst.txt new file mode 100644 index 000000000..64b0babb6 --- /dev/null +++ b/stable/0.4/_sources/userguide/how_to_configure_simulations.rst.txt @@ -0,0 +1,332 @@ +.. _configuring simulations: + +How-to customize simulations using model transformations and evaluation modes +============================================================================= + +Qiskit Dynamics provides various options for configuring simulations +that can impact solver performance. These options include choosing between +dense and sparse array representations, different differential equation +solvers, and model transformations that modify the definition of the problem. +Depending on the specifics of the problem, different configurations can +yield better performance. + +Here we walk through some of these options, covering: + +1. How-to set up a simulation in a rotating frame, and its potential + benefits +2. How-to perform a rotating wave approximation, and its potential + benefits +3. How-to use a sparse evaluation mode, and how-to appropriately set a + rotating frame to preserve sparsity + + +Throughout this guide we work at the level of the :class:`.Solver` interface, +and consider Hamiltonian dynamics for simplicity, however all of the +considerations have their analogs for Lindblad dynamics. + +1. How-to set up a simulation in a rotating frame, and its potential benefits +----------------------------------------------------------------------------- + +Here we show how to perform a simulation in a rotating frame by setting the +optional ``rotating_frame`` argument when instantiating a :class:`.Solver`, and demonstrate how a +well-chosen frame operator :math:`F = -iH_0` can reduce solving time. +See the :ref:`Rotating frames section of the Models API documentation ` +for details on rotating frames. + +We will simulate the unitary generated by a transmon model with +Hamiltonian: + +.. math:: H(t) = 2 \pi \nu N + \pi \alpha N(N-I) + s(t) \times 2 \pi r (a + a^\dagger) + +where: + + - :math:`N`, :math:`a`, and :math:`a^\dagger` are, respectively, + the number, annihilation, and creation operators. + - :math:`\nu` is the qubit frequency and :math:`r` is the drive strength. + - :math:`s(t)` is the drive signal, which we will take to be on resonance with constant + envelope :math:`1`. + +First, construct the components of the model: + +.. jupyter-execute:: + + import numpy as np + from qiskit.quantum_info import Operator + from qiskit_dynamics import Solver, Signal + + dim = 5 + + v = 5. + anharm = -0.33 + r = 0.1 + + a = np.diag(np.sqrt(np.arange(1, dim)), 1) + adag = np.diag(np.sqrt(np.arange(1, dim)), -1) + N = np.diag(np.arange(dim)) + + # static part + static_hamiltonian = 2 * np.pi * v * N + np.pi * anharm * N * (N - np.eye(dim)) + # drive term + drive_hamiltonian = 2 * np.pi * r * (a + adag) + # drive signal + drive_signal = Signal(1., carrier_freq=v) + + # total simulation time + T = 1. / r + +Construct a :class:`.Solver` for the model as stated, without entering a rotating frame, and solve, +timing the solver. + +.. jupyter-execute:: + + solver = Solver( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=[drive_hamiltonian], + ) + + y0 = np.eye(dim, dtype=complex) + %time results = solver.solve(t_span=[0., T], y0=y0, signals=[drive_signal], atol=1e-10, rtol=1e-10) + +Next, define a :class:`.Solver` in the rotating frame of the static +Hamiltonian by setting the ``rotating_frame`` kwarg, and solve, again timing the solver. + +.. jupyter-execute:: + + rf_solver = Solver( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=[drive_hamiltonian], + rotating_frame=static_hamiltonian + ) + + y0 = np.eye(dim, dtype=complex) + %time rf_results = rf_solver.solve(t_span=[0., T], y0=y0, signals=[drive_signal], atol=1e-10, rtol=1e-10) + +Observe that despite the two simulation problems being mathematically equivalent, it takes +less time to solve in the rotating frame. + +Next, verify that the results are numerically equivalent. This requires +transforming the results to a common frame, which may be done via utility +functions in the ``RotatingFrame`` instance stored within ``Solver.model.rotating_frame``. + +To compare the results, we use the fidelity function for unitary matrices: + +.. math:: f(U, V) = \frac{|Tr(U^\dagger V)|^2}{d^2}, + +where :math:`d` is the dimension. A value of :math:`1` indicates equality of the unitaries. + +.. jupyter-execute:: + + def fidelity(U, V): + # the fidelity function + inner_product = (U.conj() * V).sum() + return (np.abs(inner_product) / dim) ** 2 + + U = results.y[-1] + # transform the results of the solver in the rotating frame out of the rotating frame + U_rf = rf_solver.model.rotating_frame.state_out_of_frame(T, rf_results.y[-1]) + + fidelity(U, U_rf) + +Based on the fidelity, we see that the two simulations are numerically equivalent +with reasonable accuracy based on our specified tolerances. + +The discrepancy in solving times can be understood by examining the number of +right-hand side (RHS) evaluations when solving the differential equation in each instance. +The number of RHS evaluations for the first simulation (not in the rotating frame) was: + +.. jupyter-execute:: + + results.nfev + +Whereas the number of evaluations for the second simulation in the rotating frame was: + +.. jupyter-execute:: + + rf_results.nfev + +This demonstrates that the speedup from entering the rotating frame is a result of +reducing the number of RHS calls required to solve with a given accuracy. + +2. How-to perform a rotating wave approximation, and its potential benefits +--------------------------------------------------------------------------- + +Next we show how to perform a simulation with the rotating wave approximation (RWA) +by setting the ``rwa_cutoff_freq`` argument at :class:`.Solver` instantiation, and show +how it results in further speed ups at the expense of solution accuracy. See the API +documentation for the :meth:`~qiskit_dynamics.models.rotating_wave_approximation` function +for specific details about the RWA. + +Construct a solver for the same problem, now specifying an RWA cutoff frequency and +the carrier frequencies relative to which the cutoff should be applied: + +.. jupyter-execute:: + + rwa_solver = Solver( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=[drive_hamiltonian], + rotating_frame=static_hamiltonian, + rwa_cutoff_freq=1.5 * v, + rwa_carrier_freqs=[v] + ) + + y0 = np.eye(dim, dtype=complex) + %time rwa_results = rwa_solver.solve(t_span=[0., T], y0=y0, signals=[drive_signal], atol=1e-10, rtol=1e-10) + +We observe a further reduction in time, which is a result of the solver requiring even fewer RHS +evaluations with the RWA: + +.. jupyter-execute:: + + rwa_results.nfev + +This speed comes at the cost of lower accuracy, owing to the fact that RWA is a +legitimate *approximation*, which modifies the structure of the solution: + +.. jupyter-execute:: + + U_rwa = rwa_solver.model.rotating_frame.state_out_of_frame(T, rwa_results.y[-1]) + + fidelity(U_rwa, U) + +3. How-to use a sparse evaluation mode, and how-to appropriately set a rotating frame to preserve sparsity +---------------------------------------------------------------------------------------------------------- + +Here we show how to perform a simulation using sparse arrays for evaluating the RHS +via the ``evaluation_mode`` initialization kwarg, +with extra emphasis on the following: + +.. note:: + + As stated in the + :ref:`evaluation modes section of the Models API documentation `, + when using a sparse evaluation mode, to preserve sparsity, it is recommended to + only use *diagonal* rotating frames, which can be specified as a 1d array to the + ``rotating_frame`` kwarg of :class:`.Solver` instantiation. + +For this section we use JAX as it is more performant. See the +:ref:`userguide on using JAX ` for a more detailed +explanation of how to work with JAX in Qiskit Dynamics. + +.. note:: + + JAX sparse arrays are only recommended for use on CPU. + +Start off by configuring to use JAX. + +.. jupyter-execute:: + + from qiskit_dynamics.array import Array + + # configure jax to use 64 bit mode + import jax + jax.config.update("jax_enable_x64", True) + + # tell JAX we are using CPU + jax.config.update('jax_platform_name', 'cpu') + + # set default backend + Array.set_default_backend('jax') + +Reconstruct the model pieces at a much larger dimension, to observe the +benefits of using sparse arrays. Furthermore, set up the initial state to +be a single column vector, to +further highlight the benefits of the sparse representation. + +.. jupyter-execute:: + + dim = 300 + + v = 5. + anharm = -0.33 + r = 0.02 + + a = np.diag(np.sqrt(np.arange(1, dim, dtype=complex)), 1) + adag = np.diag(np.sqrt(np.arange(1, dim, dtype=complex)), -1) + N = np.diag(np.arange(dim, dtype=complex)) + + static_hamiltonian = 2 * np.pi * v * N + np.pi * anharm * N * (N - np.eye(dim)) + drive_hamiltonian = 2 * np.pi * r * (a + adag) + drive_signal = Signal(Array(1.), carrier_freq=v) + + y0 = np.zeros(dim, dtype=complex) + y0[1] = 1. + + T = 1 / r + +Construct standard dense solver in the rotating frame of the static +Hamiltonian, define a function to solve the system for a given +amplitude, and just-in-time compile it using JAX. + +.. jupyter-execute:: + + solver = Solver( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=[drive_hamiltonian], + rotating_frame=static_hamiltonian + ) + + def dense_func(amp): + drive_signal = Signal(Array(amp), carrier_freq=v) + res = solver.solve( + t_span=[0., T], + y0=y0, + signals=[drive_signal], + method='jax_odeint', + atol=1e-10, + rtol=1e-10 + ) + return res.y[-1] + + jitted_dense_func = jax.jit(dense_func) + +Construct sparse solver **in the frame of the diagonal of the static +Hamiltonian**, define a function to solve the system for a given amplitude, +and just-in-time compile it. Note that in this case the static Hamiltonian is already +diagonal, but we explicitly highlight the need for this. + +.. jupyter-execute:: + + sparse_solver = Solver(static_hamiltonian=static_hamiltonian, + hamiltonian_operators=[drive_hamiltonian], + rotating_frame=np.diag(static_hamiltonian), + evaluation_mode='sparse') + + def sparse_func(amp): + drive_signal = Signal(Array(amp), carrier_freq=v) + res = sparse_solver.solve( + t_span=[0., T], + y0=y0, + signals = [drive_signal], + method='jax_odeint', + atol=1e-10, + rtol=1e-10 + ) + return res.y[-1] + + jitted_sparse_func = jax.jit(sparse_func) + +Run the dense simulation (twice to see the true compiled speed). + +.. jupyter-execute:: + + yf = jitted_dense_func(1.).block_until_ready() + %time yf = jitted_dense_func(1.).block_until_ready() + +Run the sparse solver (twice to see the true compiled speed). + +.. jupyter-execute:: + + yf_sparse = jitted_sparse_func(1.).block_until_ready() + %time yf_sparse = jitted_sparse_func(1.).block_until_ready() + +Verify equality of the results in a common frame. + +.. jupyter-execute:: + + yf = solver.model.rotating_frame.state_out_of_frame(T, yf) + yf_sparse = sparse_solver.model.rotating_frame.state_out_of_frame(T, yf_sparse) + + np.linalg.norm(yf - yf_sparse) + +We observe that the final states are extremely close, and that the +sparse representation provides a speed advantage for this problem. diff --git a/stable/0.4/_sources/userguide/how_to_use_jax.rst.txt b/stable/0.4/_sources/userguide/how_to_use_jax.rst.txt new file mode 100644 index 000000000..905013e0a --- /dev/null +++ b/stable/0.4/_sources/userguide/how_to_use_jax.rst.txt @@ -0,0 +1,250 @@ +.. _how-to use jax: + +How-to use JAX with ``qiskit-dynamics`` +======================================= + +JAX enables just-in-time compilation, automatic differentation, and GPU +execution. JAX is integrated into ``qiskit-dynamics`` via the +:class:`.Array` class, which allows most parts of the package to be +executed with either ``numpy`` or ``jax.numpy``. + +This guide addresses the following topics: + +1. How do I configure dynamics to run with JAX? +2. How do I write code using dispatch that can be executed with either + ``numpy`` or JAX? +3. How do I write JAX-transformable functions using the objects and + functions in ``qiskit-dynamics``? +4. Gotchas when using JAX with dynamics. + +1. How do I configure dynamics to run with JAX? +----------------------------------------------- + +The :class:`.Array` class provides a means of controlling whether array +operations are performed using ``numpy`` or ``jax.numpy``. In many +cases, the “default backend” is used to determine which of the two +options is used. + +.. jupyter-execute:: + + # configure jax to use 64 bit mode + import jax + jax.config.update("jax_enable_x64", True) + + # tell JAX we are using CPU + jax.config.update('jax_platform_name', 'cpu') + + # import Array and set default backend + from qiskit_dynamics.array import Array + Array.set_default_backend('jax') + +The default backend can be observed via: + +.. jupyter-execute:: + + Array.default_backend() + + +2. How do I write code using Array that can be executed with either ``numpy`` or JAX? +------------------------------------------------------------------------------------- + +The ``Array`` class wraps both ``numpy`` and ``jax.numpy`` +arrays. The particular type is indicated by the ``backend`` property, +and ``numpy`` functions called on an :class:`.Array` will automatically be +dispatched to ``numpy`` or ``jax.numpy`` based on the :class:`.Array`\ ’s +backend. See the API documentation for ``qiskit_dynamics.array`` for +details. + +3. How do I write JAX-transformable functions using the objects and functions in ``qiskit-dynamics``? +----------------------------------------------------------------------------------------------------- + +JAX-transformable functions must be: + + - JAX-executable. + - Take JAX arrays as input and output (see the + `JAX documentation `__ + for more details on accepted input and output types). + - Pure, in the sense that they have no side-effects. + +The previous section shows how to handle the first two points using +:class:`.Array`. The last point further restricts the type of +code that can be safely transformed. Qiskit Dynamics uses various objects which +can be updated by setting properties (models, solvers). If a function to +be transformed requires updating an already-constructed object of this +form, it is necessary to first make a *copy*. + +We demonstrate this process for both just-in-time compilation and +automatic differentiation in the context of an anticipated common +use-case: parameterized simulation of a model of a quantum system. + +3.1 Just-in-time compiling a parameterized simulation +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +"Just-in-time compiling" a function means to compile it at run time. Just-in-time compilation +incurs an initial cost associated with the construction of the compiled function, +but subsequent calls to the function will generally be faster than the uncompiled version. +In JAX, just-in-time compilation is performed using the ``jax.jit`` function, +which transforms a JAX-compatible function into optimized code using +`XLA `__. We demonstrate here how, using the JAX backend, +functions built using Qiskit Dynamics can be +just-in-time compiled, resulting in faster simulation times. + +For convenience, the ``wrap`` function can be used to transform +``jax.jit`` to also work on functions that have :class:`.Array` objects as +inputs and outputs. + +.. jupyter-execute:: + + from qiskit_dynamics.array import wrap + + jit = wrap(jax.jit, decorator=True) + +Construct a :class:`.Solver` instance with a model that will be used to solve. + +.. jupyter-execute:: + + import numpy as np + from qiskit.quantum_info import Operator + from qiskit_dynamics import Solver, Signal + from qiskit_dynamics.array import Array + + r = 0.5 + w = 1. + X = Operator.from_label('X') + Z = Operator.from_label('Z') + + static_hamiltonian = 2 * np.pi * w * Z/2 + hamiltonian_operators = [2 * np.pi * r * X/2] + + solver = Solver( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=hamiltonian_operators, + rotating_frame=static_hamiltonian + ) + + +Next, define the function to be compiled: + + - The input is the amplitude of a constant-envelope signal on resonance, driven over time + :math:`[0, 3]`. + - The output is the state of the system, starting in the ground state, at + ``100`` points over the total evolution time. + +Note, as described at the beginning of this section, we need to make a copy of ``solver`` +before setting the signals, to ensure the simulation function remains pure. + +.. jupyter-execute:: + + def sim_function(amp): + + # define a constant signal + amp = Array(amp) + signals = [Signal(amp, carrier_freq=w)] + + # simulate and return results + results = solver.solve( + t_span=[0, 3.], + y0=np.array([0., 1.], dtype=complex), + signals=signals, + t_eval=np.linspace(0, 3., 100), + method='jax_odeint' + ) + + return results.y + +Compile the function. + +.. jupyter-execute:: + + fast_sim = jit(sim_function) + +The first time the function is called, JAX will compile an +`XLA `__ version of the function, which is then executed. +Hence, the time taken on the first call *includes* compilation time. + +.. jupyter-execute:: + + %time ys = fast_sim(1.).block_until_ready() + + +On subsequent calls the compiled function is directly executed, +demonstrating the true speed of the compiled function. + +.. jupyter-execute:: + + %timeit fast_sim(1.).block_until_ready() + + +We use this function to plot the :math:`Z` expectation value over a +range of input amplitudes. + +.. jupyter-execute:: + + import matplotlib.pyplot as plt + + for amp in np.linspace(0, 1, 10): + ys = fast_sim(amp) + plt.plot(np.linspace(0, 3., 100), np.real(np.abs(ys[:, 0])**2-np.abs(ys[:, 1])**2)) + + +3.2 Automatically differentiating a parameterized simulation +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Next, we use ``jax.grad`` to automatically differentiate a parameterized +simulation. In this case, ``jax.grad`` requires that the output be a +real number, so we specifically compute the population in the excited +state at the end of the previous simulation + +.. jupyter-execute:: + + def excited_state_pop(amp): + yf = sim_function(amp)[-1] + return np.abs(Array(yf[0]))**2 + +Wrap ``jax.grad`` in the same way, then differentiate and compile +``excited_state_pop``. + +.. jupyter-execute:: + + grad = wrap(jax.grad, decorator=True) + + excited_pop_grad = jit(grad(excited_state_pop)) + +As before, the first execution includes compilation time. + +.. jupyter-execute:: + + %time excited_pop_grad(1.).block_until_ready() + + +Subsequent runs of the function reveal the execution time once compiled. + +.. jupyter-execute:: + + %timeit excited_pop_grad(1.).block_until_ready() + + +4. Pitfalls when using JAX with Dynamics +---------------------------------------- + +4.1 JAX must be set as the default backend before building any objects in Qiskit Dynamics +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +To get dynamics to run with JAX, it is necessary to configure dynamics +to run with JAX *before* building any objects or running any functions. +The internal behaviour of some objects is modified by what the default +backend is *at the time of instantiation*. For example, at instantiation +the operators in a model or :class:`.Solver` instance will be wrapped in an +:class:`.Array` whose backend is the current default backend, and changing the +default backend after building the object won’t change this. + +4.2 Running Dynamics with JAX on CPU vs GPU +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Certain JAX-based features in Dynamics are primarily recommended for use only with CPU +or only with GPU. In such cases, a warning is raised if non-recommended hardware is used, +however users are not prevented from configuring Dynamics and JAX in whatever way they choose. + +Instances of such features are: + * Setting ``evaluation_mode='sparse'`` for solvers and models is only recommended for use on CPU. + * Parallel fixed step solver options in ``solve_lmde`` are recommended only for use on GPU. diff --git a/stable/0.4/_sources/userguide/how_to_use_pulse_schedule_for_jax_jit.rst.txt b/stable/0.4/_sources/userguide/how_to_use_pulse_schedule_for_jax_jit.rst.txt new file mode 100644 index 000000000..59b399f1b --- /dev/null +++ b/stable/0.4/_sources/userguide/how_to_use_pulse_schedule_for_jax_jit.rst.txt @@ -0,0 +1,145 @@ +.. _how-to use pulse schedules for jax-jit: + +How-to use pulse schedules generated by ``qiskit-pulse`` with JAX transformations +================================================================================= + +``Qiskit-pulse`` enables specification of time-dependence in quantum systems as pulse schedules, +built from sequences of a variety of instructions, including the specification of shaped pulses (see +the detailed API information about `Qiskit pulse API Reference +`__). As of ``qiskit-terra`` 0.23.0, JAX support +was added for the :class:`~qiskit.pulse.library.ScalableSymbolicPulse` class. This user guide entry +demonstrates the technical elements of utilizing this class within JAX-transformable functions. + +.. note:: + At present, only the :class:`~qiskit.pulse.library.ScalableSymbolicPulse` class is supported by + JAX, as the validation present in other pulse types, such as + :class:`~qiskit.pulse.library.Gaussian`, is not JAX-compatible. + +This guide addresses the following topics. See the :ref:`userguide on using JAX ` +for a more detailed explanation of how to work with JAX in Qiskit Dynamics. + +1. Configure to use JAX. +2. How to define a Gaussian pulse using :class:`~qiskit.pulse.library.ScalableSymbolicPulse`. +3. JAX transforming Pulse to Signal conversion involving + :class:`~qiskit.pulse.library.ScalableSymbolicPulse`. + + +1. Configure to use JAX +----------------------- + +First, configure Dynamics to use JAX. + +.. jupyter-execute:: + + # configure jax to use 64 bit mode + import jax + jax.config.update("jax_enable_x64", True) + + # tell JAX we are using CPU + jax.config.update('jax_platform_name', 'cpu') + + # import Array and set default backend + from qiskit_dynamics.array import Array + Array.set_default_backend('jax') + + +2. How to define a Gaussian pulse using :class:`~qiskit.pulse.library.ScalableSymbolicPulse` +-------------------------------------------------------------------------------------------- + +As the standard :class:`~qiskit.pulse.library.Gaussian` pulse is not JAX-compatible, to define a +Gaussian pulse to use in optimization, we need to instantiate a +:class:`~qiskit.pulse.library.ScalableSymbolicPulse` with a Gaussian parameterization. First, define +the symbolic representation in `sympy`. + +.. jupyter-execute:: + + from qiskit import pulse + from qiskit_dynamics.pulse import InstructionToSignals + import sympy as sym + + dt = 0.222 + w = 5. + + # Helper function that returns a lifted Gaussian symbolic equation. + def lifted_gaussian( + t: sym.Symbol, + center, + t_zero, + sigma, + ) -> sym.Expr: + t_shifted = (t - center).expand() + t_offset = (t_zero - center).expand() + + gauss = sym.exp(-((t_shifted / sigma) ** 2) / 2) + offset = sym.exp(-((t_offset / sigma) ** 2) / 2) + + return (gauss - offset) / (1 - offset) + + +Next, define the :class:`~qiskit.pulse.library.ScalableSymbolicPulse` using the above expression. + +.. jupyter-execute:: + + _t, _duration, _amp, _sigma, _angle = sym.symbols("t, duration, amp, sigma, angle") + _center = _duration / 2 + + envelope_expr = ( + _amp * sym.exp(sym.I * _angle) * lifted_gaussian(_t, _center, _duration + 1, _sigma) + ) + + gaussian_pulse = pulse.ScalableSymbolicPulse( + pulse_type="Gaussian", + duration=160, + amp=0.3, + angle=0, + parameters={"sigma": 40}, + envelope=envelope_expr, + constraints=_sigma > 0, + valid_amp_conditions=sym.Abs(_amp) <= 1.0, + ) + + gaussian_pulse.draw() + + +3. JAX transforming Pulse to Signal conversion involving :class:`~qiskit.pulse.library.ScalableSymbolicPulse` +------------------------------------------------------------------------------------------------------------- + +Using a Gaussian pulse as an example, we show that a function involving +:class:`~qiskit.pulse.library.ScalableSymbolicPulse` and the pulse to signal converter can be +JAX-compiled (or more generally, JAX-transformed). + +.. jupyter-execute:: + + # use amplitude as the function argument + def jit_func(amp): + _t, _duration, _amp, _sigma, _angle = sym.symbols("t, duration, amp, sigma, angle") + _center = _duration / 2 + + envelope_expr = ( + _amp * sym.exp(sym.I * _angle) * lifted_gaussian(_t, _center, _duration + 1, _sigma) + ) + + # we need to set disable_validation True to enable jax-jitting. + pulse.ScalableSymbolicPulse.disable_validation = True + + gaussian_pulse = pulse.ScalableSymbolicPulse( + pulse_type="Gaussian", + duration=160, + amp=amp, + angle=0, + parameters={"sigma": 40}, + envelope=envelope_expr, + constraints=_sigma > 0, + valid_amp_conditions=sym.Abs(_amp) <= 1.0, + ) + + # build a pulse schedule + with pulse.build() as schedule: + pulse.play(gaussian_pulse, pulse.DriveChannel(0)) + + # convert from a pulse schedule to a list of signals + converter = InstructionToSignals(dt, carriers={"d0": w}) + + return converter.get_signals(schedule)[0].samples.data + + jax.jit(jit_func)(0.4) diff --git a/stable/0.4/_sources/userguide/index.rst.txt b/stable/0.4/_sources/userguide/index.rst.txt new file mode 100644 index 000000000..8ff8721c2 --- /dev/null +++ b/stable/0.4/_sources/userguide/index.rst.txt @@ -0,0 +1,21 @@ +.. _qiskit-dynamics-userguide: + +.. module:: qiskit_dynamics_userguide + +========================== +Qiskit Dynamics User Guide +========================== + +.. toctree:: + :maxdepth: 2 + + how_to_use_jax.rst + how_to_configure_simulations.rst + perturbative_solvers.rst + how_to_use_pulse_schedule_for_jax_jit.rst + + +.. Hiding - Indices and tables + :ref:`genindex` + :ref:`modindex` + :ref:`search` diff --git a/stable/0.4/_sources/userguide/perturbative_solvers.rst.txt b/stable/0.4/_sources/userguide/perturbative_solvers.rst.txt new file mode 100644 index 000000000..df9c15417 --- /dev/null +++ b/stable/0.4/_sources/userguide/perturbative_solvers.rst.txt @@ -0,0 +1,331 @@ +How-to use Dyson and Magnus based solvers +========================================= + +.. warning:: + + This is an advanced topic --- utilizing perturbation-theory based solvers + requires detailed knowledge of the structure of the differential equations + involved, as well as manual tuning of the solver parameters. + See the :class:`.DysonSolver` and :class:`.MagnusSolver` documentation for API details. + Also, see :footcite:`puzzuoli_sensitivity_2022` for a detailed explanation of the solvers, + which varies and builds on the core idea introduced in :footcite:`shillito_fast_2020`. + +.. note:: + + The circumstances under which perturbative solvers outperform + traditional solvers, and which parameter sets to use, is nuanced. + Perturbative solvers executed with JAX are setup to use more parallelization within a + single solver run than typical solvers, and thus it is circumstance-specific whether + the trade-off between speed of a single run and resource consumption is advantageous. + Due to the parallelized nature, the comparison of execution times demonstrated in this + userguide are highly hardware-dependent. + + +In this tutorial we walk through how to use perturbation-theory based solvers. For +information on how these solvers work, see the :class:`.DysonSolver` and :class:`.MagnusSolver` +class documentation, as well as the perturbative expansion background information provided in +:ref:`Time-dependent perturbation theory and multi-variable +series expansions review `. + +We use a simple transmon model: + +.. math:: H(t) = 2 \pi \nu N + \pi \alpha N(N-I) + s(t) \times 2 \pi r (a + a^\dagger) + +where: + +- :math:`N`, :math:`a`, and :math:`a^\dagger` are, respectively, the + number, annihilation, and creation operators. +- :math:`\nu` is the qubit frequency and :math:`r` is the drive + strength. +- :math:`s(t)` is the drive signal, which we will take to be on + resonance with envelope :math:`f(t) = A \frac{4t (T - t)}{T^2}` + for a given amplitude :math:`A` and total time :math:`T`. + +We will walk through the following steps: + +1. Configure ``qiskit-dynamics`` to work with JAX. +2. Construct the model. +3. How-to construct and simulate using the Dyson-based perturbative solver. +4. Simulate using a traditional ODE solver, comparing speed. +5. How-to construct and simulate using the Magnus-based perturbative solver. + +1. Configure to use JAX +----------------------- + +These simulations will be done with JAX array backend to enable +compilation. See the :ref:`userguide on using JAX ` for a more detailed +explanation of how to work with JAX in Qiskit Dynamics. + +.. jupyter-execute:: + + from qiskit_dynamics.array import Array + + # configure jax to use 64 bit mode + import jax + jax.config.update("jax_enable_x64", True) + + # tell JAX we are using CPU if using a system without a GPU + jax.config.update('jax_platform_name', 'cpu') + + # set default backend + Array.set_default_backend('jax') + +2. Construct the model +---------------------- + +First, we construct the model described in the introduction. We use a relatively +high dimension for the oscillator system state space to accentuate the speed +difference between the perturbative solvers and the traditional ODE solver. The higher +dimensionality introduces higher frequencies into the model, which will +slow down both the ODE solver and the initial construction of the perturbative solver. However +after the initial construction, the higher frequencies in the model have no impact +on the perturbative solver speed. + +.. jupyter-execute:: + + import numpy as np + + dim = 10 # Oscillator dimension + + v = 5. # Transmon frequency in GHz + anharm = -0.33 # Transmon anharmonicity in GHz + r = 0.02 # Transmon drive coupling in GHz + + # Construct cavity operators + a = np.diag(np.sqrt(np.arange(1, dim)), 1) + adag = np.diag(np.sqrt(np.arange(1, dim)), -1) + N = np.diag(np.arange(dim)) + + # Static part of Hamiltonian + static_hamiltonian = 2 * np.pi * v * N + np.pi * anharm * N * (N - np.eye(dim)) + # Drive term of Hamiltonian + drive_hamiltonian = 2 * np.pi * r * (a + adag) + + # total simulation time + T = 1. / r + + # Drive envelope function + envelope_func = lambda t: t * (T - t) / (T**2 / 4) + +3. How-to construct and simulate using the Dyson-based perturbative solver +-------------------------------------------------------------------------- + +Setting up a :class:`.DysonSolver` requires more setup than the standard +:class:`.Solver`, as the user must specify several configuration parameters, +along with the structure of the differential equation: + +- The :class:`.DysonSolver` requires direct specification of the LMDE to the + solver. If we are simulating the Schrodinger equation, we need to + multiply the Hamiltonian terms by ``-1j`` when describing the LMDE operators. +- The :class:`.DysonSolver` is a fixed step solver, with the step size + being fixed at instantiation. This step size must be chosen in conjunction + with the ``expansion_order`` to ensure that a suitable accuracy is attained. +- Over each fixed time-step the :class:`.DysonSolver` solves by computing a + truncated perturbative expansion. + + - To compute the truncated perturbative expansion, the signal envelopes are + approximated as a linear combination of Chebyshev polynomials. + - The order of the Chebyshev approximations, along with central carrier frequencies + for defining the “envelope” of each :class:`.Signal`, must be provided at instantiation. + +See the :class:`.DysonSolver` API docs for more details. + +For our example Hamiltonian we configure the :class:`.DysonSolver` as follows: + +.. jupyter-execute:: + + %%time + + from qiskit_dynamics import DysonSolver + + dt = 0.1 + dyson_solver = DysonSolver( + operators=[-1j * drive_hamiltonian], + rotating_frame=-1j * static_hamiltonian, + dt=dt, + carrier_freqs=[v], + chebyshev_orders=[1], + expansion_order=7, + integration_method='jax_odeint', + atol=1e-12, + rtol=1e-12 + ) + +The above parameters are chosen so that the :class:`.DysonSolver` is fast and produces +high accuracy solutions (measured and confirmed after the fact). The relatively large +step size ``dt = 0.1`` is chosen for speed: the larger the step size, the fewer steps required. +To ensure high accuracy given the large step size, we choose a high expansion order, +and utilize a linear envelope approximation scheme by setting the ``chebyshev_order`` to ``1`` +for the single drive signal. + +Similar to the :class:`.Solver` interface, the :meth:`.DysonSolver.solve` method can be +called to simulate the system for a given list of signals, initial state, start time, +and number of time steps of length ``dt``. + +To properly compare the speed of :class:`.DysonSolver` to a traditional ODE solver, +we write JAX-compilable functions wrapping each that, given an amplitude value, +returns the final unitary over the interval ``[0, (T // dt) * dt]`` for an on-resonance +drive with envelope shape given by ``envelope_func`` above. Running compiled versions of +these functions gives a sense of the speeds attainable by these solvers. + +.. jupyter-execute:: + + from qiskit_dynamics import Signal + from jax import jit + + # Jit the function to improve performance for repeated calls + @jit + def dyson_sim(amp): + """For a given envelope amplitude, simulate the final unitary using the + Dyson solver. + """ + drive_signal = Signal(lambda t: Array(amp) * envelope_func(t), carrier_freq=v) + return dyson_solver.solve( + signals=[drive_signal], + y0=np.eye(dim, dtype=complex), + t0=0., + n_steps=int(T // dt) + ).y[-1] + +First run includes compile time. + +.. jupyter-execute:: + + %time yf_dyson = dyson_sim(1.).block_until_ready() + + +Once JIT compilation has been performance we can benchmark the performance of the +JIT-compiled solver: + +.. jupyter-execute:: + + %time yf_dyson = dyson_sim(1.).block_until_ready() + + +4. Comparison to traditional ODE solver +--------------------------------------- + +We now construct the same simulation using a standard solver to compare +accuracy and simulation speed. + +.. jupyter-execute:: + + from qiskit_dynamics import Solver + + solver = Solver( + static_hamiltonian=static_hamiltonian, + hamiltonian_operators=[drive_hamiltonian], + rotating_frame=static_hamiltonian + ) + + # specify tolerance as an argument to run the simulation at different tolerances + def ode_sim(amp, tol): + drive_signal = Signal(lambda t: Array(amp) * envelope_func(t), carrier_freq=v) + res = solver.solve( + t_span=[0., int(T // dt) * dt], + y0=np.eye(dim, dtype=complex), + signals=[drive_signal], + method='jax_odeint', + atol=tol, + rtol=tol + ) + return res.y[-1] + +Simulate with low tolerance for comparison to high accuracy solution. + +.. jupyter-execute:: + + yf_low_tol = ode_sim(1., 1e-13) + np.linalg.norm(yf_low_tol - yf_dyson) + + +For speed comparison, compile at a tolerance with similar accuracy. + +.. jupyter-execute:: + + jit_ode_sim = jit(lambda amp: ode_sim(amp, 1e-8)) + + %time yf_ode = jit_ode_sim(1.).block_until_ready() + +Measure compiled time. + +.. jupyter-execute:: + + %time yf_ode = jit_ode_sim(1.).block_until_ready() + + +Confirm similar accuracy solution. + +.. jupyter-execute:: + + np.linalg.norm(yf_low_tol - yf_ode) + +Here we see that, once compiled, the Dyson-based solver has a +significant speed advantage over the traditional solver, at the expense +of the initial compilation time and the technical aspect of using the solver. + +5. How-to construct and simulate using the Magnus-based perturbation solver +--------------------------------------------------------------------------- + +Next, we repeat our example using the Magnus-based perturbative solver. +Setup of the :class:`.MagnusSolver` is similar to the :class:`.DysonSolver`, +but it uses the Magnus expansion and matrix exponentiation to simulate over +each fixed time step. + +.. jupyter-execute:: + + %%time + + from qiskit_dynamics import MagnusSolver + + dt = 0.1 + magnus_solver = MagnusSolver( + operators=[-1j * drive_hamiltonian], + rotating_frame=-1j * static_hamiltonian, + dt=dt, + carrier_freqs=[v], + chebyshev_orders=[1], + expansion_order=3, + integration_method='jax_odeint', + atol=1e-12, + rtol=1e-12 + ) + + +Setup simulation function. + +.. jupyter-execute:: + + @jit + def magnus_sim(amp): + drive_signal = Signal(lambda t: Array(amp) * envelope_func(t), carrier_freq=v) + return magnus_solver.solve( + signals=[drive_signal], + y0=np.eye(dim, dtype=complex), + t0=0., + n_steps=int(T // dt) + ).y[-1] + + +First run includes compile time. + +.. jupyter-execute:: + + %time yf_magnus = magnus_sim(1.).block_until_ready() + +Second run demonstrates speed of the simulation. + +.. jupyter-execute:: + + %time yf_magnus = magnus_sim(1.).block_until_ready() + + +.. jupyter-execute:: + + np.linalg.norm(yf_magnus - yf_low_tol) + + +Observe comparable accuracy at a lower order in the expansion, albeit +with a modest speed up as compared to the Dyson-based solver. + +.. footbibliography:: diff --git a/stable/0.4/_static/_sphinx_javascript_frameworks_compat.js b/stable/0.4/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 000000000..81415803e --- /dev/null +++ b/stable/0.4/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. 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lightgoldenrodyellow; +} +.sb-footer-content { + background: plum; +} +.sb-footer-content__inner { + background: palevioletred; +} +.sb-footer { + background: pink; +} +.sb-footer__inner { + background: salmon; +} +.sb-article { + background: white; +} diff --git a/stable/0.4/_static/doctools.js b/stable/0.4/_static/doctools.js new file mode 100644 index 000000000..d06a71d75 --- /dev/null +++ b/stable/0.4/_static/doctools.js @@ -0,0 +1,156 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Base JavaScript utilities for all Sphinx HTML documentation. + * + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([ + "TEXTAREA", + "INPUT", + "SELECT", + "BUTTON", +]); + +const _ready = (callback) => { + if (document.readyState !== "loading") { + callback(); + } else { + document.addEventListener("DOMContentLoaded", callback); + } +}; + +/** + * Small JavaScript module for the documentation. + */ +const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 0 : 1), + LOCALE: "unknown", + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext: (string) => { + const translated = Documentation.TRANSLATIONS[string]; + switch (typeof translated) { + case "undefined": + return string; // no translation + case "string": + return translated; // translation exists + default: + return translated[0]; // (singular, plural) translation tuple exists + } + }, + + ngettext: (singular, plural, n) => { + const translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated !== "undefined") + return translated[Documentation.PLURAL_EXPR(n)]; + return n === 1 ? singular : plural; + }, + + addTranslations: (catalog) => { + 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All rights reserved. + * This code may only be used under the BSD style license found at + * http://polymer.github.io/LICENSE.txt + * The complete set of authors may be found at + * http://polymer.github.io/AUTHORS.txt + * The complete set of contributors may be found at + * http://polymer.github.io/CONTRIBUTORS.txt + * Code distributed by Google as part of the polymer project is also + * subject to an additional IP rights grant found at + * http://polymer.github.io/PATENTS.txt + */ +const li=new WeakMap,ci=ye((e=>t=>{const i=li.get(t);if(void 0===e&&t instanceof De){if(void 0!==i||!li.has(t)){const e=t.committer.name;t.committer.element.removeAttribute(e)}}else e!==i&&t.setValue(e);li.set(t,e)}));let hi,ui,pi=e=>e;const{prefix:vi}=xe;ue([kt(`${vi}-header-name`)],(function(e,t){return{F:class extends t{constructor(...t){super(...t),e(this)}},d:[{kind:"field",decorators:[St()],key:"href",value:void 0},{kind:"field",decorators:[St()],key:"prefix",value:void 0},{kind:"method",key:"createRenderRoot",value:function(){var e;return this.attachShadow({mode:"open",delegatesFocus:Number((null!==(e=/Safari\/(\d+)/.exec(navigator.userAgent))&&void 0!==e?e:["",0])[1])<=537})}},{kind:"method",key:"render",value:function(){const{href:e,prefix:t}=this,i=t?it(hi||(hi=pi` ${0} `),vi,t):void 0;return it(ui||(ui=pi` ${0}  `),vi,ci(e),i)}},{kind:"field",static:!0,key:"styles",value:()=>Dt}]}}),It(Nt));let mi,bi=e=>e;const{prefix:fi}=xe;ue([kt(`${fi}-header-nav`)],(function(e,t){class i extends t{constructor(...t){super(...t),e(this)}}return{F:i,d:[{kind:"field",decorators:[St({attribute:"menu-bar-label"})],key:"menuBarLabel",value:void 0},{kind:"method",key:"connectedCallback",value:function(){this.hasAttribute("role")||this.setAttribute("role","navigation"),Bt(Vt(i.prototype),"connectedCallback",this).call(this)}},{kind:"method",key:"render",value:function(){const{menuBarLabel:e}=this;return it(mi||(mi=bi`
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+/** + * @license + * + * Copyright IBM Corp. 2019, 2020 + * + * This source code is licensed under the Apache-2.0 license found in the + * LICENSE file in the root directory of this source tree. + */ +const Oi=({children:e,...t}={})=>nt`` +/** + * @license + * + * Copyright IBM Corp. 2019, 2020 + * + * This source code is licensed under the Apache-2.0 license found in the + * LICENSE file in the root directory of this source tree. + */,Ri=({children:e,...t}={})=>nt`` +/** + * @license + * + * Copyright IBM Corp. 2019, 2022 + * + * This source code is licensed under the Apache-2.0 license found in the + * LICENSE file in the root directory of this source tree. + */;let Ii,Ui=e=>e;const{prefix:Hi}=xe;let ji=ue([kt(`${Hi}-header-menu-button`)],(function(e,t){return{F:class extends t{constructor(...t){super(...t),e(this)}},d:[{kind:"method",key:"_handleClick",value:function(){const e=!this.active;this.active=e,this.dispatchEvent(new CustomEvent(this.constructor.eventToggle,{bubbles:!0,cancelable:!0,composed:!0,detail:{active:e}}))}},{kind:"field",decorators:[St({type:Boolean,reflect:!0})],key:"active",value:()=>!1},{kind:"field",decorators:[St({attribute:"button-label-active"})],key:"buttonLabelActive",value:()=>"Close navigation menu"},{kind:"field",decorators:[St({attribute:"button-label-inactive"})],key:"buttonLabelInactive",value:()=>"Open navigation menu"},{kind:"field",decorators:[St({reflect:!0,attribute:"collapse-mode"})],key:"collapseMode",value:()=>ni.RESPONSIVE},{kind:"field",decorators:[St({type:Boolean,reflect:!0})],key:"disabled",value:()=>!1},{kind:"field",decorators:[St({reflect:!0,attribute:"usage-mode"})],key:"usageMode",value:()=>si.REGULAR},{kind:"method",key:"createRenderRoot",value:function(){var e;return this.attachShadow({mode:"open",delegatesFocus:Number((null!==(e=/Safari\/(\d+)/.exec(navigator.userAgent))&&void 0!==e?e:["",0])[1])<=537})}},{kind:"method",key:"render",value:function(){const{active:e,buttonLabelActive:t,buttonLabelInactive:i,disabled:n,_handleClick:s}=this,a=e?t:i,r=rt({[`${Hi}--header__action`]:!0,[`${Hi}--header__menu-trigger`]:!0,[`${Hi}--header__menu-toggle`]:!0,[`${Hi}--header__action--active`]:e});return it(Ii||(Ii=Ui` `),r,n,ci(null!=(o=a)?o:void 0),s,(e?Oi:Ri)({slot:"toggle-icon"}));var o}},{kind:"get",static:!0,key:"eventToggle",value:function(){return`${Hi}-header-menu-button-toggled`}},{kind:"field",static:!0,key:"styles",value:()=>Dt}]}}),It(Nt)); +/** + * @license + * + * Copyright IBM Corp. 2019, 2020 + * + * This source code is licensed under the Apache-2.0 license found in the + * LICENSE file in the root directory of this source tree. + */let Li,Vi=e=>e;const{prefix:Bi}=xe;ue([kt(`${Bi}-side-nav-menu`)],(function(e,t){class i extends t{constructor(...t){super(...t),e(this)}}return{F:i,d:[{kind:"field",key:"_hasIcon",value:()=>!1},{kind:"field",decorators:[At("#title-icon-container")],key:"_titleIconContainerNode",value:void 0},{kind:"method",key:"_handleUserInitiatedToggle",value:function(e=!this.expanded){const{eventBeforeToggle:t,eventToggle:i}=this.constructor,n={bubbles:!0,cancelable:!0,composed:!0,detail:{expanded:e}};this.dispatchEvent(new CustomEvent(t,n))&&(this.expanded=e,this.dispatchEvent(new CustomEvent(i,n)))}},{kind:"method",key:"_handleClickExpando",value:function(){this._handleUserInitiatedToggle()}},{kind:"method",key:"_handleSlotChange",value:function({target:e}){const{_hasIcon:t}=this;ii(e.assignedNodes(),(e=>{e.nodeType===Node.ELEMENT_NODE&&e.toggleAttribute(this.constructor.attribItemHasIcon,t)}))}},{kind:"method",key:"_handleSlotChangeTitleIcon",value:function({target:e}){var t;const i=this.constructor,n=e.assignedNodes().length>0;this._hasIcon=n,null===(t=this._titleIconContainerNode)||void 0===t||t.toggleAttribute("hidden",!n),ii(this.querySelectorAll(i.selectorItem),(e=>{e.toggleAttribute(i.attribItemHasIcon,n)}))}},{kind:"field",decorators:[St({type:Boolean,reflect:!0})],key:"active",value:()=>!1},{kind:"field",decorators:[St({type:Boolean,reflect:!0})],key:"expanded",value:()=>!1},{kind:"field",decorators:[St({type:Boolean,reflect:!0,attribute:"force-collapsed"})],key:"forceCollapsed",value:()=>!1},{kind:"field",decorators:[St()],key:"title",value:()=>""},{kind:"method",key:"createRenderRoot",value:function(){var e;return this.attachShadow({mode:"open",delegatesFocus:Number((null!==(e=/Safari\/(\d+)/.exec(navigator.userAgent))&&void 0!==e?e:["",0])[1])<=537})}},{kind:"method",key:"connectedCallback",value:function(){this.hasAttribute("role")||this.setAttribute("role","listitem"),Bt(Vt(i.prototype),"connectedCallback",this).call(this)}},{kind:"method",key:"updated",value:function(e){if(e.has("expanded")){const{selectorItem:e}=this.constructor,{expanded:t}=this;ii(this.querySelectorAll(e),(e=>{e.tabIndex=t?0:-1}))}}},{kind:"method",key:"render",value:function(){const{expanded:e,forceCollapsed:t,title:i,_handleClickExpando:n,_handleSlotChange:s,_handleSlotChangeTitleIcon:a}=this;return it(Li||(Li=Vi`
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0 0 / 10%) 0 2px 3px 0;display:block;font-family:'IBM Plex Sans','Helvetica Neue',Arial,sans-serif}:host(qiskit-ui-shell){margin-top:var(--header-height)}bx-header ~ bx-side-nav{height:calc(100% - var(--header-height));margin-top:var(--header-height)}bx-header{display:flex;justify-content:space-between;height:var(--header-height);border-color:var(--cds-border-subtle);background-color:var(--cds-ui-background);color:var(--cds-text-secondary)}bx-header svg.menu__account__icon{display:block;overflow:hidden;box-sizing:border-box;width:2rem;height:2rem;border:.125rem solid var(--cds-icon-on-color);border-radius:50%;fill:var(--cds-icon-on-color)}bx-header svg{width:100%;height:auto}bx-header .qiskit-header-content{display:flex;justify-content:space-between;width:100%;max-width:var(--header-content-max-width);margin-right:auto;margin-left:auto}bx-header-name::part(link){width:8.75rem;height:calc(var(--header-height) - 1px);fill:var(--cool-gray-80)}bx-header-nav{height:calc(var(--header-height) 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1px)}bx-header-nav::before,bx-header-nav::part(divider){display:none}bx-header-nav-item.qiskit-user-account-icon::part(link),bx-header-nav-item.qiskit-user-account-icon::part(link):focus,bx-header-nav-item.qiskit-user-account-icon::part(link):hover{background-color:var(--purple-70);color:var(--cds-ui-background)}bx-header-nav-item::part(link),bx-header-menu-item::part(link),qiskit-header-menu::part(trigger),qiskit-header-menu-mega::part(trigger){font-size:1rem;font-weight:400;line-height:1.5;letter-spacing:0;background:var(--cds-ui-background);color:var(--cds-text-secondary)}bx-header-nav-item::part(link):active,bx-header-nav-item::part(link):focus,bx-header-nav-item::part(link):hover,bx-header-menu-item::part(link):active,bx-header-menu-item::part(link):focus,bx-header-menu-item::part(link):hover,qiskit-header-menu::part(trigger):active,qiskit-header-menu::part(trigger):focus,qiskit-header-menu::part(trigger):hover,qiskit-header-menu-mega::part(trigger):active,qiskit-header-menu-mega::part(trigger):focus,qiskit-header-menu-mega::part(trigger):hover{background-color:var(--cds-ui-background);color:var(--cds-text-secondary)}bx-header-nav-item::part(link):hover,bx-header-menu-item::part(link):hover,qiskit-header-menu::part(trigger):hover,qiskit-header-menu-mega::part(trigger):hover{text-decoration:underline}bx-header-nav-item::part(link):focus,bx-header-menu-item::part(link):focus,qiskit-header-menu::part(trigger):focus,qiskit-header-menu-mega::part(trigger):focus{border-color:var(--cds-border-subtle)}:host(qiskit-header-menu)::part(trigger-icon){fill:var(--cds-text-secondary) !important}:host(qiskit-header-menu)::part(menu-body){box-shadow:var(--box-shadow)}:host(qiskit-header-menu) .bx--header__menu-title{background-color:var(--cds-ui-background);color:var(--cds-text-secondary)}:host(qiskit-header-menu) .bx--header__menu-title[aria-expanded=true]{background-color:var(--cool-gray-10)}bx-header-menu-item{height:3rem;background-color:var(--cds-ui-01);color:var(--cds-text-secondary)}bx-header-menu-item::part(link),bx-header-menu-item::part(link):focus,bx-header-menu-item::part(link):hover{background-color:var(--cool-gray-10)}:host(qiskit-header-menu-mega)::part(trigger-icon){fill:var(--cds-text-secondary) !important}:host(qiskit-header-menu-mega) .bx--header__menu-title{color:var(--cds-text-secondary)}:host(qiskit-header-menu-mega) .bx--header__menu-title[aria-expanded=true]{background-color:var(--cool-gray-10)}:host(qiskit-header-menu-mega) .bx--header__menu-title[aria-expanded=true]+.bx--header__menu{position:fixed;top:var(--header-height);bottom:auto;left:0;display:grid;grid-template-columns:repeat(6,1fr);width:100vw;height:auto;padding:var(--cds-spacing-05) var(--cds-spacing-03);background-color:var(--cool-gray-10);box-shadow:var(--box-shadow);transform:translateZ(0)}:host(qiskit-header-menu-item-mega){padding:0 var(--cds-spacing-04)}:host(qiskit-header-menu-item-mega) .qiskit-header-menu-item-mega-heading{font-size:1rem;font-weight:600;line-height:1.375;letter-spacing:0;margin-bottom:var(--cds-spacing-04);color:var(--cds-text-primary)}:host(qiskit-header-menu-item-mega) .qiskit-header-menu-item-mega-list{font-size:1rem;font-weight:400;line-height:1.5;letter-spacing:0}:host(qiskit-header-menu-item-mega) .qiskit-header-menu-item-mega-list li{margin-bottom:var(--cds-spacing-03)}:host(qiskit-header-menu-item-mega) .qiskit-header-menu-item-mega-list a{color:var(--cds-text-primary);text-decoration:none}:host(qiskit-header-menu-item-mega) .qiskit-header-menu-item-mega-list a:hover{text-decoration:underline}:host(qiskit-header-menu-item-mega) .qiskit-header-menu-item-mega-list a:focus{outline:2px solid var(--cds-border-subtle)}:host(qiskit-header-menu-button) .bx--header__menu-toggle,:host(qiskit-header-menu-button) .bx--header__menu-trigger{width:var(--header-height);height:var(--header-height);border:0}:host(qiskit-header-menu-button) .bx--header__menu-toggle>svg,:host(qiskit-header-menu-button) .bx--header__menu-trigger>svg{fill:var(--cds-text-secondary)}:host(qiskit-header-menu-button) .bx--header__menu-toggle:focus,:host(qiskit-header-menu-button) .bx--header__menu-toggle:active,:host(qiskit-header-menu-button) .bx--header__menu-toggle:hover,:host(qiskit-header-menu-button) .bx--header__menu-trigger:focus,:host(qiskit-header-menu-button) .bx--header__menu-trigger:active,:host(qiskit-header-menu-button) .bx--header__menu-trigger:hover{background-color:var(--cds-ui-01)}bx-side-nav{right:0;left:auto;box-shadow:0 .5rem .5rem rgba(0,0,0,0.25)}@media(max-width:41.98rem){bx-side-nav[expanded]{width:100%;max-width:none}}bx-side-nav svg.menu__account__icon{display:block;overflow:hidden;box-sizing:border-box;width:2rem;height:2rem;margin-right:var(--cds-spacing-03);border:.125rem solid var(--purple-70);border-radius:50%;fill:var(--purple-70)}bx-side-nav bx-side-nav-divider{margin-top:-1px;margin-bottom:-1px}bx-side-nav bx-side-nav-items{overflow-y:scroll;padding:0}bx-side-nav-link.qiskit-user-account-icon::part(link):hover,bx-side-nav-link.qiskit-user-account-icon::part(link){height:3rem;text-decoration-color:var(--purple-70)}bx-side-nav-link.qiskit-user-account-icon::part(title){display:flex;align-items:center;color:var(--purple-70)}bx-side-nav-link::part(link){min-height:var(--sidenav-item-height)}bx-side-nav-link::part(link):hover{text-decoration:underline;text-decoration-color:var(--cds-text-secondary)}bx-side-nav-link::part(link):focus{outline-color:var(--cds-border-subtle)}bx-side-nav-link::part(title){font-size:1rem;font-weight:400;line-height:1.5;letter-spacing:0}bx-side-nav-menu::part(expando){font-size:1rem;font-weight:400;line-height:1.5;letter-spacing:0;min-height:var(--sidenav-item-height)}bx-side-nav-menu::part(expando):hover{background-color:transparent;text-decoration:underline;text-decoration-color:var(--cds-text-secondary)}bx-side-nav-menu::part(expando):focus{outline-color:var(--cds-border-subtle)}bx-side-nav-menu[expanded]:not(.qiskit-side-nav-submenu)::part(title){font-weight:500}bx-side-nav-menu.qiskit-side-nav-submenu::part(expando){min-height:var(--sidenav-item-height-short);background-color:var(--cool-gray-10)}bx-side-nav-menu-item::part(link){min-height:var(--sidenav-item-height-short) !important}bx-side-nav-menu-item::part(link):hover{text-decoration:underline;text-decoration-color:var(--cds-text-secondary)}bx-side-nav-menu-item::part(link):focus{outline-color:var(--cds-border-subtle)}bx-side-nav-menu-item::part(title){font-size:1rem;font-weight:400;line-height:1.5;letter-spacing:0}bx-side-nav-menu-item.qiskit-nav-menu-item::part(link){background-color:var(--cool-gray-10) !important}bx-side-nav-menu-item.qiskit-nav-submenu-item{position:relative}bx-side-nav-menu-item.qiskit-nav-submenu-item::part(link){background-color:var(--cool-gray-20) !important}bx-side-nav-menu-item.qiskit-nav-submenu-item::part(link):focus{outline-color:var(--cool-gray-30)}bx-side-nav-menu-item.qiskit-nav-submenu-item::after{content:"";position:absolute;right:var(--cds-spacing-07);left:var(--cds-spacing-07);z-index:1;height:1px;background-color:var(--cool-gray-30)}bx-side-nav-menu-item.qiskit-nav-submenu-item:first-of-type{border-top:1px solid var(--cool-gray-30)}bx-side-nav-menu-item.qiskit-nav-submenu-item:last-of-type{border-bottom:1px solid var(--cool-gray-30)}@media(min-width:42rem){.qiskit-side-nav-footer{display:none}}.qiskit-side-nav-footer__social-container{margin:var(--cds-spacing-03) var(--cds-spacing-05)}.qiskit-side-nav-footer__social-icons{display:grid;grid-template-rows:1fr 1fr;grid-template-columns:25px 25px;grid-gap:var(--cds-spacing-02) var(--cds-spacing-05)}.qiskit-side-nav-footer__social-icons__icon{color:var(--cool-gray-60)}.qiskit-side-nav-footer__social-heading{font-size:.875rem;font-weight:600;line-height:1.29;letter-spacing:.16px;margin-bottom:var(--cds-spacing-04);color:var(--cool-gray-60)}.qiskit-side-nav-footer__copyright{font-size:.75rem;font-weight:400;line-height:1.34;letter-spacing:.32px;padding:var(--cds-spacing-05);background-color:var(--cool-gray-10)}`;let Fi=class extends zi{};Fi.styles=[Di],Fi=t([ne("qiskit-header-menu")],Fi);let Xi=class extends ji{};Xi.styles=[Di],Xi=t([ne("qiskit-header-menu-button")],Xi);let Wi=class extends zi{};Wi.styles=[Di],Wi=t([ne("qiskit-header-menu-mega")],Wi);let Gi=class extends te{constructor(){super(...arguments),this.item={},this.parentLabel="",this._handleClick=e=>{this.dispatchEvent(new CustomEvent("on-click",{detail:{label:`${this.parentLabel}-${e.label}`,url:e.url},bubbles:!0,composed:!0}))}}render(){var e,t,i;return R` +
    +

    ${null===(e=this.item)||void 0===e?void 0:e.label}

    +
      + ${null===(i=null===(t=this.item)||void 0===t?void 0:t.children)||void 0===i?void 0:i.map((e=>R`
    • + + ${e.label} + +
    • `))} +
    +
    + `}};Gi.styles=[Di],t([ae({type:Object}),i("design:type",Object)],Gi.prototype,"item",void 0),t([ae({type:String}),i("design:type",Object)],Gi.prototype,"parentLabel",void 0),Gi=t([ne("qiskit-header-menu-item-mega")],Gi);const Yi=R` + +`,Qi=R` + +`,Ji=R` + +`,Zi=R` + +`;var Ki;!function(e){e.DEFAULT="",e.HIDE_ACCOUNT="hide-account"}(Ki||(Ki={}));const en=[{icon:Ji,label:"Twitter",url:"https://twitter.com/Qiskit"},{icon:Qi,label:"Slack",url:"https://qisk.it/join-slack"},{icon:Zi,label:"YouTube",url:"https://youtube.com/Qiskit"},{icon:Yi,label:"Medium",url:"https://medium.com/Qiskit"}],tn=[{label:"Documentation",children:[{label:"Home",url:"https://qiskit.org/documentation/"},{label:"Installation",url:"https://qiskit.org/documentation/getting_started.html"},{label:"Tutorials",url:"https://qiskit.org/documentation/tutorials.html"},{label:"API Reference",url:"https://qiskit.org/documentation/apidoc/index.html"},{label:"Contribute",url:"https://qiskit.org/documentation/contributing_to_qiskit.html"}]},{label:"Providers",url:"https://qiskit.org/providers/"},{label:"Community",children:[{label:"Events",url:"https://qiskit.org/events/"},{label:"Advocates",url:"https://qiskit.org/advocates/"},{label:"Ecosystem",url:"https://qiskit.org/ecosystem/"}]},{label:"Learn",url:"https://qiskit.org/learn/"}],nn=R` + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +`,sn=R` + +`,an="https://qiskit.org"===window.origin?"https://learn.qiskit.org":window.origin;e.QiskitUIShell=class extends te{constructor(){super(...arguments),this.variant=Ki.DEFAULT,this._NAV_ITEMS=tn,this._SOCIAL_LINKS=en,this._handleClick=(e,t)=>{const i=t?`${t}-${e.label}`:e.label;this.dispatchEvent(new CustomEvent("on-click",{detail:{label:i,url:e.url},bubbles:!0,composed:!0}))}}render(){return R` + +
    + + ${nn} + + + ${this._getHeaderItems()} + ${this.variant===Ki.HIDE_ACCOUNT?null:this._getAccountHeaderNavItem()} + + + +
    +
    + + + + ${this._getSideNavItems()} + ${this.variant===Ki.HIDE_ACCOUNT?null:this._getAccountSideNavLink()} + + + + `}_getHeaderItems(){return this._NAV_ITEMS.map((e=>e.children?this._getHeaderMenu(e):this._getHeaderNavItem(e)))}_getHeaderNavItem(e){return R` + + ${null==e?void 0:e.label} + + `}_getHeaderMenu(e){var t;return R` + + ${null===(t=null==e?void 0:e.children)||void 0===t?void 0:t.map((t=>this._getHeaderMenuItem(t,null==e?void 0:e.label)))} + + `}_getHeaderMenuItem(e,t){return R` + + ${null==e?void 0:e.label} + + `}_getAccountHeaderNavItem(){return R` + + `}_getSideNavItems(){return this._NAV_ITEMS.map((e=>(null==e?void 0:e.children)?this._getSideNavMenu(e):this._getSideNavLink(e)))}_getSideNavLink(e){return R` + + ${null==e?void 0:e.label} + + + `}_getSideNavMenu(e){var t;return R` + + ${null===(t=null==e?void 0:e.children)||void 0===t?void 0:t.map((t=>this._getSideNavMenuItem(t,null==e?void 0:e.label)))} + + + `}_getSideNavMenuItem(e,t,i=!1){const n=i?"qiskit-nav-submenu-item":"qiskit-nav-menu-item";return R` + + ${null==e?void 0:e.label} + + `}_getAccountSideNavLink(){return R` + + `}_getSocialLinks(){return this._SOCIAL_LINKS.map((e=>R` + + `))}},e.QiskitUIShell.styles=[Di],t([ae({type:String}),i("design:type",String)],e.QiskitUIShell.prototype,"variant",void 0),e.QiskitUIShell=t([ne("qiskit-ui-shell")],e.QiskitUIShell)}({}); diff --git a/stable/0.4/_static/jupyter-sphinx.css b/stable/0.4/_static/jupyter-sphinx.css new file mode 100644 index 000000000..87724dfcc --- /dev/null +++ b/stable/0.4/_static/jupyter-sphinx.css @@ -0,0 +1,123 @@ +/* Stylesheet for jupyter-sphinx + +These styles mimic the Jupyter HTML styles. + +The default CSS (Cascading Style Sheet) class structure of jupyter-sphinx +is the following: + +jupyter_container + code_cell (optional) + stderr (optional) + output (optional) + +If the code_cell is not displayed, then there is not a jupyter_container, and +the output is provided without CSS. + +This stylesheet attempts to override the defaults of all packaged Sphinx themes +to display jupter-sphinx cells in a Jupyter-like style. + +If you want to adjust the styles, add additional custom CSS to override these +styles. + +After a build, this stylesheet is loaded from ./_static/jupyter-sphinx.css . + +*/ + + +div.jupyter_container { + padding: .4em; + margin: 0 0 .4em 0; + background-color: #FFFF; + border: 1px solid #CCC; + -moz-box-shadow: 2px 2px 4px rgba(87, 87, 87, 0.2); + -webkit-box-shadow: 2px 2px 4px rgba(87, 87, 87, 0.2); + box-shadow: 2px 2px 4px rgba(87, 87, 87, 0.2); +} +.jupyter_container div.code_cell { + border: 1px solid #cfcfcf; + border-radius: 2px; + background-color: #f7f7f7; + margin: 0 0; + overflow: auto; +} + +.jupyter_container div.code_cell pre { + padding: 4px; + margin: 0 0; + background-color: #f7f7f7; + border: none; + background: none; + box-shadow: none; + -webkit-box-shadow: none; /* for nature */ + -moz-box-shadow: none; /* for nature */ +} + +.jupyter_container div.code_cell * { + margin: 0 0; +} +div.jupyter_container div.highlight { + background-color: #f7f7f7; /* for haiku */ +} +div.jupyter_container { + padding: 0; + margin: 0; +} + +/* Prevent alabaster breaking highlight alignment */ +div.jupyter_container .hll { + padding: 0; + margin: 0; +} + +/* overrides for sphinx_rtd_theme */ +.rst-content .jupyter_container div[class^='highlight'], +.document .jupyter_container div[class^='highlight'], +.rst-content .jupyter_container pre.literal-block { + border:none; + margin: 0; + padding: 0; + background: none; + padding: 3px; + background-color: transparent; +} +/* restore Mathjax CSS, as it assumes a vertical margin. */ +.jupyter_container .MathJax_Display { + margin: 1em 0em; + text-align: center; +} +.jupyter_container .stderr { + background-color: #FCC; + border: none; + padding: 3px; +} +.jupyter_container .output { + border: none; +} +.jupyter_container div.output pre { + background-color: white; + background: none; + padding: 4px; + border: none; + box-shadow: none; + -webkit-box-shadow: none; /* for nature */ + -moz-box-shadow: none; /* for nature */ +} +.jupyter_container .code_cell td.linenos { + text-align: right; + padding: 4px 4px 4px 8px; + border-right: 1px solid #cfcfcf; + color: #999; +} +.jupyter_container .output .highlight { + background-color: #ffffff; +} +/* combine sequential jupyter cells, + by moving sequential ones up higher on y-axis */ +div.jupyter_container + div.jupyter_container { + margin: -.5em 0 .4em 0; +} + +/* Fix for sphinx_rtd_theme spacing after jupyter_container #91 */ +.rst-content .jupyter_container { + margin: 0 0 24px 0; +} diff --git a/stable/0.4/_static/language_data.js b/stable/0.4/_static/language_data.js new file mode 100644 index 000000000..250f5665f --- /dev/null +++ b/stable/0.4/_static/language_data.js @@ -0,0 +1,199 @@ +/* + * language_data.js + * ~~~~~~~~~~~~~~~~ + * + * This script contains the language-specific data used by searchtools.js, + * namely the list of stopwords, stemmer, scorer and splitter. + * + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; + + +/* Non-minified version is copied as a separate JS file, is available */ + +/** + * Porter Stemmer + */ +var Stemmer = function() { + + var step2list = { + ational: 'ate', + tional: 'tion', + enci: 'ence', + anci: 'ance', + izer: 'ize', + bli: 'ble', + alli: 'al', + entli: 'ent', + eli: 'e', + ousli: 'ous', + ization: 'ize', + ation: 'ate', + ator: 'ate', + alism: 'al', + iveness: 'ive', + fulness: 'ful', + ousness: 'ous', + aliti: 'al', + iviti: 'ive', + biliti: 'ble', + logi: 'log' + }; + + var step3list = { + icate: 'ic', + ative: '', + alize: 'al', + iciti: 'ic', + ical: 'ic', + ful: '', + ness: '' + }; + + var c = "[^aeiou]"; // consonant + var v = "[aeiouy]"; // vowel + var C = c + "[^aeiouy]*"; // consonant sequence + var V = v + "[aeiou]*"; // vowel sequence + + var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0 + var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1 + var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1 + var s_v = "^(" + C + ")?" + v; // vowel in stem + + this.stemWord = function (w) { + var stem; + var suffix; + var firstch; + var origword = w; + + if (w.length < 3) + return w; + + var re; + var re2; + var re3; + var re4; + + firstch = w.substr(0,1); + if (firstch == "y") + w = firstch.toUpperCase() + w.substr(1); + + // Step 1a + re = /^(.+?)(ss|i)es$/; + re2 = /^(.+?)([^s])s$/; + + if (re.test(w)) + w = w.replace(re,"$1$2"); + else if (re2.test(w)) + w = w.replace(re2,"$1$2"); + + // Step 1b + re = /^(.+?)eed$/; + re2 = /^(.+?)(ed|ing)$/; + if (re.test(w)) { + var fp = re.exec(w); + re = new RegExp(mgr0); + if (re.test(fp[1])) { + re = /.$/; + w = w.replace(re,""); + } + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1]; + re2 = new RegExp(s_v); + if (re2.test(stem)) { + w = stem; + re2 = /(at|bl|iz)$/; + re3 = new RegExp("([^aeiouylsz])\\1$"); + re4 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re2.test(w)) + w = w + "e"; + else if (re3.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + else if (re4.test(w)) + w = w + "e"; + } + } + + // Step 1c + re = /^(.+?)y$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(s_v); + if (re.test(stem)) + w = stem + "i"; + } + + // Step 2 + re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step2list[suffix]; + } + + // Step 3 + re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step3list[suffix]; + } + + // Step 4 + re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/; + re2 = /^(.+?)(s|t)(ion)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + if (re.test(stem)) + w = stem; + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1] + fp[2]; + re2 = new RegExp(mgr1); + if (re2.test(stem)) + w = stem; + } + + // Step 5 + re = /^(.+?)e$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + re2 = new RegExp(meq1); + re3 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re.test(stem) || (re2.test(stem) && !(re3.test(stem)))) + w = stem; + } + re = /ll$/; + re2 = new RegExp(mgr1); + if (re.test(w) && re2.test(w)) { + re = /.$/; + w = w.replace(re,""); 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false,\n nestedClass: \"active\",\n\n // Offset & reflow\n offset: 0,\n reflow: false,\n\n // Event support\n events: true,\n };\n\n //\n // Methods\n //\n\n /**\n * Merge two or more objects together.\n * @param {Object} objects The objects to merge together\n * @returns {Object} Merged values of defaults and options\n */\n var extend = function () {\n var merged = {};\n Array.prototype.forEach.call(arguments, function (obj) {\n for (var key in obj) {\n if (!obj.hasOwnProperty(key)) return;\n merged[key] = obj[key];\n }\n });\n return merged;\n };\n\n /**\n * Emit a custom event\n * @param {String} type The event type\n * @param {Node} elem The element to attach the event to\n * @param {Object} detail Any details to pass along with the event\n */\n var emitEvent = function (type, elem, detail) {\n // Make sure events are enabled\n if (!detail.settings.events) return;\n\n // Create a new event\n var event = new CustomEvent(type, {\n bubbles: true,\n cancelable: true,\n detail: detail,\n });\n\n // Dispatch the event\n elem.dispatchEvent(event);\n };\n\n /**\n * Get an element's distance from the top of the Document.\n * @param {Node} elem The element\n * @return {Number} Distance from the top in pixels\n */\n var getOffsetTop = function (elem) {\n var location = 0;\n if (elem.offsetParent) {\n while (elem) {\n location += elem.offsetTop;\n elem = elem.offsetParent;\n }\n }\n return location >= 0 ? location : 0;\n };\n\n /**\n * Sort content from first to last in the DOM\n * @param {Array} contents The content areas\n */\n var sortContents = function (contents) {\n if (contents) {\n contents.sort(function (item1, item2) {\n var offset1 = getOffsetTop(item1.content);\n var offset2 = getOffsetTop(item2.content);\n if (offset1 < offset2) return -1;\n return 1;\n });\n }\n };\n\n /**\n * Get the offset to use for calculating position\n * @param {Object} settings The settings for this instantiation\n * @return {Float} The number of pixels to offset the calculations\n */\n var getOffset = function (settings) {\n // if the offset is a function run it\n if (typeof settings.offset === \"function\") {\n return parseFloat(settings.offset());\n }\n\n // Otherwise, return it as-is\n return parseFloat(settings.offset);\n };\n\n /**\n * Get the document element's height\n * @private\n * @returns {Number}\n */\n var getDocumentHeight = function () {\n return Math.max(\n document.body.scrollHeight,\n document.documentElement.scrollHeight,\n document.body.offsetHeight,\n document.documentElement.offsetHeight,\n document.body.clientHeight,\n document.documentElement.clientHeight,\n );\n };\n\n /**\n * Determine if an element is in view\n * @param {Node} elem The element\n * @param {Object} settings The settings for this instantiation\n * @param {Boolean} bottom If true, check if element is above bottom of viewport instead\n * @return {Boolean} Returns true if element is in the viewport\n */\n var isInView = function (elem, settings, bottom) {\n 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content areas\n * @param {Object} settings The settings for this instantiation\n * @return {Object} The content area and matching navigation link\n */\n var getActive = function (contents, settings) {\n var last = contents[contents.length - 1];\n if (useLastItem(last, settings)) return last;\n for (var i = contents.length - 1; i >= 0; i--) {\n if (isInView(contents[i].content, settings)) return contents[i];\n }\n };\n\n /**\n * Deactivate parent navs in a nested navigation\n * @param {Node} nav The starting navigation element\n * @param {Object} settings The settings for this instantiation\n */\n var deactivateNested = function (nav, settings) {\n // If nesting isn't activated, bail\n if (!settings.nested || !nav.parentNode) return;\n\n // Get the parent navigation\n var li = nav.parentNode.closest(\"li\");\n if (!li) return;\n\n // Remove the active class\n li.classList.remove(settings.nestedClass);\n\n // Apply recursively to any parent navigation elements\n deactivateNested(li, settings);\n };\n\n /**\n * Deactivate a nav and content area\n * @param {Object} items The nav item and content to deactivate\n * @param {Object} settings The settings for this instantiation\n */\n var deactivate = function (items, settings) {\n // Make sure there are items to deactivate\n if (!items) return;\n\n // Get the parent list item\n var li = items.nav.closest(\"li\");\n if (!li) return;\n\n // Remove the active class from the nav and content\n li.classList.remove(settings.navClass);\n items.content.classList.remove(settings.contentClass);\n\n // Deactivate any parent navs in a nested navigation\n deactivateNested(li, settings);\n\n // Emit a custom event\n emitEvent(\"gumshoeDeactivate\", li, {\n link: items.nav,\n content: items.content,\n settings: settings,\n });\n };\n\n /**\n * Activate parent navs in a nested navigation\n * @param {Node} nav The starting navigation element\n * @param {Object} settings The settings for this instantiation\n */\n var activateNested = function (nav, settings) {\n // If nesting isn't activated, bail\n if (!settings.nested) return;\n\n // Get the parent navigation\n var li = nav.parentNode.closest(\"li\");\n if (!li) return;\n\n // Add the active class\n li.classList.add(settings.nestedClass);\n\n // Apply recursively to any parent navigation elements\n activateNested(li, settings);\n };\n\n /**\n * Activate a nav and content area\n * @param {Object} items The nav item and content to activate\n * @param {Object} settings The settings for this instantiation\n */\n var activate = function (items, settings) {\n // Make sure there are items to activate\n if (!items) return;\n\n // Get the parent list item\n var li = items.nav.closest(\"li\");\n if (!li) return;\n\n // Add the active class to the nav and content\n li.classList.add(settings.navClass);\n items.content.classList.add(settings.contentClass);\n\n // Activate any parent navs in a nested navigation\n activateNested(li, settings);\n\n // Emit a custom event\n emitEvent(\"gumshoeActivate\", li, {\n link: items.nav,\n content: items.content,\n settings: settings,\n });\n };\n\n /**\n * Create the Constructor object\n * @param {String} selector The selector to use for navigation items\n * @param {Object} options User options and settings\n */\n var Constructor = function (selector, options) {\n //\n // Variables\n //\n\n var publicAPIs = {};\n var navItems, contents, current, timeout, settings;\n\n //\n // Methods\n //\n\n /**\n * Set variables from DOM elements\n */\n publicAPIs.setup = function () {\n // Get all nav items\n navItems = document.querySelectorAll(selector);\n\n // Create contents array\n contents = [];\n\n // Loop through each item, get it's matching content, and push to the array\n Array.prototype.forEach.call(navItems, function (item) {\n // Get the content for the nav item\n var content = document.getElementById(\n decodeURIComponent(item.hash.substr(1)),\n );\n if (!content) return;\n\n // Push to the contents array\n 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This file is vendored from Furo (created by Pradyun Gedam) and used under the MIT license. */\n/*!\n * gumshoejs v5.1.2 (patched by @pradyunsg)\n * A simple, framework-agnostic scrollspy script.\n * (c) 2019 Chris Ferdinandi\n * MIT License\n * http://github.com/cferdinandi/gumshoe\n */\n\n(function (root, factory) {\n if (typeof define === \"function\" && define.amd) {\n define([], function () {\n return factory(root);\n });\n } else if (typeof exports === \"object\") {\n module.exports = factory(root);\n } else {\n root.Gumshoe = factory(root);\n }\n})(\n typeof global !== \"undefined\"\n ? global\n : typeof window !== \"undefined\"\n ? window\n : this,\n function (window) {\n \"use strict\";\n\n //\n // Defaults\n //\n\n var defaults = {\n // Active classes\n navClass: \"active\",\n contentClass: \"active\",\n\n // Nested navigation\n nested: false,\n nestedClass: \"active\",\n\n // Offset & reflow\n offset: 0,\n reflow: false,\n\n // Event support\n events: true,\n };\n\n //\n // Methods\n //\n\n /**\n * Merge two or more objects together.\n * @param {Object} objects The objects to merge together\n * @returns {Object} Merged values of defaults and options\n */\n var extend = function () {\n var merged = {};\n Array.prototype.forEach.call(arguments, function (obj) {\n for (var key in obj) {\n if (!obj.hasOwnProperty(key)) return;\n merged[key] = obj[key];\n }\n });\n return merged;\n };\n\n /**\n * Emit a custom event\n * @param {String} type The event type\n * @param {Node} elem The element to attach the event to\n * @param {Object} detail Any details to pass along with the event\n */\n var emitEvent = function (type, elem, detail) {\n // Make sure events are enabled\n if (!detail.settings.events) return;\n\n // Create a new event\n var event = new CustomEvent(type, {\n bubbles: true,\n cancelable: true,\n detail: detail,\n });\n\n // Dispatch the event\n elem.dispatchEvent(event);\n };\n\n /**\n * Get an element's distance from the top of the Document.\n * 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(window.innerHeight || document.documentElement.clientHeight)\n );\n }\n return parseInt(bounds.top, 10) <= offset;\n };\n\n /**\n * Check if at the bottom of the viewport\n * @return {Boolean} If true, page is at the bottom of the viewport\n */\n var isAtBottom = function () {\n if (\n Math.ceil(window.innerHeight + window.pageYOffset) >=\n getDocumentHeight()\n )\n return true;\n return false;\n };\n\n /**\n * Check if the last item should be used (even if not at the top of the page)\n * @param {Object} item The last item\n * @param {Object} settings The settings for this instantiation\n * @return {Boolean} If true, use the last item\n */\n var useLastItem = function (item, settings) {\n if (isAtBottom() && isInView(item.content, settings, true)) return true;\n return false;\n };\n\n /**\n * Get the active content\n * @param {Array} contents The content areas\n * @param {Object} settings The settings for this instantiation\n * @return {Object} The content area and matching navigation 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+ +/** + * Simple result scoring code. + */ +if (typeof Scorer === "undefined") { + var Scorer = { + // Implement the following function to further tweak the score for each result + // The function takes a result array [docname, title, anchor, descr, score, filename] + // and returns the new score. + /* + score: result => { + const [docname, title, anchor, descr, score, filename] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms, highlightTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + const contentRoot = document.documentElement.dataset.content_root; + + const [docName, title, anchor, descr, score, _filename] = item; + + let listItem = document.createElement("li"); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = contentRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = contentRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) { + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + // highlight search terms in the description + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + } + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms) + ); + // highlight search terms in the summary + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = _( + `Search finished, found ${resultCount} page(s) matching the search query.` + ); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms, + highlightTerms, +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms, highlightTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms, highlightTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() }); + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent !== undefined) return docContent.textContent; + console.warn( + "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + /** + * execute search (requires search index to be loaded) + */ + query: (query) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + // array of [docname, title, anchor, descr, score, filename] + let results = []; + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + let score = Math.round(100 * queryLower.length / title.length) + results.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id] of foundEntries) { + let score = Math.round(100 * queryLower.length / entry.length) + results.push([ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // lookup as object + objectTerms.forEach((term) => + results.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + results.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item))); + + // now sort the results by score (in opposite order of appearance, since the + // display function below uses pop() to retrieve items) and then + // alphabetically + results.sort((a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; + }); + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + results = results.reverse(); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms, highlightTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord) && !terms[word]) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord) && !titleTerms[word]) + arr.push({ files: titleTerms[word], score: Scorer.partialTitle }); + }); + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1) + fileMap.get(file).push(word); + else fileMap.set(file, [word]); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords) => { + const text = Search.htmlToText(htmlText); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/stable/0.4/_static/skeleton.css b/stable/0.4/_static/skeleton.css new file mode 100644 index 000000000..467c878c6 --- /dev/null +++ b/stable/0.4/_static/skeleton.css @@ -0,0 +1,296 @@ +/* Some sane resets. */ +html { + height: 100%; +} + +body { + margin: 0; + min-height: 100%; +} + +/* All the flexbox magic! */ +body, +.sb-announcement, +.sb-content, +.sb-main, +.sb-container, +.sb-container__inner, +.sb-article-container, +.sb-footer-content, +.sb-header, +.sb-header-secondary, +.sb-footer { + display: flex; +} + +/* These order things vertically */ +body, +.sb-main, +.sb-article-container { + flex-direction: column; +} + +/* Put elements in the center */ +.sb-header, +.sb-header-secondary, +.sb-container, +.sb-content, +.sb-footer, +.sb-footer-content { + justify-content: center; +} +/* Put elements at the ends */ +.sb-article-container { + justify-content: space-between; +} + +/* These elements grow. */ +.sb-main, +.sb-content, +.sb-container, +article { + flex-grow: 1; +} + +/* Because padding making this wider is not fun */ +article { + box-sizing: border-box; +} + +/* The announcements element should never be wider than the page. */ +.sb-announcement { + max-width: 100%; +} + +.sb-sidebar-primary, +.sb-sidebar-secondary { + flex-shrink: 0; + width: 17rem; +} + +.sb-announcement__inner { + justify-content: center; + + box-sizing: border-box; + height: 3rem; + + overflow-x: auto; + white-space: nowrap; +} + +/* Sidebars, with checkbox-based toggle */ +.sb-sidebar-primary, +.sb-sidebar-secondary { + position: fixed; + height: 100%; + top: 0; +} + +.sb-sidebar-primary { + left: -17rem; + transition: left 250ms ease-in-out; +} +.sb-sidebar-secondary { + right: -17rem; + transition: right 250ms ease-in-out; +} + +.sb-sidebar-toggle { + display: none; +} +.sb-sidebar-overlay { + position: fixed; + top: 0; + width: 0; + height: 0; + + transition: width 0ms ease 250ms, height 0ms ease 250ms, opacity 250ms ease; + + opacity: 0; + background-color: rgba(0, 0, 0, 0.54); +} + +#sb-sidebar-toggle--primary:checked + ~ .sb-sidebar-overlay[for="sb-sidebar-toggle--primary"], +#sb-sidebar-toggle--secondary:checked + ~ .sb-sidebar-overlay[for="sb-sidebar-toggle--secondary"] { + width: 100%; + height: 100%; + opacity: 1; + transition: width 0ms ease, height 0ms ease, opacity 250ms ease; +} + +#sb-sidebar-toggle--primary:checked ~ .sb-container .sb-sidebar-primary { + left: 0; +} +#sb-sidebar-toggle--secondary:checked ~ .sb-container .sb-sidebar-secondary { + right: 0; +} + +/* Full-width mode */ +.drop-secondary-sidebar-for-full-width-content + .hide-when-secondary-sidebar-shown { + display: none !important; +} +.drop-secondary-sidebar-for-full-width-content .sb-sidebar-secondary { + display: none !important; +} + +/* Mobile views */ +.sb-page-width { + width: 100%; +} + +.sb-article-container, +.sb-footer-content__inner, +.drop-secondary-sidebar-for-full-width-content .sb-article, +.drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 100vw; +} + +.sb-article, +.match-content-width { + padding: 0 1rem; + box-sizing: border-box; +} + +@media (min-width: 32rem) { + .sb-article, + .match-content-width { + padding: 0 2rem; + } +} + +/* Tablet views */ +@media (min-width: 42rem) { + .sb-article-container { + width: auto; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 42rem; + } + .sb-article, + .match-content-width { + width: 42rem; + } +} +@media (min-width: 46rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 46rem; + } + .sb-article, + .match-content-width { + width: 46rem; + } +} +@media (min-width: 50rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 50rem; + } + .sb-article, + .match-content-width { + width: 50rem; + } +} + +/* Tablet views */ +@media (min-width: 59rem) { + .sb-sidebar-secondary { + position: static; + } + .hide-when-secondary-sidebar-shown { + display: none !important; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 59rem; + } + .sb-article, + .match-content-width { + width: 42rem; + } +} +@media (min-width: 63rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 63rem; + } + .sb-article, + .match-content-width { + width: 46rem; + } +} +@media (min-width: 67rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 67rem; + } + .sb-article, + .match-content-width { + width: 50rem; + } +} + +/* Desktop views */ +@media (min-width: 76rem) { + .sb-sidebar-primary { + position: static; + } + .hide-when-primary-sidebar-shown { + display: none !important; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 59rem; + } + .sb-article, + .match-content-width { + width: 42rem; + } +} + +/* Full desktop views */ +@media (min-width: 80rem) { + .sb-article, + .match-content-width { + width: 46rem; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 63rem; + } +} + +@media (min-width: 84rem) { + .sb-article, + .match-content-width { + width: 50rem; + } + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 67rem; + } +} + +@media (min-width: 88rem) { + .sb-footer-content__inner, + .drop-secondary-sidebar-for-full-width-content .sb-article, + .drop-secondary-sidebar-for-full-width-content .match-content-width { + width: 67rem; + } + .sb-page-width { + width: 88rem; + } +} diff --git a/stable/0.4/_static/sphinx_highlight.js b/stable/0.4/_static/sphinx_highlight.js new file mode 100644 index 000000000..8a96c69a1 --- /dev/null +++ b/stable/0.4/_static/sphinx_highlight.js @@ -0,0 +1,154 @@ +/* Highlighting utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + const rest = document.createTextNode(val.substr(pos + text.length)); + parent.insertBefore( + span, + parent.insertBefore( + rest, + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + /* There may be more occurrences of search term in this node. So call this + * function recursively on the remaining fragment. + */ + _highlight(rest, addItems, text, className); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(() => { + /* Do not call highlightSearchWords() when we are on the search page. + * It will highlight words from the *previous* search query. + */ + if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords(); + SphinxHighlight.initEscapeListener(); +}); diff --git a/stable/0.4/_static/styles/furo-extensions.css b/stable/0.4/_static/styles/furo-extensions.css new file mode 100644 index 000000000..bc447f228 --- /dev/null +++ b/stable/0.4/_static/styles/furo-extensions.css @@ -0,0 +1,2 @@ +#furo-sidebar-ad-placement{padding:var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)}#furo-sidebar-ad-placement .ethical-sidebar{background:var(--color-background-secondary);border:none;box-shadow:none}#furo-sidebar-ad-placement 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Correct the color inheritance from `fieldset` elements in IE.\n * 3. Remove the padding so developers are not caught out when they zero out\n * `fieldset` elements in all browsers.\n */\n\nlegend {\n box-sizing: border-box; /* 1 */\n color: inherit; /* 2 */\n display: table; /* 1 */\n max-width: 100%; /* 1 */\n padding: 0; /* 3 */\n white-space: normal; /* 1 */\n}\n\n/**\n * Add the correct vertical alignment in Chrome, Firefox, and Opera.\n */\n\nprogress {\n vertical-align: baseline;\n}\n\n/**\n * Remove the default vertical scrollbar in IE 10+.\n */\n\ntextarea {\n overflow: auto;\n}\n\n/**\n * 1. Add the correct box sizing in IE 10.\n * 2. Remove the padding in IE 10.\n */\n\n[type=\"checkbox\"],\n[type=\"radio\"] {\n box-sizing: border-box; /* 1 */\n padding: 0; /* 2 */\n}\n\n/**\n * Correct the cursor style of increment and decrement buttons in Chrome.\n */\n\n[type=\"number\"]::-webkit-inner-spin-button,\n[type=\"number\"]::-webkit-outer-spin-button {\n height: auto;\n}\n\n/**\n * 1. Correct the odd appearance in Chrome and Safari.\n * 2. Correct the outline style in Safari.\n */\n\n[type=\"search\"] {\n -webkit-appearance: textfield; /* 1 */\n outline-offset: -2px; /* 2 */\n}\n\n/**\n * Remove the inner padding in Chrome and Safari on macOS.\n */\n\n[type=\"search\"]::-webkit-search-decoration {\n -webkit-appearance: none;\n}\n\n/**\n * 1. Correct the inability to style clickable types in iOS and Safari.\n * 2. Change font properties to `inherit` in Safari.\n */\n\n::-webkit-file-upload-button {\n -webkit-appearance: button; /* 1 */\n font: inherit; /* 2 */\n}\n\n/* Interactive\n ========================================================================== */\n\n/*\n * Add the correct display in Edge, IE 10+, and Firefox.\n */\n\ndetails {\n display: block;\n}\n\n/*\n * Add the correct display in all browsers.\n */\n\nsummary {\n display: list-item;\n}\n\n/* Misc\n ========================================================================== */\n\n/**\n * Add the correct display in IE 10+.\n */\n\ntemplate {\n display: none;\n}\n\n/**\n * Add the correct display in IE 10.\n */\n\n[hidden] {\n display: none;\n}\n","// This file contains styles for managing print media.\n\n////////////////////////////////////////////////////////////////////////////////\n// Hide elements not relevant to print media.\n////////////////////////////////////////////////////////////////////////////////\n@media print\n // Hide icon container.\n .content-icon-container\n display: none !important\n\n // Hide showing header links if hovering over when printing.\n .headerlink\n display: none !important\n\n // Hide mobile header.\n .mobile-header\n display: none !important\n\n // Hide navigation links.\n .related-pages\n display: none !important\n\n////////////////////////////////////////////////////////////////////////////////\n// Tweaks related to decolorization.\n////////////////////////////////////////////////////////////////////////////////\n@media print\n // Apply a border around code which no longer have a color background.\n .highlight\n border: 0.1pt solid var(--color-foreground-border)\n\n////////////////////////////////////////////////////////////////////////////////\n// Avoid page break in some relevant cases.\n////////////////////////////////////////////////////////////////////////////////\n@media print\n ul, ol, dl, a, table, pre, blockquote\n page-break-inside: avoid\n\n h1, h2, h3, h4, h5, h6, img, figure, caption\n page-break-inside: avoid\n page-break-after: avoid\n\n ul, ol, dl\n page-break-before: avoid\n",".visually-hidden\n position: absolute !important\n width: 1px !important\n height: 1px !important\n padding: 0 !important\n margin: -1px !important\n overflow: hidden !important\n clip: rect(0,0,0,0) !important\n white-space: nowrap !important\n border: 0 !important\n\n:-moz-focusring\n outline: auto\n","// This file serves as the \"skeleton\" of the theming logic.\n//\n// This contains the bulk of the logic for handling dark mode, color scheme\n// toggling and the handling of color-scheme-specific hiding of elements.\n\nbody\n @include fonts\n @include spacing\n @include icons\n @include admonitions\n @include default-admonition(#651fff, \"abstract\")\n @include default-topic(#14B8A6, \"pencil\")\n\n @include colors\n\n.only-light\n display: block !important\nhtml body .only-dark\n display: none !important\n\n// Ignore dark-mode hints if print media.\n@media not print\n // Enable dark-mode, if requested.\n body[data-theme=\"dark\"]\n @include colors-dark\n\n html & .only-light\n display: none !important\n .only-dark\n display: block !important\n\n // Enable dark mode, unless explicitly told to avoid.\n @media (prefers-color-scheme: dark)\n body:not([data-theme=\"light\"])\n @include colors-dark\n\n html & .only-light\n display: none !important\n .only-dark\n display: block !important\n\n//\n// Theme toggle presentation\n//\nbody[data-theme=\"auto\"]\n .theme-toggle svg.theme-icon-when-auto\n display: block\n\nbody[data-theme=\"dark\"]\n .theme-toggle svg.theme-icon-when-dark\n display: block\n\nbody[data-theme=\"light\"]\n .theme-toggle svg.theme-icon-when-light\n display: block\n","// Fonts used by this theme.\n//\n// There are basically two things here -- using the system font stack and\n// defining sizes for various elements in %ages. We could have also used `em`\n// but %age is easier to reason about for me.\n\n@mixin fonts {\n // These are adapted from https://systemfontstack.com/\n --font-stack: -apple-system, BlinkMacSystemFont, Segoe UI, Helvetica, Arial,\n sans-serif, Apple Color Emoji, Segoe UI Emoji;\n --font-stack--monospace: \"SFMono-Regular\", Menlo, Consolas, Monaco,\n Liberation Mono, Lucida Console, monospace;\n\n --font-size--normal: 100%;\n --font-size--small: 87.5%;\n --font-size--small--2: 81.25%;\n --font-size--small--3: 75%;\n --font-size--small--4: 62.5%;\n\n // Sidebar\n --sidebar-caption-font-size: var(--font-size--small--2);\n --sidebar-item-font-size: var(--font-size--small);\n --sidebar-search-input-font-size: var(--font-size--small);\n\n // Table of Contents\n --toc-font-size: var(--font-size--small--3);\n --toc-font-size--mobile: var(--font-size--normal);\n --toc-title-font-size: var(--font-size--small--4);\n\n // Admonitions\n //\n // These aren't defined in terms of %ages, since nesting these is permitted.\n --admonition-font-size: 0.8125rem;\n --admonition-title-font-size: 0.8125rem;\n\n // Code\n --code-font-size: var(--font-size--small--2);\n\n // API\n --api-font-size: var(--font-size--small);\n}\n","// Spacing for various elements on the page\n//\n// If the user wants to tweak things in a certain way, they are permitted to.\n// They also have to deal with the consequences though!\n\n@mixin spacing {\n // Header!\n --header-height: calc(\n var(--sidebar-item-line-height) + 4 * #{var(--sidebar-item-spacing-vertical)}\n );\n --header-padding: 0.5rem;\n\n // Sidebar\n --sidebar-tree-space-above: 1.5rem;\n --sidebar-caption-space-above: 1rem;\n\n --sidebar-item-line-height: 1rem;\n --sidebar-item-spacing-vertical: 0.5rem;\n --sidebar-item-spacing-horizontal: 1rem;\n --sidebar-item-height: calc(\n var(--sidebar-item-line-height) + 2 *#{var(--sidebar-item-spacing-vertical)}\n );\n\n --sidebar-expander-width: var(--sidebar-item-height); // be square\n\n --sidebar-search-space-above: 0.5rem;\n --sidebar-search-input-spacing-vertical: 0.5rem;\n --sidebar-search-input-spacing-horizontal: 0.5rem;\n --sidebar-search-input-height: 1rem;\n --sidebar-search-icon-size: var(--sidebar-search-input-height);\n\n // Table of Contents\n --toc-title-padding: 0.25rem 0;\n --toc-spacing-vertical: 1.5rem;\n --toc-spacing-horizontal: 1.5rem;\n --toc-item-spacing-vertical: 0.4rem;\n --toc-item-spacing-horizontal: 1rem;\n}\n","// Expose theme icons as CSS variables.\n\n$icons: (\n // Adapted from tabler-icons\n // url: https://tablericons.com/\n \"search\":\n url('data:image/svg+xml;charset=utf-8,'),\n // Factored out from mkdocs-material on 24-Aug-2020.\n // url: https://squidfunk.github.io/mkdocs-material/reference/admonitions/\n \"pencil\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"abstract\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"info\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"flame\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"question\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"warning\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"failure\":\n url('data:image/svg+xml;charset=utf-8,'),\n \"spark\":\n url('data:image/svg+xml;charset=utf-8,')\n);\n\n@mixin icons {\n @each $name, $glyph in $icons {\n --icon-#{$name}: #{$glyph};\n }\n}\n","// Admonitions\n\n// Structure of these is:\n// admonition-class: color \"icon-name\";\n//\n// The colors are translated into CSS variables below. The icons are\n// used directly in the main declarations to set the `mask-image` in\n// the title.\n\n// prettier-ignore\n$admonitions: (\n // Each of these has an reST directives for it.\n \"caution\": #ff9100 \"spark\",\n \"warning\": #ff9100 \"warning\",\n \"danger\": #ff5252 \"spark\",\n \"attention\": #ff5252 \"warning\",\n \"error\": #ff5252 \"failure\",\n \"hint\": #00c852 \"question\",\n \"tip\": #00c852 \"info\",\n \"important\": #00bfa5 \"flame\",\n \"note\": #00b0ff \"pencil\",\n \"seealso\": #448aff \"info\",\n \"admonition-todo\": #808080 \"pencil\"\n);\n\n@mixin default-admonition($color, $icon-name) {\n --color-admonition-title: #{$color};\n --color-admonition-title-background: #{rgba($color, 0.2)};\n\n --icon-admonition-default: var(--icon-#{$icon-name});\n}\n\n@mixin default-topic($color, $icon-name) {\n --color-topic-title: #{$color};\n --color-topic-title-background: #{rgba($color, 0.2)};\n\n --icon-topic-default: var(--icon-#{$icon-name});\n}\n\n@mixin admonitions {\n @each $name, $values in $admonitions {\n --color-admonition-title--#{$name}: #{nth($values, 1)};\n --color-admonition-title-background--#{$name}: #{rgba(\n nth($values, 1),\n 0.2\n )};\n }\n}\n","// Colors used throughout this theme.\n//\n// The aim is to give the user more control. Thus, instead of hard-coding colors\n// in various parts of the stylesheet, the approach taken is to define all\n// colors as CSS variables and reusing them in all the places.\n//\n// `colors-dark` depends on `colors` being included at a lower specificity.\n\n@mixin colors {\n --color-problematic: #b30000;\n\n // Base Colors\n --color-foreground-primary: black; // for main text and headings\n --color-foreground-secondary: #5a5c63; // for secondary text\n --color-foreground-muted: #646776; // for muted text\n --color-foreground-border: #878787; // for content borders\n\n --color-background-primary: white; // for content\n --color-background-secondary: #f8f9fb; // for navigation + ToC\n --color-background-hover: #efeff4ff; // for navigation-item hover\n --color-background-hover--transparent: #efeff400;\n --color-background-border: #eeebee; // for UI borders\n --color-background-item: #ccc; // for \"background\" items (eg: copybutton)\n\n // Announcements\n --color-announcement-background: #000000dd;\n --color-announcement-text: #eeebee;\n\n // Brand colors\n --color-brand-primary: #2962ff;\n --color-brand-content: #2a5adf;\n\n // API documentation\n --color-api-background: var(--color-background-hover--transparent);\n --color-api-background-hover: var(--color-background-hover);\n --color-api-overall: var(--color-foreground-secondary);\n --color-api-name: var(--color-problematic);\n --color-api-pre-name: var(--color-problematic);\n --color-api-paren: var(--color-foreground-secondary);\n --color-api-keyword: var(--color-foreground-primary);\n --color-highlight-on-target: #ffffcc;\n\n // Inline code background\n --color-inline-code-background: var(--color-background-secondary);\n\n // Highlighted text (search)\n --color-highlighted-background: #ddeeff;\n --color-highlighted-text: var(--color-foreground-primary);\n\n // GUI Labels\n --color-guilabel-background: #ddeeff80;\n --color-guilabel-border: #bedaf580;\n --color-guilabel-text: var(--color-foreground-primary);\n\n // Admonitions!\n --color-admonition-background: transparent;\n\n //////////////////////////////////////////////////////////////////////////////\n // Everything below this should be one of:\n // - var(...)\n // - *-gradient(...)\n // - special literal values (eg: transparent, none)\n //////////////////////////////////////////////////////////////////////////////\n\n // Tables\n --color-table-header-background: var(--color-background-secondary);\n --color-table-border: var(--color-background-border);\n\n // Cards\n --color-card-border: var(--color-background-secondary);\n --color-card-background: transparent;\n --color-card-marginals-background: var(--color-background-secondary);\n\n // Header\n --color-header-background: var(--color-background-primary);\n --color-header-border: var(--color-background-border);\n --color-header-text: var(--color-foreground-primary);\n\n // Sidebar (left)\n --color-sidebar-background: var(--color-background-secondary);\n --color-sidebar-background-border: var(--color-background-border);\n\n --color-sidebar-brand-text: var(--color-foreground-primary);\n --color-sidebar-caption-text: var(--color-foreground-muted);\n --color-sidebar-link-text: var(--color-foreground-secondary);\n --color-sidebar-link-text--top-level: var(--color-brand-primary);\n\n --color-sidebar-item-background: var(--color-sidebar-background);\n --color-sidebar-item-background--current: var(\n --color-sidebar-item-background\n );\n --color-sidebar-item-background--hover: linear-gradient(\n 90deg,\n var(--color-background-hover--transparent) 0%,\n var(--color-background-hover) var(--sidebar-item-spacing-horizontal),\n var(--color-background-hover) 100%\n );\n\n --color-sidebar-item-expander-background: transparent;\n --color-sidebar-item-expander-background--hover: var(\n --color-background-hover\n );\n\n --color-sidebar-search-text: var(--color-foreground-primary);\n --color-sidebar-search-background: var(--color-background-secondary);\n --color-sidebar-search-background--focus: var(--color-background-primary);\n --color-sidebar-search-border: var(--color-background-border);\n --color-sidebar-search-icon: var(--color-foreground-muted);\n\n // Table of Contents (right)\n --color-toc-background: var(--color-background-primary);\n --color-toc-title-text: var(--color-foreground-muted);\n --color-toc-item-text: var(--color-foreground-secondary);\n --color-toc-item-text--hover: var(--color-foreground-primary);\n --color-toc-item-text--active: var(--color-brand-primary);\n\n // Actual page contents\n --color-content-foreground: var(--color-foreground-primary);\n --color-content-background: transparent;\n\n // Links\n --color-link: var(--color-brand-content);\n --color-link--hover: var(--color-brand-content);\n --color-link-underline: var(--color-background-border);\n --color-link-underline--hover: var(--color-foreground-border);\n}\n\n@mixin colors-dark {\n --color-problematic: #ee5151;\n\n // Base Colors\n --color-foreground-primary: #ffffffcc; // for main text and headings\n --color-foreground-secondary: #9ca0a5; // for secondary text\n --color-foreground-muted: #81868d; // for muted text\n --color-foreground-border: #666666; // for content borders\n\n --color-background-primary: #131416; // for content\n --color-background-secondary: #1a1c1e; // for navigation + ToC\n --color-background-hover: #1e2124ff; // for navigation-item hover\n --color-background-hover--transparent: #1e212400;\n --color-background-border: #303335; // for UI borders\n --color-background-item: #444; // for \"background\" items (eg: copybutton)\n\n // Announcements\n --color-announcement-background: #000000dd;\n --color-announcement-text: #eeebee;\n\n // Brand colors\n --color-brand-primary: #2b8cee;\n --color-brand-content: #368ce2;\n\n // Highlighted text (search)\n --color-highlighted-background: #083563;\n\n // GUI Labels\n --color-guilabel-background: #08356380;\n --color-guilabel-border: #13395f80;\n\n // API documentation\n --color-api-keyword: var(--color-foreground-secondary);\n --color-highlight-on-target: #333300;\n\n // Admonitions\n --color-admonition-background: #18181a;\n\n // Cards\n --color-card-border: var(--color-background-secondary);\n --color-card-background: #18181a;\n --color-card-marginals-background: var(--color-background-hover);\n}\n","// This file contains the styling for making the content throughout the page,\n// including fonts, paragraphs, headings and spacing among these elements.\n\nbody\n font-family: var(--font-stack)\npre,\ncode,\nkbd,\nsamp\n font-family: var(--font-stack--monospace)\n\n// Make fonts look slightly nicer.\nbody\n -webkit-font-smoothing: antialiased\n -moz-osx-font-smoothing: grayscale\n\n// Line height from Bootstrap 4.1\narticle\n line-height: 1.5\n\n//\n// Headings\n//\nh1,\nh2,\nh3,\nh4,\nh5,\nh6\n line-height: 1.25\n font-weight: bold\n\n border-radius: 0.5rem\n margin-top: 0.5rem\n margin-bottom: 0.5rem\n margin-left: -0.5rem\n margin-right: -0.5rem\n padding-left: 0.5rem\n padding-right: 0.5rem\n\n + p\n margin-top: 0\n\nh1\n font-size: 2.5em\n margin-top: 1.75rem\n margin-bottom: 1rem\nh2\n font-size: 2em\n margin-top: 1.75rem\nh3\n font-size: 1.5em\nh4\n font-size: 1.25em\nh5\n font-size: 1.125em\nh6\n font-size: 1em\n\nsmall\n opacity: 75%\n font-size: 80%\n\n// Paragraph\np\n margin-top: 0.5rem\n margin-bottom: 0.75rem\n\n// Horizontal rules\nhr.docutils\n height: 1px\n padding: 0\n margin: 2rem 0\n background-color: var(--color-background-border)\n border: 0\n\n.centered\n text-align: center\n\n// Links\na\n text-decoration: underline\n\n color: var(--color-link)\n text-decoration-color: var(--color-link-underline)\n\n &:hover\n color: var(--color-link--hover)\n text-decoration-color: var(--color-link-underline--hover)\n &.muted-link\n color: inherit\n &:hover\n color: var(--color-link)\n text-decoration-color: var(--color-link-underline--hover)\n","// This file contains the styles for the overall layouting of the documentation\n// skeleton, including the responsive changes as well as sidebar toggles.\n//\n// This is implemented as a mobile-last design, which isn't ideal, but it is\n// reasonably good-enough and I got pretty tired by the time I'd finished this\n// to move the rules around to fix this. Shouldn't take more than 3-4 hours,\n// if you know what you're doing tho.\n\n// HACK: Not all browsers account for the scrollbar width in media queries.\n// This results in horizontal scrollbars in the breakpoint where we go\n// from displaying everything to hiding the ToC. We accomodate for this by\n// adding a bit of padding to the TOC drawer, disabling the horizontal\n// scrollbar and allowing the scrollbars to cover the padding.\n// https://www.456bereastreet.com/archive/201301/media_query_width_and_vertical_scrollbars/\n\n// HACK: Always having the scrollbar visible, prevents certain browsers from\n// causing the content to stutter horizontally between taller-than-viewport and\n// not-taller-than-viewport pages.\n\nhtml\n overflow-x: hidden\n overflow-y: scroll\n scroll-behavior: smooth\n\n.sidebar-scroll, .toc-scroll, article[role=main] *\n // Override Firefox scrollbar style\n scrollbar-width: thin\n scrollbar-color: var(--color-foreground-border) transparent\n\n // Override Chrome scrollbar styles\n &::-webkit-scrollbar\n width: 0.25rem\n height: 0.25rem\n &::-webkit-scrollbar-thumb\n background-color: var(--color-foreground-border)\n border-radius: 0.125rem\n\n//\n// Overalls\n//\nhtml,\nbody\n height: 100%\n color: var(--color-foreground-primary)\n background: var(--color-background-primary)\n\narticle\n color: var(--color-content-foreground)\n background: var(--color-content-background)\n overflow-wrap: break-word\n\n.page\n display: flex\n // fill the viewport for pages with little content.\n min-height: 100%\n\n.mobile-header\n width: 100%\n height: var(--header-height)\n background-color: var(--color-header-background)\n color: var(--color-header-text)\n border-bottom: 1px solid var(--color-header-border)\n\n // Looks like sub-script/super-script have this, and we need this to\n // be \"on top\" of those.\n z-index: 10\n\n // We don't show the header on large screens.\n display: none\n\n // Add shadow when scrolled\n &.scrolled\n border-bottom: none\n box-shadow: 0 0 0.2rem rgba(0, 0, 0, 0.1), 0 0.2rem 0.4rem rgba(0, 0, 0, 0.2)\n\n .header-center\n a\n color: var(--color-header-text)\n text-decoration: none\n\n.main\n display: flex\n flex: 1\n\n// Sidebar (left) also covers the entire left portion of screen.\n.sidebar-drawer\n box-sizing: border-box\n\n border-right: 1px solid var(--color-sidebar-background-border)\n background: var(--color-sidebar-background)\n\n display: flex\n justify-content: flex-end\n // These next two lines took me two days to figure out.\n width: calc((100% - #{$full-width}) / 2 + #{$sidebar-width})\n min-width: $sidebar-width\n\n// Scroll-along sidebars\n.sidebar-container,\n.toc-drawer\n box-sizing: border-box\n width: $sidebar-width\n\n.toc-drawer\n background: var(--color-toc-background)\n // See HACK described on top of this document\n padding-right: 1rem\n\n.sidebar-sticky,\n.toc-sticky\n position: sticky\n top: 0\n height: min(100%, 100vh)\n height: 100vh\n\n display: flex\n flex-direction: column\n\n.sidebar-scroll,\n.toc-scroll\n flex-grow: 1\n flex-shrink: 1\n\n overflow: auto\n scroll-behavior: smooth\n\n// Central items.\n.content\n padding: 0 $content-padding\n width: $content-width\n\n display: flex\n flex-direction: column\n justify-content: space-between\n\n.icon\n display: inline-block\n height: 1rem\n width: 1rem\n svg\n width: 100%\n height: 100%\n\n//\n// Accommodate announcement banner\n//\n.announcement\n background-color: var(--color-announcement-background)\n color: var(--color-announcement-text)\n\n height: var(--header-height)\n display: flex\n align-items: center\n overflow-x: auto\n & + .page\n min-height: calc(100% - var(--header-height))\n\n.announcement-content\n box-sizing: border-box\n padding: 0.5rem\n min-width: 100%\n white-space: nowrap\n text-align: center\n\n a\n color: var(--color-announcement-text)\n text-decoration-color: var(--color-announcement-text)\n\n &:hover\n color: var(--color-announcement-text)\n text-decoration-color: var(--color-link--hover)\n\n////////////////////////////////////////////////////////////////////////////////\n// Toggles for theme\n////////////////////////////////////////////////////////////////////////////////\n.no-js .theme-toggle-container // don't show theme toggle if there's no JS\n display: none\n\n.theme-toggle-container\n vertical-align: middle\n\n.theme-toggle\n cursor: pointer\n border: none\n padding: 0\n background: transparent\n\n.theme-toggle svg\n vertical-align: middle\n height: 1rem\n width: 1rem\n color: var(--color-foreground-primary)\n display: none\n\n.theme-toggle-header\n float: left\n padding: 1rem 0.5rem\n\n////////////////////////////////////////////////////////////////////////////////\n// Toggles for elements\n////////////////////////////////////////////////////////////////////////////////\n.toc-overlay-icon, .nav-overlay-icon\n display: none\n cursor: pointer\n\n .icon\n color: var(--color-foreground-secondary)\n height: 1rem\n width: 1rem\n\n.toc-header-icon, .nav-overlay-icon\n // for when we set display: flex\n justify-content: center\n align-items: center\n\n.toc-content-icon\n height: 1.5rem\n width: 1.5rem\n\n.content-icon-container\n float: right\n display: flex\n margin-top: 1.5rem\n margin-left: 1rem\n margin-bottom: 1rem\n gap: 0.5rem\n\n .edit-this-page svg\n color: inherit\n height: 1rem\n width: 1rem\n\n.sidebar-toggle\n position: absolute\n display: none\n// \n.sidebar-toggle[name=\"__toc\"]\n left: 20px\n.sidebar-toggle:checked\n left: 40px\n// \n\n.overlay\n position: fixed\n top: 0\n width: 0\n height: 0\n\n transition: width 0ms, height 0ms, opacity 250ms ease-out\n\n opacity: 0\n background-color: rgba(0, 0, 0, 0.54)\n.sidebar-overlay\n z-index: 20\n.toc-overlay\n z-index: 40\n\n// Keep things on top and smooth.\n.sidebar-drawer\n z-index: 30\n transition: left 250ms ease-in-out\n.toc-drawer\n z-index: 50\n transition: right 250ms ease-in-out\n\n// Show the Sidebar\n#__navigation:checked\n & ~ .sidebar-overlay\n width: 100%\n height: 100%\n opacity: 1\n & ~ .page\n .sidebar-drawer\n top: 0\n left: 0\n // Show the toc sidebar\n#__toc:checked\n & ~ .toc-overlay\n width: 100%\n height: 100%\n opacity: 1\n & ~ .page\n .toc-drawer\n top: 0\n right: 0\n\n////////////////////////////////////////////////////////////////////////////////\n// Back to top\n////////////////////////////////////////////////////////////////////////////////\n.back-to-top\n text-decoration: none\n\n display: none\n position: fixed\n left: 0\n top: 1rem\n padding: 0.5rem\n padding-right: 0.75rem\n border-radius: 1rem\n font-size: 0.8125rem\n\n background: var(--color-background-primary)\n box-shadow: 0 0.2rem 0.5rem rgba(0, 0, 0, 0.05), #6b728080 0px 0px 1px 0px\n\n z-index: 10\n\n margin-left: 50%\n transform: translateX(-50%)\n svg\n height: 1rem\n width: 1rem\n fill: currentColor\n display: inline-block\n\n span\n margin-left: 0.25rem\n\n .show-back-to-top &\n display: flex\n align-items: center\n\n////////////////////////////////////////////////////////////////////////////////\n// Responsive layouting\n////////////////////////////////////////////////////////////////////////////////\n// Make things a bit bigger on bigger screens.\n@media (min-width: $full-width + $sidebar-width)\n html\n font-size: 110%\n\n@media (max-width: $full-width)\n // Collapse \"toc\" into the icon.\n .toc-content-icon\n display: flex\n .toc-drawer\n position: fixed\n height: 100vh\n top: 0\n right: -$sidebar-width\n border-left: 1px solid var(--color-background-muted)\n .toc-tree\n border-left: none\n font-size: var(--toc-font-size--mobile)\n\n // Accomodate for a changed content width.\n .sidebar-drawer\n width: calc((100% - #{$full-width - $sidebar-width}) / 2 + #{$sidebar-width})\n\n@media (max-width: $full-width - $sidebar-width)\n // Collapse \"navigation\".\n .nav-overlay-icon\n display: flex\n .sidebar-drawer\n position: fixed\n height: 100vh\n width: $sidebar-width\n\n top: 0\n left: -$sidebar-width\n\n // Swap which icon is visible.\n .toc-header-icon\n display: flex\n .toc-content-icon, .theme-toggle-content\n display: none\n .theme-toggle-header\n display: block\n\n // Show the header.\n .mobile-header\n position: sticky\n top: 0\n display: flex\n justify-content: space-between\n align-items: center\n\n .header-left,\n .header-right\n display: flex\n height: var(--header-height)\n padding: 0 var(--header-padding)\n label\n height: 100%\n width: 100%\n user-select: none\n\n .nav-overlay-icon .icon,\n .theme-toggle svg\n height: 1.25rem\n width: 1.25rem\n\n // Add a scroll margin for the content\n :target\n scroll-margin-top: var(--header-height)\n\n // Show back-to-top below the header\n .back-to-top\n top: calc(var(--header-height) + 0.5rem)\n\n // Center the page, and accommodate for the header.\n .page\n flex-direction: column\n justify-content: center\n .content\n margin-left: auto\n margin-right: auto\n\n@media (max-width: $content-width + 2* $content-padding)\n // Content should respect window limits.\n .content\n width: 100%\n overflow-x: auto\n\n@media (max-width: $content-width)\n .content\n padding: 0 $content-padding--small\n // Don't float sidebars to the right.\n article aside.sidebar\n float: none\n width: 100%\n margin: 1rem 0\n","//\n// The design here is strongly inspired by mkdocs-material.\n.admonition, .topic\n margin: 1rem auto\n padding: 0 0.5rem 0.5rem 0.5rem\n\n background: var(--color-admonition-background)\n\n border-radius: 0.2rem\n box-shadow: 0 0.2rem 0.5rem rgba(0, 0, 0, 0.05), 0 0 0.0625rem rgba(0, 0, 0, 0.1)\n\n font-size: var(--admonition-font-size)\n\n overflow: hidden\n page-break-inside: avoid\n\n // First element should have no margin, since the title has it.\n > :nth-child(2)\n margin-top: 0\n\n // Last item should have no margin, since we'll control that w/ padding\n > :last-child\n margin-bottom: 0\n\n.admonition p.admonition-title,\np.topic-title\n position: relative\n margin: 0 -0.5rem 0.5rem\n padding-left: 2rem\n padding-right: .5rem\n padding-top: .4rem\n padding-bottom: .4rem\n\n font-weight: 500\n font-size: var(--admonition-title-font-size)\n line-height: 1.3\n\n // Our fancy icon\n &::before\n content: \"\"\n position: absolute\n left: 0.5rem\n width: 1rem\n height: 1rem\n\n// Default styles\np.admonition-title\n background-color: var(--color-admonition-title-background)\n &::before\n background-color: var(--color-admonition-title)\n mask-image: var(--icon-admonition-default)\n mask-repeat: no-repeat\n\np.topic-title\n background-color: var(--color-topic-title-background)\n &::before\n background-color: var(--color-topic-title)\n mask-image: var(--icon-topic-default)\n mask-repeat: no-repeat\n\n//\n// Variants\n//\n.admonition\n border-left: 0.2rem solid var(--color-admonition-title)\n\n @each $type, $value in $admonitions\n &.#{$type}\n border-left-color: var(--color-admonition-title--#{$type})\n > .admonition-title\n background-color: var(--color-admonition-title-background--#{$type})\n &::before\n background-color: var(--color-admonition-title--#{$type})\n mask-image: var(--icon-#{nth($value, 2)})\n\n.admonition-todo > .admonition-title\n text-transform: uppercase\n","// This file stylizes the API documentation (stuff generated by autodoc). It's\n// deeply nested due to how autodoc structures the HTML without enough classes\n// to select the relevant items.\n\n// API docs!\ndl[class]:not(.option-list):not(.field-list):not(.footnote):not(.glossary):not(.simple)\n // Tweak the spacing of all the things!\n dd\n margin-left: 2rem\n > :first-child\n margin-top: 0.125rem\n > :last-child\n margin-bottom: 0.75rem\n\n // This is used for the arguments\n .field-list\n margin-bottom: 0.75rem\n\n // \"Headings\" (like \"Parameters\" and \"Return\")\n > dt\n text-transform: uppercase\n font-size: var(--font-size--small)\n\n dd:empty\n margin-bottom: 0.5rem\n dd > ul\n margin-left: -1.2rem\n > li\n > p:nth-child(2)\n margin-top: 0\n // When the last-empty-paragraph follows a paragraph, it doesn't need\n // to augument the existing spacing.\n > p + p:last-child:empty\n margin-top: 0\n margin-bottom: 0\n\n // Colorize the elements\n > dt\n color: var(--color-api-overall)\n\n.sig:not(.sig-inline)\n font-weight: bold\n\n font-size: var(--api-font-size)\n font-family: var(--font-stack--monospace)\n\n margin-left: -0.25rem\n margin-right: -0.25rem\n padding-top: 0.25rem\n padding-bottom: 0.25rem\n padding-right: 0.5rem\n\n // These are intentionally em, to properly match the font size.\n padding-left: 3em\n text-indent: -2.5em\n\n border-radius: 0.25rem\n\n background: var(--color-api-background)\n transition: background 100ms ease-out\n\n &:hover\n background: var(--color-api-background-hover)\n\n // adjust the size of the [source] link on the right.\n a.reference\n .viewcode-link\n font-weight: normal\n width: 3.5rem\n\nem.property\n font-style: normal\n &:first-child\n color: var(--color-api-keyword)\n.sig-name\n color: var(--color-api-name)\n.sig-prename\n font-weight: normal\n color: var(--color-api-pre-name)\n.sig-paren\n color: var(--color-api-paren)\n.sig-param\n font-style: normal\n\n.versionmodified\n font-style: italic\ndiv.versionadded, div.versionchanged, div.deprecated\n p\n margin-top: 0.125rem\n margin-bottom: 0.125rem\n\n// Align the [docs] and [source] to the right.\n.viewcode-link, .viewcode-back\n float: right\n text-align: right\n",".line-block\n margin-top: 0.5rem\n margin-bottom: 0.75rem\n .line-block\n margin-top: 0rem\n margin-bottom: 0rem\n padding-left: 1rem\n","// Captions\narticle p.caption,\ntable > caption,\n.code-block-caption\n font-size: var(--font-size--small)\n text-align: center\n\n// Caption above a TOCTree\n.toctree-wrapper.compound\n .caption, :not(.caption) > .caption-text\n font-size: var(--font-size--small)\n text-transform: uppercase\n\n text-align: initial\n margin-bottom: 0\n\n > ul\n margin-top: 0\n margin-bottom: 0\n","// Inline code\ncode.literal, .sig-inline\n background: var(--color-inline-code-background)\n border-radius: 0.2em\n // Make the font smaller, and use padding to recover.\n font-size: var(--font-size--small--2)\n padding: 0.1em 0.2em\n\n pre.literal-block &\n font-size: inherit\n padding: 0\n\n p &\n border: 1px solid var(--color-background-border)\n\n.sig-inline\n font-family: var(--font-stack--monospace)\n\n// Code and Literal Blocks\n$code-spacing-vertical: 0.625rem\n$code-spacing-horizontal: 0.875rem\n\n// Wraps every literal block + line numbers.\ndiv[class*=\" highlight-\"],\ndiv[class^=\"highlight-\"]\n margin: 1em 0\n display: flex\n\n .table-wrapper\n margin: 0\n padding: 0\n\npre\n margin: 0\n padding: 0\n overflow: auto\n\n // Needed to have more specificity than pygments' \"pre\" selector. :(\n article[role=\"main\"] .highlight &\n line-height: 1.5\n\n &.literal-block,\n .highlight &\n font-size: var(--code-font-size)\n padding: $code-spacing-vertical $code-spacing-horizontal\n\n // Make it look like all the other blocks.\n &.literal-block\n margin-top: 1rem\n margin-bottom: 1rem\n\n border-radius: 0.2rem\n background-color: var(--color-code-background)\n color: var(--color-code-foreground)\n\n// All code is always contained in this.\n.highlight\n width: 100%\n border-radius: 0.2rem\n\n // Make line numbers and prompts un-selectable.\n .gp, span.linenos\n user-select: none\n pointer-events: none\n\n // Expand the line-highlighting.\n .hll\n display: block\n margin-left: -$code-spacing-horizontal\n margin-right: -$code-spacing-horizontal\n padding-left: $code-spacing-horizontal\n padding-right: $code-spacing-horizontal\n\n/* Make code block captions be nicely integrated */\n.code-block-caption\n display: flex\n padding: $code-spacing-vertical $code-spacing-horizontal\n\n border-radius: 0.25rem\n border-bottom-left-radius: 0\n border-bottom-right-radius: 0\n font-weight: 300\n border-bottom: 1px solid\n\n background-color: var(--color-code-background)\n color: var(--color-code-foreground)\n border-color: var(--color-background-border)\n\n + div[class]\n margin-top: 0\n pre\n border-top-left-radius: 0\n border-top-right-radius: 0\n\n// When `html_codeblock_linenos_style` is table.\n.highlighttable\n width: 100%\n display: block\n tbody\n display: block\n\n tr\n display: flex\n\n // Line numbers\n td.linenos\n background-color: var(--color-code-background)\n color: var(--color-code-foreground)\n padding: $code-spacing-vertical $code-spacing-horizontal\n padding-right: 0\n border-top-left-radius: 0.2rem\n border-bottom-left-radius: 0.2rem\n\n .linenodiv\n padding-right: $code-spacing-horizontal\n font-size: var(--code-font-size)\n box-shadow: -0.0625rem 0 var(--color-foreground-border) inset\n\n // Actual code\n td.code\n padding: 0\n display: block\n flex: 1\n overflow: hidden\n\n .highlight\n border-top-left-radius: 0\n border-bottom-left-radius: 0\n\n// When `html_codeblock_linenos_style` is inline.\n.highlight\n span.linenos\n display: inline-block\n padding-left: 0\n padding-right: $code-spacing-horizontal\n margin-right: $code-spacing-horizontal\n box-shadow: -0.0625rem 0 var(--color-foreground-border) inset\n","// Inline Footnote Reference\n.footnote-reference\n font-size: var(--font-size--small--4)\n vertical-align: super\n\n// Definition list, listing the content of each note.\n// docutils <= 0.17\ndl.footnote.brackets\n font-size: var(--font-size--small)\n color: var(--color-foreground-secondary)\n\n display: grid\n grid-template-columns: max-content auto\n dt\n margin: 0\n > .fn-backref\n margin-left: 0.25rem\n\n &:after\n content: \":\"\n\n .brackets\n &:before\n content: \"[\"\n &:after\n content: \"]\"\n\n dd\n margin: 0\n padding: 0 1rem\n\n// docutils >= 0.18\naside.footnote\n font-size: var(--font-size--small)\n color: var(--color-foreground-secondary)\n\naside.footnote > span,\ndiv.citation > span\n float: left\n font-weight: 500\n padding-right: 0.25rem\n\naside.footnote > p,\ndiv.citation > p\n margin-left: 2rem\n","//\n// Figures\n//\nimg\n box-sizing: border-box\n max-width: 100%\n height: auto\n\narticle\n figure, .figure\n border-radius: 0.2rem\n\n margin: 0\n :last-child\n margin-bottom: 0\n\n .align-left\n float: left\n clear: left\n margin: 0 1rem 1rem\n\n .align-right\n float: right\n clear: right\n margin: 0 1rem 1rem\n\n .align-default,\n .align-center\n display: block\n text-align: center\n margin-left: auto\n margin-right: auto\n\n // WELL, table needs to be stylised like a table.\n table.align-default\n display: table\n text-align: initial\n",".genindex-jumpbox, .domainindex-jumpbox\n border-top: 1px solid var(--color-background-border)\n border-bottom: 1px solid var(--color-background-border)\n padding: 0.25rem\n\n.genindex-section, .domainindex-section\n h2\n margin-top: 0.75rem\n margin-bottom: 0.5rem\n ul\n margin-top: 0\n margin-bottom: 0\n","ul,\nol\n padding-left: 1.2rem\n\n // Space lists out like paragraphs\n margin-top: 1rem\n margin-bottom: 1rem\n // reduce margins within li.\n li\n > p:first-child\n margin-top: 0.25rem\n margin-bottom: 0.25rem\n\n > p:last-child\n margin-top: 0.25rem\n\n > ul,\n > ol\n margin-top: 0.5rem\n margin-bottom: 0.5rem\n\nol\n &.arabic\n list-style: decimal\n &.loweralpha\n list-style: lower-alpha\n &.upperalpha\n list-style: upper-alpha\n &.lowerroman\n list-style: lower-roman\n &.upperroman\n list-style: upper-roman\n\n// Don't space lists out when they're \"simple\" or in a `.. toctree::`\n.simple,\n.toctree-wrapper\n li\n > ul,\n > ol\n margin-top: 0\n margin-bottom: 0\n\n// Definition Lists\n.field-list,\n.option-list,\ndl:not([class]),\ndl.simple,\ndl.footnote,\ndl.glossary\n dt\n font-weight: 500\n margin-top: 0.25rem\n + dt\n margin-top: 0\n\n .classifier::before\n content: \":\"\n margin-left: 0.2rem\n margin-right: 0.2rem\n\n dd\n > p:first-child,\n ul\n margin-top: 0.125rem\n\n ul\n margin-bottom: 0.125rem\n",".math-wrapper\n width: 100%\n overflow-x: auto\n\ndiv.math\n position: relative\n text-align: center\n\n .headerlink,\n &:focus .headerlink\n display: none\n\n &:hover .headerlink\n display: inline-block\n\n span.eqno\n position: absolute\n right: 0.5rem\n top: 50%\n transform: translate(0, -50%)\n z-index: 1\n","// Abbreviations\nabbr[title]\n cursor: help\n\n// \"Problematic\" content, as identified by Sphinx\n.problematic\n color: var(--color-problematic)\n\n// Keyboard / Mouse \"instructions\"\nkbd:not(.compound)\n margin: 0 0.2rem\n padding: 0 0.2rem\n border-radius: 0.2rem\n border: 1px solid var(--color-foreground-border)\n color: var(--color-foreground-primary)\n vertical-align: text-bottom\n\n font-size: var(--font-size--small--3)\n display: inline-block\n\n box-shadow: 0 0.0625rem 0 rgba(0, 0, 0, 0.2), inset 0 0 0 0.125rem var(--color-background-primary)\n\n background-color: var(--color-background-secondary)\n\n// Blockquote\nblockquote\n border-left: 4px solid var(--color-background-border)\n background: var(--color-background-secondary)\n\n margin-left: 0\n margin-right: 0\n padding: 0.5rem 1rem\n\n .attribution\n font-weight: 600\n text-align: right\n\n &.pull-quote,\n &.highlights\n font-size: 1.25em\n\n &.epigraph,\n &.pull-quote\n border-left-width: 0\n border-radius: 0.5rem\n\n &.highlights\n border-left-width: 0\n background: transparent\n\n// Center align embedded-in-text images\np .reference img\n vertical-align: middle\n","p.rubric\n line-height: 1.25\n font-weight: bold\n font-size: 1.125em\n\n // For Numpy-style documentation that's got rubrics within it.\n // https://github.com/pradyunsg/furo/discussions/505\n dd &\n line-height: inherit\n font-weight: inherit\n\n font-size: var(--font-size--small)\n text-transform: uppercase\n","article .sidebar\n float: right\n clear: right\n width: 30%\n\n margin-left: 1rem\n margin-right: 0\n\n border-radius: 0.2rem\n background-color: var(--color-background-secondary)\n border: var(--color-background-border) 1px solid\n\n > *\n padding-left: 1rem\n padding-right: 1rem\n\n > ul, > ol // lists need additional padding, because bullets.\n padding-left: 2.2rem\n\n .sidebar-title\n margin: 0\n padding: 0.5rem 1rem\n border-bottom: var(--color-background-border) 1px solid\n\n font-weight: 500\n\n// TODO: subtitle\n// TODO: dedicated variables?\n",".table-wrapper\n width: 100%\n overflow-x: auto\n margin-top: 1rem\n margin-bottom: 0.5rem\n padding: 0.2rem 0.2rem 0.75rem\n\ntable.docutils\n border-radius: 0.2rem\n border-spacing: 0\n border-collapse: collapse\n\n box-shadow: 0 0.2rem 0.5rem rgba(0, 0, 0, 0.05), 0 0 0.0625rem rgba(0, 0, 0, 0.1)\n\n th\n background: var(--color-table-header-background)\n\n td,\n th\n // Space things out properly\n padding: 0 0.25rem\n\n // Get the borders looking just-right.\n border-left: 1px solid var(--color-table-border)\n border-right: 1px solid var(--color-table-border)\n border-bottom: 1px solid var(--color-table-border)\n\n p\n margin: 0.25rem\n\n &:first-child\n border-left: none\n &:last-child\n border-right: none\n\n // MyST-parser tables set these classes for control of column alignment\n &.text-left\n text-align: left\n &.text-right\n text-align: right\n &.text-center\n text-align: center\n",":target\n scroll-margin-top: 0.5rem\n\n@media (max-width: $full-width - $sidebar-width)\n :target\n scroll-margin-top: calc(0.5rem + var(--header-height))\n\n // When a heading is selected\n section > span:target\n scroll-margin-top: calc(0.8rem + var(--header-height))\n\n// Permalinks\n.headerlink\n font-weight: 100\n user-select: none\n\nh1,\nh2,\nh3,\nh4,\nh5,\nh6,\ndl dt,\np.caption,\nfigcaption p,\ntable > caption,\n.code-block-caption\n > .headerlink\n margin-left: 0.5rem\n visibility: hidden\n &:hover > .headerlink\n visibility: visible\n\n // Don't change to link-like, if someone adds the contents directive.\n > .toc-backref\n color: inherit\n text-decoration-line: none\n\n// Figure and table captions are special.\nfigure:hover > figcaption > p > .headerlink,\ntable:hover > caption > .headerlink\n visibility: visible\n\n:target >, // Regular section[id] style anchors\nspan:target ~ // Non-regular span[id] style \"extra\" anchors\n h1,\n h2,\n h3,\n h4,\n h5,\n h6\n &:nth-of-type(1)\n background-color: var(--color-highlight-on-target)\n // .headerlink\n // visibility: visible\n code.literal\n background-color: transparent\n\ntable:target > caption,\nfigure:target\n background-color: var(--color-highlight-on-target)\n\n// Inline page contents\n.this-will-duplicate-information-and-it-is-still-useful-here li :target\n background-color: var(--color-highlight-on-target)\n\n// Code block permalinks\n.literal-block-wrapper:target .code-block-caption\n background-color: var(--color-highlight-on-target)\n\n// When a definition list item is selected\n//\n// There isn't really an alternative to !important here, due to the\n// high-specificity of API documentation's selector.\ndt:target\n background-color: var(--color-highlight-on-target) !important\n\n// When a footnote reference is selected\n.footnote > dt:target + dd,\n.footnote-reference:target\n background-color: var(--color-highlight-on-target)\n",".guilabel\n background-color: var(--color-guilabel-background)\n border: 1px solid var(--color-guilabel-border)\n color: var(--color-guilabel-text)\n\n padding: 0 0.3em\n border-radius: 0.5em\n font-size: 0.9em\n","// This file contains the styles used for stylizing the footer that's shown\n// below the content.\n\nfooter\n font-size: var(--font-size--small)\n display: flex\n flex-direction: column\n\n margin-top: 2rem\n\n// Bottom of page information\n.bottom-of-page\n display: flex\n align-items: center\n justify-content: space-between\n\n margin-top: 1rem\n padding-top: 1rem\n padding-bottom: 1rem\n\n color: var(--color-foreground-secondary)\n border-top: 1px solid var(--color-background-border)\n\n line-height: 1.5\n\n @media (max-width: $content-width)\n text-align: center\n flex-direction: column-reverse\n gap: 0.25rem\n\n .left-details\n font-size: var(--font-size--small)\n\n .right-details\n display: flex\n flex-direction: column\n gap: 0.25rem\n text-align: right\n\n .icons\n display: flex\n justify-content: flex-end\n gap: 0.25rem\n font-size: 1rem\n\n a\n text-decoration: none\n\n svg,\n img\n font-size: 1.125rem\n height: 1em\n width: 1em\n\n// Next/Prev page information\n.related-pages\n a\n display: flex\n align-items: center\n\n text-decoration: none\n &:hover .page-info .title\n text-decoration: underline\n color: var(--color-link)\n text-decoration-color: var(--color-link-underline)\n\n svg.furo-related-icon,\n svg.furo-related-icon > use\n flex-shrink: 0\n\n color: var(--color-foreground-border)\n\n width: 0.75rem\n height: 0.75rem\n margin: 0 0.5rem\n\n &.next-page\n max-width: 50%\n\n float: right\n clear: right\n text-align: right\n\n &.prev-page\n max-width: 50%\n\n float: left\n clear: left\n\n svg\n transform: rotate(180deg)\n\n.page-info\n display: flex\n flex-direction: column\n overflow-wrap: anywhere\n\n .next-page &\n align-items: flex-end\n\n .context\n display: flex\n align-items: center\n\n padding-bottom: 0.1rem\n\n color: var(--color-foreground-muted)\n font-size: var(--font-size--small)\n text-decoration: none\n","// This file contains the styles for the contents of the left sidebar, which\n// contains the navigation tree, logo, search etc.\n\n////////////////////////////////////////////////////////////////////////////////\n// Brand on top of the scrollable tree.\n////////////////////////////////////////////////////////////////////////////////\n.sidebar-brand\n display: flex\n flex-direction: column\n flex-shrink: 0\n\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)\n text-decoration: none\n\n.sidebar-brand-text\n color: var(--color-sidebar-brand-text)\n overflow-wrap: break-word\n margin: var(--sidebar-item-spacing-vertical) 0\n font-size: 1.5rem\n\n.sidebar-logo-container\n margin: var(--sidebar-item-spacing-vertical) 0\n\n.sidebar-logo\n margin: 0 auto\n display: block\n max-width: 100%\n\n////////////////////////////////////////////////////////////////////////////////\n// Search\n////////////////////////////////////////////////////////////////////////////////\n.sidebar-search-container\n display: flex\n align-items: center\n margin-top: var(--sidebar-search-space-above)\n\n position: relative\n\n background: var(--color-sidebar-search-background)\n &:hover,\n &:focus-within\n background: var(--color-sidebar-search-background--focus)\n\n &::before\n content: \"\"\n position: absolute\n left: var(--sidebar-item-spacing-horizontal)\n width: var(--sidebar-search-icon-size)\n height: var(--sidebar-search-icon-size)\n\n background-color: var(--color-sidebar-search-icon)\n mask-image: var(--icon-search)\n\n.sidebar-search\n box-sizing: border-box\n\n border: none\n border-top: 1px solid var(--color-sidebar-search-border)\n border-bottom: 1px solid var(--color-sidebar-search-border)\n\n padding-top: var(--sidebar-search-input-spacing-vertical)\n padding-bottom: var(--sidebar-search-input-spacing-vertical)\n padding-right: var(--sidebar-search-input-spacing-horizontal)\n padding-left: calc(var(--sidebar-item-spacing-horizontal) + var(--sidebar-search-input-spacing-horizontal) + var(--sidebar-search-icon-size))\n\n width: 100%\n\n color: var(--color-sidebar-search-foreground)\n background: transparent\n z-index: 10\n\n &:focus\n outline: none\n\n &::placeholder\n font-size: var(--sidebar-search-input-font-size)\n\n//\n// Hide Search Matches link\n//\n#searchbox .highlight-link\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal) 0\n margin: 0\n text-align: center\n\n a\n color: var(--color-sidebar-search-icon)\n font-size: var(--font-size--small--2)\n\n////////////////////////////////////////////////////////////////////////////////\n// Structure/Skeleton of the navigation tree (left)\n////////////////////////////////////////////////////////////////////////////////\n.sidebar-tree\n font-size: var(--sidebar-item-font-size)\n margin-top: var(--sidebar-tree-space-above)\n margin-bottom: var(--sidebar-item-spacing-vertical)\n\n ul\n padding: 0\n margin-top: 0\n margin-bottom: 0\n\n display: flex\n flex-direction: column\n\n list-style: none\n\n li\n position: relative\n margin: 0\n\n > ul\n margin-left: var(--sidebar-item-spacing-horizontal)\n\n .icon\n color: var(--color-sidebar-link-text)\n\n .reference\n box-sizing: border-box\n color: var(--color-sidebar-link-text)\n\n // Fill the parent.\n display: inline-block\n line-height: var(--sidebar-item-line-height)\n text-decoration: none\n\n // Don't allow long words to cause wrapping.\n overflow-wrap: anywhere\n\n height: 100%\n width: 100%\n\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)\n\n &:hover\n background: var(--color-sidebar-item-background--hover)\n\n // Add a nice little \"external-link\" arrow here.\n &.external::after\n content: url('data:image/svg+xml,')\n margin: 0 0.25rem\n vertical-align: middle\n color: var(--color-sidebar-link-text)\n\n // Make the current page reference bold.\n .current-page > .reference\n font-weight: bold\n\n label\n position: absolute\n top: 0\n right: 0\n height: var(--sidebar-item-height)\n width: var(--sidebar-expander-width)\n\n cursor: pointer\n user-select: none\n\n display: flex\n justify-content: center\n align-items: center\n\n .caption, :not(.caption) > .caption-text\n font-size: var(--sidebar-caption-font-size)\n color: var(--color-sidebar-caption-text)\n\n font-weight: bold\n text-transform: uppercase\n\n margin: var(--sidebar-caption-space-above) 0 0 0\n padding: var(--sidebar-item-spacing-vertical) var(--sidebar-item-spacing-horizontal)\n\n // If it has children, add a bit more padding to wrap the content to avoid\n // overlapping with the

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