From 41f4f56d4412565bd76bc599c261d2a5fcbfe6de Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Elena=20Pe=C3=B1a=20Tapia?= Date: Thu, 17 Aug 2023 14:16:29 +0200 Subject: [PATCH] Update tutorials content Quick update of content Add aer to requirements-dev.txt Add networkx to requirements-dev.txt Fix spelling Recover grover try pin sphinx Delete IQPE Apply review comments Use short urls Apply comments from code review Update tweedledum reqs Add thumbnails to metadata Add try-except Fix gradients tag Default thumbnail Update docs/tutorials/02_vqe_advanced_options.ipynb Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> Update docs/tutorials/02_vqe_advanced_options.ipynb Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> Update docs/tutorials/05_qaoa.ipynb Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> Update docs/tutorials/10_pvqd.ipynb Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> Apply suggestions --- .pylintdict | 10 + .../01_algorithms_introduction.ipynb | 120 +- docs/tutorials/02_vqe_advanced_options.ipynb | 119 +- .../03_vqe_simulation_with_noise.ipynb | 49 +- docs/tutorials/04_vqd.ipynb | 56 +- docs/tutorials/05_qaoa.ipynb | 85 +- docs/tutorials/06_grover.ipynb | 84 +- docs/tutorials/07_grover_examples.ipynb | 71 +- docs/tutorials/09_IQPE.ipynb | 1046 --------- docs/tutorials/10_pvqd.ipynb | 482 ++++- docs/tutorials/11_VarQTE.ipynb | 1864 +++++++++-------- docs/tutorials/12_gradients_framework.ipynb | 137 +- requirements-dev.txt | 10 +- 13 files changed, 1772 insertions(+), 2361 deletions(-) delete mode 100644 docs/tutorials/09_IQPE.ipynb diff --git a/.pylintdict b/.pylintdict index 86e8d542..95fd821a 100644 --- a/.pylintdict +++ b/.pylintdict @@ -28,6 +28,7 @@ bfgs bielza bitstring bitstrings +bloch boltzmann bool boyer @@ -101,6 +102,7 @@ fmin formatter fourier frac +frobenius f'spsa ftol fujii @@ -112,11 +114,13 @@ gaussian generalised getter getters +gilliam giuseppe globals gogolin goldfarb goldstone +gonciulea gqt grinko grover @@ -124,6 +128,7 @@ gsls gtol gutmann hadamard +hadamards hadfield hamiltonian hamiltonians @@ -170,6 +175,7 @@ lin linalg loglik loglikelihood +lov lr lsb lse @@ -200,6 +206,7 @@ nakanishi nan nannicini nathan +nd ndarray negoro nelder @@ -286,6 +293,7 @@ runarsson rz sanjiv sashank +satisfiability satyen schrödinger schroediger @@ -334,6 +342,7 @@ toctree todo tol trainability +transpilation transpile transpiled trotterization @@ -349,6 +358,7 @@ vec vectorized vicentini ville +voilà vqd vqe wavefunction diff --git a/docs/tutorials/01_algorithms_introduction.ipynb b/docs/tutorials/01_algorithms_introduction.ipynb index fdb2c581..5976277f 100644 --- a/docs/tutorials/01_algorithms_introduction.ipynb +++ b/docs/tutorials/01_algorithms_introduction.ipynb @@ -4,9 +4,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# An Introduction to Algorithms in Qiskit\n", + "# An Introduction to Algorithms using Qiskit\n", "\n", - "This is an introduction to algorithms in Qiskit and provides a high-level overview to help understand the various aspects of the functionality to get started. Other tutorials will provide more in-depth material, on given algorithms, and ways to use them etc." + "This introduction to algorithms using Qiskit provides a high-level overview to get started with the `qiskit_algorithms` library." ] }, { @@ -15,11 +15,11 @@ "source": [ "## How is the algorithm library structured?\n", "\n", - "Qiskit provides a number of [Algorithms](https://qiskit.org/documentation/apidoc/algorithms.html) and they are grouped by category according to the task they can perform. For instance `Minimum Eigensolvers` to find the smallest eigen value of an operator, for example ground state energy of a chemistry Hamiltonian or a solution to an optimization problem when expressed as an Ising Hamiltonian. There are `Time Evolvers` for the time evolution of quantum systems and `Amplitude Estimators` for value estimation that can be used say in financial applications. The full set of categories can be seen in the Algorithms documentation link above.\n", + "`qiskit_algorithms` provides a number of [algorithms](https://qiskit.org/ecosystem/algorithms/apidocs/algorithms.html) grouped by category, according to the task they can perform. For instance `Minimum Eigensolvers` to find the smallest eigen value of an operator, for example ground state energy of a chemistry Hamiltonian or a solution to an optimization problem when expressed as an Ising Hamiltonian. There are `Time Evolvers` for the time evolution of quantum systems and `Amplitude Estimators` for value estimation that can be used say in financial applications. The full set of categories can be seen in the documentation link above.\n", "\n", - "Algorithms are configurable and often part of the configuration will be in the form of smaller building blocks, of which different instances of the building block type can be given. For instance with `VQE`, the Variational Quantum Eigensolver, it takes a trial wavefunction, in the form of a `QuantumCircuit` and a classical optimizer among other things.\n", + "Algorithms are configurable, and part of the configuration will often be in the form of smaller building blocks. For instance `VQE`, the Variational Quantum Eigensolver, it takes a trial wavefunction, in the form of a `QuantumCircuit` and a classical optimizer among other things.\n", "\n", - "Let's take a look at an example to construct a VQE instance. Here `TwoLocal` is the variational form (trial wavefunction), a parameterized circuit which can be varied, and `SLSQP` a classical optimizer. These are created as separate instances and passed to VQE when it is constructed. Trying, for example, a different classical optimizer, or variational form is simply a case of creating an instance of the one you want and passing it into VQE." + "Let's take a look at an example to construct a VQE instance. Here, `TwoLocal` is the variational form (trial wavefunction), a parameterized circuit which can be varied, and `SLSQP` a classical optimizer. These are created as separate instances and passed to VQE when it is constructed. Trying, for example, a different classical optimizer, or variational form is simply a case of creating an instance of the one you want and passing it into VQE." ] }, { @@ -46,11 +46,15 @@ { "cell_type": "code", "execution_count": 2, - "metadata": {}, + "metadata": { + "tags": [ + "nbsphinx-thumbnail" + ] + }, "outputs": [ { "data": { - "image/png": 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\n", 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" ] @@ -61,7 +65,7 @@ } ], "source": [ - "ansatz.decompose().draw('mpl', style='iqx')" + "ansatz.decompose().draw(\"mpl\", style=\"iqx\")" ] }, { @@ -79,7 +83,7 @@ "\n", "Algorithms rely on the primitives to evaluate expectation values or sample circuits. The primitives can be based on a simulator or real device and can be used interchangeably in the algorithms, as they all implement the same interface.\n", "\n", - "In the VQE, we have to evaluate expectation values, so for example we can use the [qiskit.primitives.Estimator](https://qiskit.org/documentation/stubs/qiskit.primitives.Estimator.html) which is shipped with the default Qiskit Terra installation." + "In the VQE, we have to evaluate expectation values, so for example we can use the [qiskit.primitives.Estimator](https://qiskit.org/documentation/stubs/qiskit.primitives.Estimator.html) which is shipped with the default Qiskit installation." ] }, { @@ -108,7 +112,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit_algorithms.minimum_eigensolvers import VQE\n", + "from qiskit_algorithms import VQE\n", "\n", "vqe = VQE(estimator, ansatz, optimizer)" ] @@ -117,7 +121,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we can call the [compute_mininum_eigenvalue()](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.VQE.compute_minimum_eigenvalue.html#qiskit.algorithms.minimum_eigensolvers.VQE.compute_minimum_eigenvalue) method. The latter is the interface of choice for the application modules, such as Nature and Optimization, in order that they can work interchangeably with any algorithm within the specific category." + "Now we can call the [compute_mininum_eigenvalue()](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.VQE.html#qiskit_algorithms.VQE.compute_minimum_eigenvalue) method. The latter is the interface of choice for the application modules, such as Nature and Optimization, in order that they can work interchangeably with any algorithm within the specific category." ] }, { @@ -126,7 +130,7 @@ "source": [ "## A complete working example\n", "\n", - "Let's put what we have learned from above together and create a complete working example. VQE will find the minimum eigenvalue, i.e. minimum energy value of a Hamiltonian operator and hence we need such an operator for VQE to work with. Such an operator is given below. This was originally created by the Nature application module as the Hamiltonian for an H2 molecule at 0.735A interatomic distance. It's a sum of Pauli terms as below, but for now I am not going to say anything further about it since the goal is to run the algorithm, but further information on operators can be found in other tutorials." + "Let's put what we have learned from above together and create a complete working example. VQE will find the minimum eigenvalue, i.e. minimum energy value of a Hamiltonian operator and hence we need such an operator for VQE to work with. Such an operator is given below. This was originally created by the Nature application module as the Hamiltonian for an H2 molecule at 0.735A interatomic distance. It's a sum of Pauli terms as below." ] }, { @@ -165,23 +169,23 @@ "output_type": "stream", "text": [ "{ 'aux_operators_evaluated': None,\n", - " 'cost_function_evals': 102,\n", - " 'eigenvalue': -1.857275020719397,\n", - " 'optimal_circuit': ,\n", - " 'optimal_parameters': { ParameterVectorElement(θ[0]): -2.403507257619715,\n", - " ParameterVectorElement(θ[5]): 1.7060524493254914,\n", - " ParameterVectorElement(θ[1]): 3.085467047665086,\n", - " ParameterVectorElement(θ[2]): -2.1949965223522487,\n", - " ParameterVectorElement(θ[3]): 4.276089268519914,\n", - " ParameterVectorElement(θ[4]): -3.098644972035885,\n", - " ParameterVectorElement(θ[6]): 0.032773583818940334,\n", - " ParameterVectorElement(θ[7]): 2.8861019033185396},\n", - " 'optimal_point': array([-2.40350726, 3.08546705, -2.19499652, 4.27608927, -3.09864497,\n", - " 1.70605245, 0.03277358, 2.8861019 ]),\n", - " 'optimal_value': -1.857275020719397,\n", + " 'cost_function_evals': 93,\n", + " 'eigenvalue': -1.8572749955763543,\n", + " 'optimal_circuit': ,\n", + " 'optimal_parameters': { ParameterVectorElement(θ[0]): -1.9883952951273307,\n", + " ParameterVectorElement(θ[1]): -6.620477717609146,\n", + " ParameterVectorElement(θ[2]): 0.46963076148711375,\n", + " ParameterVectorElement(θ[3]): -1.7278142973779242,\n", + " ParameterVectorElement(θ[4]): 1.5485040172432238,\n", + " ParameterVectorElement(θ[5]): -4.606121578619843,\n", + " ParameterVectorElement(θ[6]): -4.718174400033961,\n", + " ParameterVectorElement(θ[7]): -1.5433782121089836},\n", + " 'optimal_point': array([-1.9883953 , -6.62047772, 0.46963076, -1.7278143 , 1.54850402,\n", + " -4.60612158, -4.7181744 , -1.54337821]),\n", + " 'optimal_value': -1.8572749955763543,\n", " 'optimizer_evals': None,\n", - " 'optimizer_result': ,\n", - " 'optimizer_time': 0.29071593284606934}\n" + " 'optimizer_result': ,\n", + " 'optimizer_time': 0.1901099681854248}\n" ] } ], @@ -205,9 +209,9 @@ "\n", "To close off let's also change the estimator primitive inside the a VQE. Maybe you're satisfied with the simulation results and now want to use a shot-based simulator, or run on hardware!\n", "\n", - "In this example we're changing to a shot-based estimator, still using Qiskit Terra's reference primitive. However you could replace the primitive by e.g. Qiskit Aer's estimator ([qiskit_aer.primitives.Estimator](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html#qiskit_aer.primitives.Estimator)) or even a real backend ([qiskit_ibm_runtime.Estimator](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/stubs/qiskit_ibm_runtime.Estimator.html#qiskit_ibm_runtime.Estimator)).\n", + "In this example we're changing to a shot-based estimator, still using Qiskit's reference primitive. However, you could replace the primitive by e.g. Qiskit Aer's estimator ([qiskit_aer.primitives.Estimator](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html#qiskit_aer.primitives.Estimator)) or even a real backend ([qiskit_ibm_runtime.Estimator](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/stubs/qiskit_ibm_runtime.Estimator.html#qiskit_ibm_runtime.Estimator)).\n", "\n", - "For noisy loss functions, the SPSA optimizer typically performs well, so we also update the optimizer. See also the [noisy VQE tutorial](https://qiskit.org/documentation/tutorials/algorithms/03_vqe_simulation_with_noise.html) for more details on shot-based and noisy simulations. " + "For noisy loss functions, the SPSA optimizer typically performs well, so we also update the optimizer. See also the [noisy VQE tutorial](03_vqe_simulation_with_noise.ipynb) for more details on shot-based and noisy simulations." ] }, { @@ -221,22 +225,22 @@ "text": [ "{ 'aux_operators_evaluated': None,\n", " 'cost_function_evals': 200,\n", - " 'eigenvalue': -1.8574503552440247,\n", - " 'optimal_circuit': ,\n", - " 'optimal_parameters': { ParameterVectorElement(θ[0]): -7.7940259581467375,\n", - " ParameterVectorElement(θ[5]): 0.28827257835035214,\n", - " ParameterVectorElement(θ[1]): -1.8091021117029589,\n", - " ParameterVectorElement(θ[2]): -2.460381278734678,\n", - " ParameterVectorElement(θ[3]): -7.725013961075425,\n", - " ParameterVectorElement(θ[4]): -1.3793338621798832,\n", - " ParameterVectorElement(θ[6]): -2.4148423942537587,\n", - " ParameterVectorElement(θ[7]): -1.8555574263247812},\n", - " 'optimal_point': array([-7.79402596, -1.80910211, -2.46038128, -7.72501396, -1.37933386,\n", - " 0.28827258, -2.41484239, -1.85555743]),\n", - " 'optimal_value': -1.8574503552440247,\n", + " 'eigenvalue': -1.857504752055675,\n", + " 'optimal_circuit': ,\n", + " 'optimal_parameters': { ParameterVectorElement(θ[0]): -5.352503932134073,\n", + " ParameterVectorElement(θ[1]): 4.188987269642941,\n", + " ParameterVectorElement(θ[2]): 2.6224504402179103,\n", + " ParameterVectorElement(θ[3]): 1.8547996096847021,\n", + " ParameterVectorElement(θ[4]): -1.521565816440424,\n", + " ParameterVectorElement(θ[5]): -6.983851253012009,\n", + " ParameterVectorElement(θ[6]): 2.2766409871993436,\n", + " ParameterVectorElement(θ[7]): 1.30771917902646},\n", + " 'optimal_point': array([-5.35250393, 4.18898727, 2.62245044, 1.85479961, -1.52156582,\n", + " -6.98385125, 2.27664099, 1.30771918]),\n", + " 'optimal_value': -1.857504752055675,\n", " 'optimizer_evals': None,\n", - " 'optimizer_result': ,\n", - " 'optimizer_time': 0.8142139911651611}\n" + " 'optimizer_result': ,\n", + " 'optimizer_time': 0.5919399261474609}\n" ] } ], @@ -268,12 +272,16 @@ { "cell_type": "code", "execution_count": 8, - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.0.dev0+f52bb33
qiskit-aer0.11.1
qiskit-ignis0.7.1
qiskit-ibmq-provider0.19.2
qiskit-nature0.5.0
qiskit-optimization0.5.0
qiskit-machine-learning0.6.0
System information
Python version3.10.4
Python compilerClang 12.0.0
Python buildmain, Mar 31 2022 03:38:35
OSDarwin
CPUs4
Memory (Gb)32.0
Wed Dec 07 11:02:26 2022 CET
" + "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Thu Aug 17 17:59:09 2023 CEST
" ], "text/plain": [ "" @@ -285,7 +293,7 @@ { "data": { "text/html": [ - "

This code is a part of Qiskit

© Copyright IBM 2017, 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.

" + "

This code is a part of Qiskit

© Copyright IBM 2017, 2023.

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.

" ], "text/plain": [ "" @@ -298,20 +306,14 @@ "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table\n", - "%qiskit_copyright" + "%qiskit_copyright\n" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { + "celltoolbar": "Edit Metadata", "kernelspec": { - "display_name": "Python 3.10.6 ('venv': venv)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -325,7 +327,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.6" + "version": "3.10.2" }, "vscode": { "interpreter": { @@ -335,4 +337,4 @@ }, "nbformat": 4, "nbformat_minor": 2 -} +} \ No newline at end of file diff --git a/docs/tutorials/02_vqe_advanced_options.ipynb b/docs/tutorials/02_vqe_advanced_options.ipynb index d0767745..ecf74726 100644 --- a/docs/tutorials/02_vqe_advanced_options.ipynb +++ b/docs/tutorials/02_vqe_advanced_options.ipynb @@ -6,7 +6,7 @@ "source": [ "# Advanced VQE Options\n", "\n", - "In the first algorithms tutorial, you learned how to set up a basic [VQE](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.VQE.html) algorithm. Now, you will see how to provide more advanced configuration parameters to explore the full range of capabilities of Qiskit's variational algorithms: [VQE](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.VQE.html), [QAOA](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.QAOA.html) and [VQD](https://qiskit.org/documentation/stubs/qiskit.algorithms.eigensolvers.VQD.html) among others. In particular, this tutorial will cover how to set up a `callback` to monitor convergence and the use of custom `initial point`s and `gradient`s." + "In the first algorithms tutorial, you learned how to set up a basic [VQE](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.VQE.html) algorithm. Now, you will see how to provide more advanced configuration parameters to explore the full range of the variational algorithms provided in this library: [VQE](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.VQE.html), [QAOA](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.QAOA.html) and [VQD](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.VQD.html) among others. In particular, this tutorial will cover how to set up a `callback` to monitor convergence and the use of custom `initial point`s and `gradient`s." ] }, { @@ -59,7 +59,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The next step is to instantiate the `Estimator` of choice for the evaluation of expectation values within `VQE`. For simplicity, you can select the [qiskit.primitives.Estimator](https://qiskit.org/documentation/stubs/qiskit.primitives.Estimator.html#qiskit.primitives.Estimator) shipped with the default [Qiskit Terra](https://qiskit.org/documentation/apidoc/terra.html) installation." + "The next step is to instantiate the `Estimator` of choice for the evaluation of expectation values within `VQE`. For simplicity, you can select the [qiskit.primitives.Estimator](https://qiskit.org/documentation/stubs/qiskit.primitives.Estimator.html#qiskit.primitives.Estimator) that comes as part of Qiskit." ] }, { @@ -101,10 +101,12 @@ ], "source": [ "import numpy as np\n", - "from qiskit.algorithms.minimum_eigensolvers import VQE\n", - "from qiskit.algorithms.optimizers import COBYLA, L_BFGS_B, SLSQP\n", + "\n", "from qiskit.circuit.library import TwoLocal\n", - "from qiskit.utils import algorithm_globals\n", + "\n", + "from qiskit_algorithms import VQE\n", + "from qiskit_algorithms.optimizers import COBYLA, L_BFGS_B, SLSQP\n", + "from qiskit_algorithms.utils import algorithm_globals\n", "\n", "# we will iterate over these different optimizers\n", "optimizers = [COBYLA(maxiter=80), L_BFGS_B(maxiter=60), SLSQP(maxiter=60)]\n", @@ -150,10 +152,8 @@ "outputs": [ { "data": { - "image/png": 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", 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\n" }, "metadata": { "needs_background": "light" @@ -177,7 +177,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Finally, since the above problem is still easily tractable classically, you can use [NumPyMinimumEigensolver](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.NumPyMinimumEigensolver.html#numpyminimumeigensolver) to compute a reference value for the solution." + "Finally, since the above problem is still easily tractable classically, you can use [NumPyMinimumEigensolver](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.NumPyMinimumEigensolver.html) to compute a reference value for the solution." ] }, { @@ -194,20 +194,17 @@ } ], "source": [ - "from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver\n", - "from qiskit.opflow import PauliSumOp\n", + "from qiskit_algorithms import NumPyMinimumEigensolver\n", "\n", "numpy_solver = NumPyMinimumEigensolver()\n", - "result = numpy_solver.compute_minimum_eigenvalue(operator=PauliSumOp(H2_op))\n", + "result = numpy_solver.compute_minimum_eigenvalue(operator=H2_op)\n", "ref_value = result.eigenvalue.real\n", "print(f\"Reference value: {ref_value:.5f}\")" ] }, { "cell_type": "markdown", - "metadata": { - "collapsed": false - }, + "metadata": {}, "source": [ "You can now plot the difference between the `VQE` solution and this exact reference value as the algorithm converges towards the minimum energy." ] @@ -219,10 +216,8 @@ "outputs": [ { "data": { - "image/png": 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", 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\n" }, "metadata": { "needs_background": "light" @@ -251,7 +246,7 @@ "source": [ "## Gradients\n", "\n", - "In Qiskit's variational algorithms, if the provided optimizer uses a gradient-based technique, the default gradient method will be finite differences. However, these classes include an option to pass custom gradients via the `gradient` parameter, which can be any of the provided methods within Qiskit's [gradient](https://qiskit.org/documentation/stubs/qiskit.algorithms.gradients.html) framework, which fully supports the use of primitives. This section shows how to use custom gradients in the VQE workflow.\n", + "In the variational algorithms, if the provided optimizer uses a gradient-based technique, the default gradient method will be finite differences. However, these classes include an option to pass custom gradients via the `gradient` parameter, which can be any of the provided methods within the [gradient](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.gradients.html) framework, which fully supports the use of primitives. This section shows how to use custom gradients in the VQE workflow.\n", "\n", "The first step is to initialize both the corresponding primitive and primitive gradient:" ] @@ -262,7 +257,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit.algorithms.gradients import FiniteDiffEstimatorGradient\n", + "from qiskit_algorithms.gradients import FiniteDiffEstimatorGradient\n", "\n", "estimator = Estimator()\n", "gradient = FiniteDiffEstimatorGradient(estimator, epsilon=0.01)" @@ -272,7 +267,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now, you can inspect an SLSQP run using the [FiniteDiffEstimatorGradient](https://qiskit.org/documentation/stubs/qiskit.algorithms.gradients.FiniteDiffEstimatorGradient.html) from above:" + "Now, you can inspect an SLSQP run using the [FiniteDiffEstimatorGradient](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.gradients.FiniteDiffEstimatorGradient.html) from above:" ] }, { @@ -318,10 +313,8 @@ "outputs": [ { "data": { - "image/png": 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", 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\n" }, "metadata": { "needs_background": "light" @@ -366,22 +359,22 @@ "text": [ "{ 'aux_operators_evaluated': None,\n", " 'cost_function_evals': 9,\n", - " 'eigenvalue': -1.8572750175655812,\n", - " 'optimal_circuit': ,\n", - " 'optimal_parameters': { ParameterVectorElement(θ[0]): 4.296519450348719,\n", - " ParameterVectorElement(θ[3]): 6.092947832767056,\n", - " ParameterVectorElement(θ[1]): 4.426962358395531,\n", - " ParameterVectorElement(θ[7]): 0.36021017470898664,\n", - " ParameterVectorElement(θ[4]): -2.598326651673288,\n", - " ParameterVectorElement(θ[5]): 1.5683250498282322,\n", - " ParameterVectorElement(θ[2]): 0.5470777607659094,\n", - " ParameterVectorElement(θ[6]): -4.717616147449751},\n", + " 'eigenvalue': -1.8572750175655814,\n", + " 'optimal_circuit': ,\n", + " 'optimal_parameters': { ParameterVectorElement(θ[2]): 0.547077760766061,\n", + " ParameterVectorElement(θ[0]): 4.296519450348804,\n", + " ParameterVectorElement(θ[1]): 4.426962358395529,\n", + " ParameterVectorElement(θ[4]): -2.598326651673345,\n", + " ParameterVectorElement(θ[3]): 6.0929478327669955,\n", + " ParameterVectorElement(θ[5]): 1.5683250498282117,\n", + " ParameterVectorElement(θ[6]): -4.717616147449735,\n", + " ParameterVectorElement(θ[7]): 0.3602101747090559},\n", " 'optimal_point': array([ 4.29651945, 4.42696236, 0.54707776, 6.09294783, -2.59832665,\n", " 1.56832505, -4.71761615, 0.36021017]),\n", - " 'optimal_value': -1.8572750175655812,\n", + " 'optimal_value': -1.8572750175655814,\n", " 'optimizer_evals': None,\n", - " 'optimizer_result': ,\n", - " 'optimizer_time': 0.3502693176269531}\n" + " 'optimizer_result': ,\n", + " 'optimizer_time': 0.21613287925720215}\n" ] } ], @@ -414,22 +407,22 @@ "text": [ "{ 'aux_operators_evaluated': None,\n", " 'cost_function_evals': 1,\n", - " 'eigenvalue': -1.8572750175655812,\n", - " 'optimal_circuit': ,\n", - " 'optimal_parameters': { ParameterVectorElement(θ[0]): 4.296519450348719,\n", - " ParameterVectorElement(θ[1]): 4.426962358395531,\n", - " ParameterVectorElement(θ[4]): -2.598326651673288,\n", - " ParameterVectorElement(θ[5]): 1.5683250498282322,\n", - " ParameterVectorElement(θ[3]): 6.092947832767056,\n", - " ParameterVectorElement(θ[2]): 0.5470777607659094,\n", - " ParameterVectorElement(θ[6]): -4.717616147449751,\n", - " ParameterVectorElement(θ[7]): 0.36021017470898664},\n", + " 'eigenvalue': -1.8572750175655814,\n", + " 'optimal_circuit': ,\n", + " 'optimal_parameters': { ParameterVectorElement(θ[0]): 4.296519450348804,\n", + " ParameterVectorElement(θ[2]): 0.547077760766061,\n", + " ParameterVectorElement(θ[1]): 4.426962358395529,\n", + " ParameterVectorElement(θ[3]): 6.0929478327669955,\n", + " ParameterVectorElement(θ[4]): -2.598326651673345,\n", + " ParameterVectorElement(θ[5]): 1.5683250498282117,\n", + " ParameterVectorElement(θ[6]): -4.717616147449735,\n", + " ParameterVectorElement(θ[7]): 0.3602101747090559},\n", " 'optimal_point': array([ 4.29651945, 4.42696236, 0.54707776, 6.09294783, -2.59832665,\n", " 1.56832505, -4.71761615, 0.36021017]),\n", - " 'optimal_value': -1.8572750175655812,\n", + " 'optimal_value': -1.8572750175655814,\n", " 'optimizer_evals': None,\n", - " 'optimizer_result': ,\n", - " 'optimizer_time': 0.05097508430480957}\n", + " 'optimizer_result': ,\n", + " 'optimizer_time': 0.033068180084228516}\n", "\n" ] } @@ -495,24 +488,16 @@ "outputs": [ { "data": { - "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.22.2
qiskit-aer0.11.1
qiskit-ignis0.7.1
qiskit-ibmq-provider0.19.2
qiskit0.39.2
System information
Python version3.10.2
Python compilerClang 13.0.0 (clang-1300.0.29.30)
Python buildv3.10.2:a58ebcc701, Jan 13 2022 14:50:16
OSDarwin
CPUs8
Memory (Gb)64.0
Fri Nov 18 01:08:34 2022 CET
" - ], - "text/plain": [ - "" - ] + "text/plain": "", + "text/html": "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Thu Aug 17 18:05:36 2023 CEST
" }, "metadata": {}, "output_type": "display_data" }, { "data": { - "text/html": [ - "

This code is a part of Qiskit

© Copyright IBM 2017, 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.

" - ], - "text/plain": [ - "" - ] + "text/plain": "", + "text/html": "

This code is a part of Qiskit

© Copyright IBM 2017, 2023.

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.

" }, "metadata": {}, "output_type": "display_data" @@ -522,7 +507,7 @@ "import qiskit.tools.jupyter\n", "\n", "%qiskit_version_table\n", - "%qiskit_copyright" + "%qiskit_copyright\n" ] } ], @@ -547,4 +532,4 @@ }, "nbformat": 4, "nbformat_minor": 2 -} +} \ No newline at end of file diff --git a/docs/tutorials/03_vqe_simulation_with_noise.ipynb b/docs/tutorials/03_vqe_simulation_with_noise.ipynb index 11479b14..7d71cd0c 100644 --- a/docs/tutorials/03_vqe_simulation_with_noise.ipynb +++ b/docs/tutorials/03_vqe_simulation_with_noise.ipynb @@ -70,11 +70,10 @@ } ], "source": [ - "from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver\n", - "from qiskit.opflow import PauliSumOp\n", + "from qiskit_algorithms import NumPyMinimumEigensolver\n", "\n", "numpy_solver = NumPyMinimumEigensolver()\n", - "result = numpy_solver.compute_minimum_eigenvalue(operator=PauliSumOp(H2_op))\n", + "result = numpy_solver.compute_minimum_eigenvalue(operator=H2_op)\n", "ref_value = result.eigenvalue.real\n", "print(f\"Reference value: {ref_value:.5f}\")" ] @@ -94,7 +93,7 @@ "source": [ "# define ansatz and optimizer\n", "from qiskit.circuit.library import TwoLocal\n", - "from qiskit.algorithms.optimizers import SPSA\n", + "from qiskit_algorithms.optimizers import SPSA\n", "\n", "iterations = 125\n", "ansatz = TwoLocal(rotation_blocks=\"ry\", entanglement_blocks=\"cz\")\n", @@ -121,7 +120,6 @@ "counts = []\n", "values = []\n", "\n", - "\n", "def store_intermediate_result(eval_count, parameters, mean, std):\n", " counts.append(eval_count)\n", " values.append(mean)" @@ -134,7 +132,7 @@ "outputs": [], "source": [ "# define Aer Estimator for noiseless statevector simulation\n", - "from qiskit.utils import algorithm_globals\n", + "from qiskit_algorithms.utils import algorithm_globals\n", "from qiskit_aer.primitives import Estimator as AerEstimator\n", "\n", "seed = 170\n", @@ -155,14 +153,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "VQE on Aer qasm simulator (no noise): -1.84322\n", - "Delta from reference energy value is 0.01406\n" + "VQE on Aer qasm simulator (no noise): -1.85160\n", + "Delta from reference energy value is 0.00567\n" ] } ], "source": [ "# instantiate and run VQE\n", - "from qiskit.algorithms.minimum_eigensolvers import VQE\n", + "from qiskit_algorithms import VQE\n", "\n", "vqe = VQE(\n", " noiseless_estimator, ansatz, optimizer=spsa, callback=store_intermediate_result\n", @@ -201,9 +199,9 @@ }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ - "
" + "
" ] }, "metadata": { @@ -244,7 +242,7 @@ "text": [ "NoiseModel:\n", " Basis gates: ['cx', 'id', 'rz', 'sx', 'x']\n", - " Instructions with noise: ['cx', 'sx', 'id', 'measure', 'x']\n", + " Instructions with noise: ['id', 'sx', 'x', 'measure', 'cx']\n", " Qubits with noise: [0, 1, 2, 3, 4]\n", " Specific qubit errors: [('id', (0,)), ('id', (1,)), ('id', (2,)), ('id', (3,)), ('id', (4,)), ('sx', (0,)), ('sx', (1,)), ('sx', (2,)), ('sx', (3,)), ('sx', (4,)), ('x', (0,)), ('x', (1,)), ('x', (2,)), ('x', (3,)), ('x', (4,)), ('cx', (3, 4)), ('cx', (4, 3)), ('cx', (3, 1)), ('cx', (1, 3)), ('cx', (1, 2)), ('cx', (2, 1)), ('cx', (0, 1)), ('cx', (1, 0)), ('measure', (0,)), ('measure', (1,)), ('measure', (2,)), ('measure', (3,)), ('measure', (4,))]\n" ] @@ -254,7 +252,7 @@ "from qiskit_aer.noise import NoiseModel\n", "from qiskit.providers.fake_provider import FakeVigo\n", "\n", - "# fake providers contain data from real IBM Quantum devices stored in Qiskit Terra,\n", + "# fake providers contain data from real IBM Quantum devices stored in Qiskit,\n", "# and are useful for extracting realistic noise models.\n", "device = FakeVigo()\n", "\n", @@ -315,8 +313,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "VQE on Aer qasm simulator (with noise): -1.74645\n", - "Delta from reference energy value is 0.11083\n" + "VQE on Aer qasm simulator (with noise): -1.75227\n", + "Delta from reference energy value is 0.10501\n" ] } ], @@ -334,11 +332,15 @@ { "cell_type": "code", "execution_count": 12, - "metadata": {}, + "metadata": { + "tags": [ + "nbsphinx-thumbnail" + ] + }, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -382,8 +384,8 @@ "output_type": "stream", "text": [ "Reference value: -1.85728\n", - "VQE on Aer qasm simulator (no noise): -1.84322\n", - "VQE on Aer qasm simulator (with noise): -1.74645\n" + "VQE on Aer qasm simulator (no noise): -1.85160\n", + "VQE on Aer qasm simulator (with noise): -1.75227\n" ] } ], @@ -414,7 +416,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.22.2
qiskit-aer0.11.1
qiskit-ignis0.7.1
qiskit-ibmq-provider0.19.2
qiskit0.39.2
System information
Python version3.10.2
Python compilerClang 13.0.0 (clang-1300.0.29.30)
Python buildv3.10.2:a58ebcc701, Jan 13 2022 14:50:16
OSDarwin
CPUs8
Memory (Gb)64.0
Fri Nov 18 01:03:00 2022 CET
" + "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
qiskit_aer0.12.2
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Thu Aug 17 18:07:03 2023 CEST
" ], "text/plain": [ "" @@ -426,7 +428,7 @@ { "data": { "text/html": [ - "

This code is a part of Qiskit

© Copyright IBM 2017, 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.

" + "

This code is a part of Qiskit

© Copyright IBM 2017, 2023.

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.

" ], "text/plain": [ "" @@ -440,11 +442,12 @@ "import qiskit.tools.jupyter\n", "\n", "%qiskit_version_table\n", - "%qiskit_copyright" + "%qiskit_copyright\n" ] } ], "metadata": { + "celltoolbar": "Edit Metadata", "kernelspec": { "display_name": "Python 3", "language": "python", @@ -465,4 +468,4 @@ }, "nbformat": 4, "nbformat_minor": 2 -} +} \ No newline at end of file diff --git a/docs/tutorials/04_vqd.ipynb b/docs/tutorials/04_vqd.ipynb index 3d1eb74e..2443800e 100644 --- a/docs/tutorials/04_vqd.ipynb +++ b/docs/tutorials/04_vqd.ipynb @@ -4,9 +4,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Variational Quantum Deflation (VQD) Algorithm \n", + "# Variational Quantum Deflation (VQD) Algorithm\n", "\n", - "This notebook demostrates how to use Qiskit's implementation of the [Variational Quantum Deflation (VQD)](https://qiskit.org/documentation/stubs/qiskit.algorithms.eigensolvers.VQD.html) algorithm for computing higher energy states of a Hamiltonian, as introduced in this [reference paper](https://arxiv.org/abs/1805.08138). " + "This notebook demonstrates how to use our implementation of the [Variational Quantum Deflation (VQD)](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.VQD.html) algorithm for computing higher energy states of a Hamiltonian, as introduced in this [reference paper](https://arxiv.org/abs/1805.08138)." ] }, { @@ -16,7 +16,7 @@ "## Introduction\n", "\n", "VQD is a quantum algorithm that uses a variational technique to find the *k* eigenvalues of the Hamiltonian *H* of a given system.\n", - " \n", + "\n", "The algorithm computes excited state energies of generalized hamiltonians by optimizing over a modified cost function. Each successive eigenvalue is calculated iteratively by introducing an overlap term with all the previously computed eigenstates that must be minimized. This ensures that higher energy eigenstates are found." ] }, @@ -71,9 +71,9 @@ "outputs": [ { "data": { - "image/png": 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FRcd+d/0FqyfywcbpNAho7ILqnM/e/pdtnkPq8rGm2EOVcp4+BjzhPcDLZrPZ3F2EVObqG2s6Qvx4DHVTQWdw9DZwhqfe+/USVXNGuLua32a0MaA54L45oD0yERExNAWZiIgYmg4t1kE2G5SVuLsK+1h8HXs1dW0D5zDSoUWjjQHNAffNAX1qsQ7y8qr751qcTdtAPH0MeHr/9tChRRERMTQFmYiIGJqCTEREDE1BJiIihqYgExERQ1OQiYiIoSnIRETE0BRkIiJiaAoyERExNAWZiIgYmoJMREQMTUEmIiKGpiATERFDU5CJiIihKchERMTQFGQiImJoCjIRETE03SG6DtItzrUNxHhjQHPAfXNAQVYHlZXAxlR3V2Gf+PGOvS27toEYbQxoDrhvDujQooiIGJqCTEREDE1BJiIihqYgExERQ1OQiYiIoSnIRETE0BRkIiJiaAoyERExNH0h2kTSszfxzPz4Ssv8/QKJbNqWhK7J3NX7cby9zftP7un9i8aAp/Zvvo6E+Ljh9Iz9AzZsFJ4pYP23bzN/1dMcPpbFU/cucHd5Tufp/YvGgKf1ryAzoZiIriR0G1nx86CbxjJmZiyfbFvI6Dum0ahBUzdW53ye3r9oDHha/zpH5gEC/AKJbXkjNpuNvBPZ7i7H5Ty9f9EYMHv/CjIPkf/vwRtcP8TNlbiHp/cvGgNm7t8jgsxqtTJp0iSio6Px9/fnmmuu4YknnuDs2bOMGTMGLy8vXnvtNXeX6TAXSs5x+qyVU0XHOZifQeryxzhwdBex1/Qksmlbd5fndJ7ev2gMeFr/pj9Htnv3bhITEykoKCAwMJD27duTl5dHamoq2dnZnDx5EoC4uDj3FupAb6+bytvrplZa1qfjEB6/+3U3VeRant7/fyouhZ058FU22P69zAas/w5ujIYgfzcW5ySePgY8rX9TB5nVamXQoEEUFBQwYcIEpk6dSlBQEAAzZ85k8uTJ+Pj44OXlRefOnd1creMMvCGFvp2HUlpWwsH8DNI2zcB6Ohc/31/fsaa9O4wyWxnPJX9Ysezncyd5eHYHUpJmc1vXEe4o3SFq0n/Gj1uYsiixynNLLxVTVnaJtTMvubJkp9lzBJZ8DeeLqz62Jh0+zYDbO5b/MdNNQTUHPGsOmDrIxo8fT25uLuPGjWP27NmVHps0aRLvv/8+6enpREVFERwc7KYqHS8iNIaubRMA6BmbSMeoPjw1rw+vLnuUZ0d+AMDjQ+aR8nInNuxawq3XDwdg7seP0SGqj6EnMNSs/06tb2bVtKJKz7OezuOx1O4Mvmmcy2t2hp058M6Xv+6FVedSGXyyBy6UwOCurqrM+TQHPGsOmPYcWVZWFmlpaYSGhjJ9+vRq1+nWrRsAXbp0qVj2S/D17NmTevXq4WWCX1M7tLqJhK7JbEpPY2/OVqD8hO+EoYt4bcU4rKfz2LxnKXuyN/HkkPlurtbxquv/PxWXXuSFt4fQsVUf7r9tiosrdDzrGXjvq98OscttzCrfezMrzQFzzwHTBtmSJUsoKytjxIgRNGjQoNp1AgICgMpBduDAAZYtW0ZYWBg9evRwSa2uMCLhOSwWb95a+7eKZT1i7+CWzvcxY8lI5i4fy9NDFxIc2MSNVTpPdf1f7tVlj1JccoGJf1zs2sKc5Mv95Xtb9vj8e+fUUldoDph3Dpg2yDZs2ABAfHz8FdfJzc0FKgdZ3759yc/PZ+XKlSQkJDi3SBeKCI0mvsswdh34jIwft1QsTxk0m6MnDtAjNpEb2g10Y4XOdaX+AT7+IpVvslbzwqgV+PvVd1OFjlNyCb6pxVeFso9B/imHl1NnaA6Ydw6Y9hzZoUOHAGjZsmW1j5eWlvLll18ClYPMYnF8tnfv3p2CgoIar+/nE8CCcfsdXsfw255l4+4lvLXub8x+dCNQ/kXJ8JDWRIV1uqrXjmkbQ3HpeUeUCThnG1TX/+4DG1m4ZjIv/r9PCAtpdVWv7+htUFtBzaIZMGFTrZ57zwNPcHjnMofWU1uuGgOaA3VjDoSFhbFjx45aPde0QXb27FkAzp+vfqOmpaVhtVoJCgoiKirKqbUUFBRw9OjRGq/v71u734i6tOnH+llXPivSsnk7p30SKT8vjwsl5xz2erXZBvb2X3Ayh7+/ex8PJ82iS5t+tSmzEkdvg9pq5tu81s8tOlds11h1JleMAUfSHHDfHDBtkIWFhVFYWMjOnTvp1atXpcfy8/OZOHEiAJ07d3b6BzrCwsLsWt/PJ8BJlThPeIsWDv9t1JkuFJ9j6uK76NX+Tu7q7ZhPaDl6G9RWYHD5trPZbHaP7cB6FiIiIpxRlt2MNg80B65uG9j7Pnk50wZZQkICWVlZzJgxg/79+9O2bfm32bdv305ycjJWqxVwzReh7d1dvlQMG1OdVIyT7N+3H28/x72es7fBloxl/JifzlHrPjalp1V5fNEzmTRrfK1dr+nobVBbZTaYvgqOn7EvxLwtsG7Z6wT5140vzRptHmgOuG8OmDbIfvme2JEjR+jQoQOxsbFcuHCBAwcOkJiYSKtWrVi7dm2l82Oe6uU/bXJ3CS7Xv1sy/bslu7sMp7B4Qe+2sOJb+54Xd605r/JRE5oDxmbaTy1GRkayZcsWBg4ciL+/Pzk5OYSEhPDGG2+wZs0a9u3bB6AgE1Pq2Roa2XGKxccC8e2cV4+IM5l2jwygXbt2rF69usryoqIicnJysFgsdOzY0Q2ViThXfT9I6QfzPoOii7+9rrcFkntDpPkuii4ewtRBdiV79+7FZrPRtm1b6tev+mvr0qVLAcjMzKz0c6tWrejevbvrChW5Ci0aw5MDYOl2+D6/+nUiG5dfmiqm9ufZRdzOI4MsIyMDuPJhxaFDh1b784MPPsjixYudWpuII4UGwaO3ll+y6ptssBaBzQZBAdCtFbRsYq6LBYtnUpBVw2ar6RXqRIwhNAgGxrm7ChHnUJCZSHZeOnOWPsy5i2do3qglk4e/w6Gf9jJlYSKRTa/jpZR1NG7QjE+3vcmyLXM4fCyLR5JmM+TmJyteY8HqiWxKTyMmoisvjFrhtl5qo6b9v/nJs3yVuRKLlzcAw279M/FxwwBj9y81HwMzPxjFzv3raRjYFIBubfuTkjQLMPYYqGn/zy++m/yTByued7BgD88/uIKbOtzJss1zWLn1dfz9GvDG07vd14wdPDLIfrkOo9nMShvFM/f9k+iIOD7d9iYLVj/DgB6jiWx6XaUBGRPZjb+O/JAPNlS9K0BK0ixaNu/A1r0rXFe4g9S0//v6TeShxGkAWE8fZcysdnSNSaBhYKih+5eajwEoHweX/xL3CyOPgZr2//yojyv+/sORHUxZeAc9rrsDgHv6PkV0xPXM+9eTLq6+9kz78XtPc+DoLgLqNSA6Ig6A/t0f5KvMlZSUVr2jYpsWXWjZvB1eXub557en/wYBjSr+fv5iETZslNnsvFS81Dn2jAEzqm3/n25bxG1dR+LrUwe+zV9LHrlHZkb5Jw9yMD+DR16Jq1h2sfgc1p/rxnXznM3e/j/+IpWVW1/HeiqXp4YupHGDZi6qVJzF7jGw5VU+3fYmzRpfy6gBf68IAKOqzXvAxZLzbNy9hDljt1xxHSNQkJlI7LU38NLDayt+vvf5pm6sxvXs6f/uPuO5u894svPSeWnJSLq3vd2096HyJDUdAw8lTiMkKByLxcIXGR/z7KJEFk/eT0C96u9daBT2vgds3rOUyKZtiQq/uiv/u5t5ji15uPCQ1hw7dbji57MXfuZC8VlCg+vGBWCdrbb9t2nRhdDgCNKzNzm5QnE2e8ZAaMOIils29el0N/X9gzly/AeX1eoMtZkDn25bxB09xriiPKdSkJlEdEQcPhZfvt23HoBVW+dxS5c/Gvq4tz3s6f/QT5kVf8+zZnMgbxfXNm/vslrFOewZA8dP5Vb8PfPQ1/x89gQRTaJdVqsz2PsecNR6gH25O4i/frgry3QKHVo0kb/c/x6zPhxN6vI/0aJJNH++/11yCr6rst7a7YtZvPavFJ0rZOveFXz0+Wz+e/QqoiOud0PVjlPT/v93zSQKTh7E2+KLt7cP4+56jZbNdaFBM6jpGJiVNorCop+weHlTzzeA55I/IjCgoRsqdqya9g/w6fY3ubnTPQT6B7u4SsdTkJlIVHgn5j3x+7eMGdBjFAN6jHJ+QS5W0/7//lDV62+KOdR0DMx85P9cUI3r1bR/gDGJLzq5GtfRoUWT8/H248y5EzzyShyFRcd+d/0FqyfywcbpNAho7ILqnM/T+xeNAXv7X7Z5DqnLx9IwMNQF1TmGl03XY6pzjHZDQYD48RjqpoLO4Oht4OmMNgY0B9w3B7RHJiIihqYgExERQ9OhxTrIZoOyEndXYR+Lr2NvB6JtIEYbA5oD7psDCjIRETE0HVoUERFDU5CJiIihKchERMTQFGQiImJoCjIRETE0BZmIiBiagkxERAxNQSYiIoamIBMREUNTkImIiKEpyERExNAUZCIiYmgKMhERMTQFmYiIGJqCTEREDE1BJiIihqYgExERQ1OQiYiIoSnIRETE0BRkIiJiaAoyERExNAWZiIgYmoJMREQMTUEmIiKGpiATERFD+//Vk3/bDtxGJQAAAABJRU5ErkJggg==", + "image/png": 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\n", "text/plain": [ - "
" + "
" ] }, "execution_count": 2, @@ -83,7 +83,7 @@ ], "source": [ "from qiskit.circuit.library import TwoLocal\n", - "from qiskit.algorithms.optimizers import SLSQP\n", + "from qiskit_algorithms.optimizers import SLSQP\n", "\n", "ansatz = TwoLocal(2, rotation_blocks=[\"ry\", \"rz\"], entanglement_blocks=\"cz\", reps=1)\n", "\n", @@ -95,7 +95,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The next step of the workflow is to define the required primitives for running `VQD`. This algorithm requires two different primitive instances: one `Estimator` for computing the expectation values for the \"VQE part\" of the algorithm, and one `Sampler`. The sampler will be passed along to the `StateFidelity` subroutine that will be used to compute the cost for higher energy states. There are several methods that you can use to compute state fidelities, but to keep things simple, you can use the `ComputeUncompute` method already available in `qiskit.algorithm.state_fidelities`." + "The next step of the workflow is to define the required primitives for running `VQD`. This algorithm requires two different primitive instances: one `Estimator` for computing the expectation values for the \"VQE part\" of the algorithm, and one `Sampler`. The sampler will be passed along to the `StateFidelity` subroutine that will be used to compute the cost for higher energy states. There are several methods that you can use to compute state fidelities, but to keep things simple, you can use the `ComputeUncompute` method already available in `qiskit_algorithm.state_fidelities`." ] }, { @@ -105,7 +105,7 @@ "outputs": [], "source": [ "from qiskit.primitives import Sampler, Estimator\n", - "from qiskit.algorithms.state_fidelities import ComputeUncompute\n", + "from qiskit_algorithms.state_fidelities import ComputeUncompute\n", "\n", "estimator = Estimator()\n", "sampler = Sampler()\n", @@ -118,7 +118,7 @@ "source": [ "In order to set up the VQD algorithm, it is important to define two additional inputs: the number of energy states to compute (`k`) and the `betas` defined in the original VQD paper. In this example, the number of states (`k`) will be set to three, which indicates that two excited states will be computed in addition to the ground state.\n", "\n", - "The `betas` balance the contribution of each overlap term to the cost function, and they are an optional argument in the `VQD` construction. If not set by the user, they can be autoevaluated for input operators of type `SparsePauliOp`. Please note that if you want to set your own `betas`, you should provide a list of values of length `k`." + "The `betas` balance the contribution of each overlap term to the cost function, and they are an optional argument in the `VQD` construction. If not set by the user, they can be auto-evaluated for input operators of type `SparsePauliOp`. Please note that if you want to set your own `betas`, you should provide a list of values of length `k`." ] }, { @@ -167,8 +167,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit.algorithms.eigensolvers import VQD\n", - "\n", + "from qiskit_algorithms import VQD\n", "\n", "vqd = VQD(estimator, fidelity, ansatz, optimizer, k=k, betas=betas, callback=callback)\n", "result = vqd.compute_eigenvalues(operator = H2_op)\n", @@ -191,7 +190,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "[-1.85727493 -1.24458457 -0.88272202]\n" + "[-1.85727482 -1.24458458 -0.88272214]\n" ] } ], @@ -209,16 +208,22 @@ { "cell_type": "code", "execution_count": 8, - "metadata": {}, + "metadata": { + "tags": [ + "nbsphinx-thumbnail" + ] + }, "outputs": [ { "data": { - "image/png": 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", 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\n", "text/plain": [ - "
" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -236,7 +241,7 @@ " _counts = counts[np.where(steps == i)]\n", " _values = values[np.where(steps == i)]\n", " pylab.plot(_counts, _values, label=f\"State {i-1}\")\n", - " \n", + "\n", "pylab.xlabel(\"Eval count\")\n", "pylab.ylabel(\"Energy\")\n", "pylab.title(\"Energy convergence for each computed state\")\n", @@ -260,7 +265,7 @@ }, "outputs": [], "source": [ - "from qiskit.algorithms.eigensolvers import NumPyEigensolver\n", + "from qiskit_algorithms import NumPyEigensolver\n", "\n", "\n", "exact_solver = NumPyEigensolver(k=3)\n", @@ -285,7 +290,7 @@ "output_type": "stream", "text": [ "Reference values: [-1.85727503 -1.24458455 -0.88272215]\n", - "VQD values: [-1.85727493 -1.24458457 -0.88272202]\n" + "VQD values: [-1.85727482 -1.24458458 -0.88272214]\n" ] } ], @@ -298,7 +303,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "As you can see, the result from VQD matches the values from the exact solution, and extends VQE to also compute excited states. " + "As you can see, the result from VQD matches the values from the exact solution, and extends VQE to also compute excited states." ] }, { @@ -309,7 +314,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.1
qiskit-aer0.12.0
qiskit-ibmq-provider0.20.2
qiskit0.43.1
System information
Python version3.11.3
Python compilerClang 14.0.0 (clang-1400.0.29.202)
Python buildmain, Apr 7 2023 20:13:31
OSDarwin
CPUs10
Memory (Gb)32.0
Fri Jun 09 14:52:12 2023 PDT
" + "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Thu Aug 17 18:08:21 2023 CEST
" ], "text/plain": [ "" @@ -334,13 +339,14 @@ "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table\n", - "%qiskit_copyright" + "%qiskit_copyright\n" ] } ], "metadata": { + "celltoolbar": "Edit Metadata", "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -354,9 +360,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.3" + "version": "3.10.2" } }, "nbformat": 4, "nbformat_minor": 4 -} +} \ No newline at end of file diff --git a/docs/tutorials/05_qaoa.ipynb b/docs/tutorials/05_qaoa.ipynb index aac50151..7a00b6fb 100644 --- a/docs/tutorials/05_qaoa.ipynb +++ b/docs/tutorials/05_qaoa.ipynb @@ -4,32 +4,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Quantum Approximate Optimization Algorithm \n", + "# Quantum Approximate Optimization Algorithm\n", "\n", - "Qiskit has an implementation of the Quantum Approximate Optimization Algorithm [QAOA](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.QAOA.html) and this notebook demonstrates using it for a graph partition problem.\n", - "\n", - "Before we begin, let's import the `annotations` module from `__future__` to allow postponed evaluation of annotations. This enables us to use simpler type hints throughout the notebook." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from __future__ import annotations" + "This notebook demonstrates the implementation of the Quantum Approximate Optimization Algorithm ([QAOA](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.QAOA.html)) for a graph partitioning problem (finding the maximum cut), and compares it to a solution using the brute-force approach." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "First we create a graph and draw it so it can be seen." + "Our goal is to partition the graph's vertices into two complementary sets, such that the number of edges between the sets is as large as possible. First, we define the graph using an adjacency matrix, this matrix defines the connectivity between nodes. We draw it to visualize the nodes and edges of the graph." ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -46,7 +35,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { "scrolled": true, "tags": [ @@ -56,7 +45,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -82,7 +71,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -94,7 +83,7 @@ } ], "source": [ - "def objective_value(x: np.ndarray, w: np.ndarray) -> float:\n", + "def objective_value(x, w):\n", " \"\"\"Compute the value of a cut.\n", " Args:\n", " x: Binary string as numpy array.\n", @@ -106,7 +95,7 @@ " w_01 = np.where(w != 0, 1, 0)\n", " return np.sum(w_01 * X)\n", "\n", - "def bitfield(n: int, L: int) -> list[int]:\n", + "def bitfield(n, L):\n", " result = np.binary_repr(n, L)\n", " return [int(digit) for digit in result] # [2:] to chop off the \"0b\" part\n", "\n", @@ -132,18 +121,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The graph partition problem can be converted to an Ising Hamiltonian. Qiskit has different capabilities in the Optimization module to do this. Here, since the goal is to show QAOA, the module is used without further explanation to create the operator. The paper [Ising formulations of many NP problems](https://arxiv.org/abs/1302.5843) may be of interest if you would like to understand the technique further." + "The graph partition problem can be converted to an Ising Hamiltonian, as is done in the following cell. Since the goal is to show QAOA, this conversion module is used to create the operator without further explanation. The paper [Ising formulations of many NP problems](https://arxiv.org/abs/1302.5843) may be of interest if you would like to understand the technique further. Another resource can be the Qiskit Optimization package, which contains functionality to do this conversion automatically for several optimization problems." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "from qiskit.quantum_info import Pauli, SparsePauliOp\n", "\n", - "def get_operator(weight_matrix: np.ndarray) -> tuple[SparsePauliOp, float]:\n", + "def get_operator(weight_matrix):\n", " r\"\"\"Generate Hamiltonian for the graph partitioning\n", " Notes:\n", " Goals:\n", @@ -187,7 +176,7 @@ " coeffs.append(1.0)\n", " else:\n", " shift += 1\n", - " \n", + "\n", " return SparsePauliOp(pauli_list, coeffs=coeffs), shift\n", "\n", "qubit_op, offset = get_operator(w)" @@ -202,7 +191,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -215,18 +204,18 @@ } ], "source": [ - "from qiskit.algorithms.minimum_eigensolvers import QAOA\n", - "from qiskit.algorithms.optimizers import COBYLA\n", - "from qiskit.circuit.library import TwoLocal\n", "from qiskit.primitives import Sampler\n", - "from qiskit.quantum_info import Pauli, Statevector\n", + "from qiskit.quantum_info import Pauli\n", "from qiskit.result import QuasiDistribution\n", - "from qiskit.utils import algorithm_globals\n", "\n", - "sampler = Sampler()\n", + "from qiskit_algorithms import QAOA\n", + "from qiskit_algorithms.optimizers import COBYLA\n", "\n", + "from qiskit_algorithms.utils import algorithm_globals\n", "\n", - "def sample_most_likely(state_vector: QuasiDistribution | Statevector) -> np.ndarray:\n", + "sampler = Sampler()\n", + "\n", + "def sample_most_likely(state_vector):\n", " \"\"\"Compute the most likely binary string from state vector.\n", " Args:\n", " state_vector: State vector or quasi-distribution.\n", @@ -266,7 +255,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -279,7 +268,7 @@ } ], "source": [ - "from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver\n", + "from qiskit_algorithms import NumPyMinimumEigensolver\n", "from qiskit.quantum_info import Operator\n", "\n", "npme = NumPyMinimumEigensolver()\n", @@ -295,12 +284,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "It is also possible to use VQE as is shown below" + "It is also possible to use SamplingVQE as shown below, which offers an alternative solution to the problem." ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -313,9 +302,10 @@ } ], "source": [ - "from qiskit.algorithms.minimum_eigensolvers import SamplingVQE\n", "from qiskit.circuit.library import TwoLocal\n", - "from qiskit.utils import algorithm_globals\n", + "\n", + "from qiskit_algorithms import SamplingVQE\n", + "from qiskit_algorithms.utils import algorithm_globals\n", "\n", "algorithm_globals.random_seed = 10598\n", "\n", @@ -328,18 +318,22 @@ "x = sample_most_likely(result.eigenstate)\n", "\n", "print(x)\n", - "print(f\"Objective value computed by VQE is {objective_value(x, w)}\")\n" + "print(f\"Objective value computed by SamplingVQE is {objective_value(x, w)}\")\n" ] }, { "cell_type": "code", - "execution_count": 9, - "metadata": {}, + "execution_count": 8, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.0
qiskit-aer0.11.1
qiskit-nature0.6.0
qiskit-finance0.4.0
qiskit-optimization0.5.0
qiskit-machine-learning0.6.0
System information
Python version3.9.13
Python compilerClang 13.0.1
Python buildmain, May 27 2022 17:01:00
OSDarwin
CPUs2
Memory (Gb)12.0
Sun Jan 08 11:35:33 2023 EST
" + "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Fri Aug 18 14:58:21 2023 CEST
" ], "text/plain": [ "" @@ -364,11 +358,12 @@ "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table\n", - "%qiskit_copyright" + "%qiskit_copyright\n" ] } ], "metadata": { + "celltoolbar": "Edit Metadata", "kernelspec": { "display_name": "Python 3", "language": "python", @@ -384,7 +379,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.13" + "version": "3.10.2" }, "vscode": { "interpreter": { @@ -394,4 +389,4 @@ }, "nbformat": 4, "nbformat_minor": 2 -} +} \ No newline at end of file diff --git a/docs/tutorials/06_grover.ipynb b/docs/tutorials/06_grover.ipynb index 1a0cbb62..5bafbdb3 100644 --- a/docs/tutorials/06_grover.ipynb +++ b/docs/tutorials/06_grover.ipynb @@ -34,26 +34,26 @@ " \\mathcal{Q} = \\mathcal{A}\\mathcal{S_0}\\mathcal{A}^\\dagger \\mathcal{S_f}\n", "$$\n", "\n", - "Here, \n", + "Here,\n", "* $\\mathcal{A}$ is the initial search state for the algorithm, which is just Hadamards, $H^{\\otimes n}$ for the textbook Grover search, but can be more elaborate for Amplitude Amplification\n", "* $\\mathcal{S_0}$ is the reflection about the all 0 state\n", "$$\n", " |x\\rangle \\mapsto \\begin{cases} -|x\\rangle, &x \\neq 0 \\\\ |x\\rangle, &x = 0\\end{cases}\n", "$$\n", - "* $\\mathcal{S_f}$ is the oracle that applies \n", + "* $\\mathcal{S_f}$ is the oracle that applies\n", "$$\n", " |x\\rangle \\mapsto (-1)^{f(x)}|x\\rangle\n", - "$$ \n", + "$$\n", "    　where $f(x)$ is 1 if $x$ is a good state and otherwise 0.\n", "\n", - "In a nutshell, Grover's algorithm applies different powers of $\\mathcal{Q}$ and after each execution checks whether a good solution has been found. \n", + "In a nutshell, Grover's algorithm applies different powers of $\\mathcal{Q}$ and after each execution checks whether a good solution has been found.\n", "\n", "\n", - "### Running Grover's algorithm \n", + "### Running Grover's algorithm\n", "\n", "To run Grover's algorithm with the `Grover` class, firstly, we need to specify an oracle for the circuit of Grover's algorithm. In the following example, we use `QuantumCircuit` as the oracle of Grover's algorithm. However, there are several other class that we can use as the oracle of Grover's algorithm. We talk about them later in this tutorial.\n", "\n", - "Note that the oracle for `Grover` must be a _phase-flip_ oracle. That is, it multiplies the amplitudes of the of \"good states\" by a factor of $-1$. We explain later how to convert a _bit-flip_ oracle to a phase-flip oracle. " + "Note that the oracle for `Grover` must be a _phase-flip_ oracle. That is, it multiplies the amplitudes of the of \"good states\" by a factor of $-1$. We explain later how to convert a _bit-flip_ oracle to a phase-flip oracle." ] }, { @@ -63,9 +63,9 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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\n", "text/plain": [ - "
" + "
" ] }, "execution_count": 1, @@ -75,7 +75,7 @@ ], "source": [ "from qiskit import QuantumCircuit\n", - "from qiskit.algorithms import AmplificationProblem\n", + "from qiskit_algorithms import AmplificationProblem\n", "\n", "# the state we desire to find is '11'\n", "good_state = ['11']\n", @@ -97,7 +97,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Then, we specify a backend and call the `run` method of `Grover` with a backend to execute the circuits. The returned result type is a `GroverResult`. \n", + "Then, we specify a backend and call the `run` method of `Grover` with a backend to execute the circuits. The returned result type is a `GroverResult`.\n", "\n", "If the search was successful, the `oracle_evaluation` attribute of the result will be `True`. In this case, the most sampled measurement, `top_measurement`, is one of the \"good states\". Otherwise, `oracle_evaluation` will be False.\n" ] @@ -111,7 +111,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Result type: \n", + "Result type: \n", "\n", "Success!\n", "Top measurement: 11\n" @@ -119,7 +119,7 @@ } ], "source": [ - "from qiskit.algorithms import Grover\n", + "from qiskit_algorithms import Grover\n", "from qiskit.primitives import Sampler\n", "\n", "\n", @@ -143,7 +143,7 @@ "metadata": {}, "source": [ "### Using the different types of classes as the oracle of `Grover`\n", - "In the above example, we used `QuantumCircuit` as the oracle of `Grover`. \n", + "In the above example, we used `QuantumCircuit` as the oracle of `Grover`.\n", "However, we can also use `qiskit.quantum_info.Statevector` as oracle.\n", "All the following examples are when $|11\\rangle$ is \"good state\"" ] @@ -157,7 +157,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Result type: \n", + "Result type: \n", "\n", "Success!\n", "Top measurement: 11\n" @@ -166,6 +166,7 @@ ], "source": [ "from qiskit.quantum_info import Statevector\n", + "\n", "oracle = Statevector.from_label('11')\n", "problem = AmplificationProblem(oracle, is_good_state=['11'])\n", "\n", @@ -191,9 +192,9 @@ "outputs": [ { "data": { - "image/png": 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l5cXw4cMZO3YsTzzxBMnJMnwVDZdZXp2uSlUhBvDz8yM5Obk+SxLioTS6w8v9QiyE2jS6I/Gd71ULYS4a3ZFYCHMjIRZC5STEQqichNgMbElbRdQ0DVvSVhldXngph6hpGuLWvFyvdYn6ISEWQuUkxKJGFEXh+s0SU5chfqfR/YtJ/Gbv4XV8k7KE7PwMKm+V4+HsTdeApxk/IB4rS2sOZe9i6ieRTH1hJTfKS9m07x8UXMxmeO8ZtHDxIf6rV+657fjXdxLm16v+dqYRkxA3Up99/w6JO+bRtkUQzz/5Fq5OXuRfzObHzHWMfnqu3qwh6/cu4lrZRfo9Ng5XR088nL3x9ujA9OFf6G1TQWHl9zN1k/yJ+iEhboSO5e4nccc8OvlF8rcx32FtZatbNrb/AoP+Fy7n8q/YY7g4NNdr93Lz1Xu9IjmWC1fymDDo77TzDK6b4oUBCXEjtP3glwC82n++XoABvemK7ujb5SWDAN/tu9RP+Wr3BwzsPsFgwntRt+TCViNyJ6Bni06i0Wjw86re98dbewRUufzAiR9YvH4CXQKeYmJ0I7pJuoGQEJsBG6vbk+7dvMdskjf+/1MU7/QD0KABI0dd49u/98ycv57LYu4Xf8TbowPvjvqaJk1kcFffJMRmwNP19rS7ueezjC6/036nX2v3ALSKltP5hx7qfYtLzjPrs2exsrTh/VeTsbdteM+0agwkxGagfavOeDh7sytjDUVX8vWWVVSWszElAY1GQ/egQQC6SfY++36m0UfBVGfGpvKKG8xeGc2lqwW89/JGPF19Hn5HxAORsY8ZaNLEkpghS5mzejCvfRTKM+FjaOnmR/G1c+w+lETOuSOM6D0T7+YdAHikTTjDIqeTtHMhbyzqTM+wYbg6eVJw6Rf2Hl5LwuT9ONg5V/meq7fOJiv3J54MeZ78olPkF53SW94lIAoXxxZ1tcvidyTEZuKxwGdZNDGFpF1xbEtfzdWyi9ha2+Pf6lFmRSXRM+wFvf5j+y/A1yuMjSkJfLU7DkWrxcPZm/BH+lfr8TDF184BsDdzHXsz1xksj399p4S4njS62S4bCpntUtQWOScWQuUkxEKonIRYCJWTEAuhchJiIVROQiyEykmIhVA5CbEQKichFkLlJMRCqJyEWAiVkxsgGom8Cyf5IGk0V0qLsLdtxrRhq/Dx7GjqskQtkCNxI/Hxutfo/9h4Vk0/wbDI6XyQ9LKpSxK1RI7EjUBxyXlO5KWzYNxWAJ4MeZ6EDZM4W3SKVu7+91yv5Pplxn0YzM2K63g086bi1k0KL56mT5dRTBn6aZ3VqyigraizzdcZC6tqz3hUqyTEjcCFy2dwdfLSzX+l0Who7tKG85dzqwyxg50zvTv9CTsbR16Mepe041tI3DGvTgMMtwOsxts0TXW7pQynRZVO5Wfg3+pRAE7m/Yx/y0dNXJG4m4S4EfBw9ubS1QJu3aoEbs+hdb44l+bObe677um7Q9xKQtzQSIgbAReH5vi36swPB/4XuD2ljrtza91QemHiS/yYucFgvaIrZ0Gjwb1ZKwBOFx6mnWdI/RUuqkVC3Ei8+fwyNv+0jJcXBrBm5wKmvbBSt+xEXjoezt4G65w6e1Bv+Oxg68ym//tnvdQrqk8ubDUS3s07sPh//s+g/XLJBdybtaKDd1eDZY8HDeDxoAG61/+ISavTGsWDkSNxI+fs4MHC8dtMXYZ4CBJiIVROQixUYUvaKqKmadiStsro8sJLOURN0xC35uV6rashkBALoXISYiHuoigK12+WmLqMapOr08Ks7T28jm9SlpCdn0HlrXI8nL3pGvA04wfEY2VpzaHsXUz9JJKpL6zkRnkpm/b9g4KL2QzvPYMWLj7Ef/XKPbcd//pOwvx61d/O3IOEWJitz75/h8Qd82jbIojnn3wLVycv8i9m82PmOkY/PRcry9++6Lx+7yKulV2k32PjcHX0xMPZG2+PDkwf/oXeNhUUVn4/k4tX83Gyd6/vXTJKQizM0rHc/STumEcnv0j+NuY7rK1sdcvG9l9g0P/C5Vz+FXsMF4fmeu1ebr56r1ckx3LhSh4TBv2ddp7BdVN8DTWKc+KioiJiY2Px9/fH1tYWb29vYmJiKC0tZcyYMWg0GhISEkxdpoHEHfOZ+8VQRs33JWqahhfn+Zi6JNXYfvBLAF7tP18vwHD7Li7NXfcM9u3ykkGA7/Zd6qd8tfsDBnafwJAn36zVeh+G2R+JMzIy6NevH4WFhdjb2xMUFER+fj6LFy8mOzubS5cuAdCpUyfTFmrEZ9/PxLGpK+1bdab0+mVTl6MKd8J5tugkGo0GP6+waq3X2iOgyuUHTvzA4vUT6BLwFBOjG9Z9kmYd4qKiIgYOHEhhYSFTpkxh9uzZODo6AhAXF8f06dOxtLREo9EQGhpq4moNff7nbN1wblx8MNfL1XPFtLbZWNkBcLOizOjyG+Wlev0ANGiqfZd+Vc9k/vVcFnO/+CPeHh14d9TXuvuyGwqzHk5PnjyZvLw8Jk2aRHx8vC7AALGxsYSFhVFZWYmPjw9OTk4mrNS4u8/HGjNP13YA5J7PMrr8Tvudfq3dA9AqWk7nH3qo9y0uOc+sz57FytKG919Nxt624f2emG2Is7KySEpKwt3dnfnz5xvt06VLFwDCwn4bct0JfXh4ODY2NgbnTsI02rfqjIezN7sy1lB0JV9vWUVlORtTEtBoNHQPGgRA70f/BNw+JamoLDfYnqIo933P8oobzF4ZzaWrBbz38kY8XX0efkfqQMMaF9SixMREtFotI0eOxMHBwWgfO7vbQ6/fh/jUqVOsW7eObt26YW1tTUpKSr3UK6rWpIklMUOWMmf1YF77KJRnwsfQ0s2P4mvn2H0oiZxzRxjReybezTsA8EibcIZFTidp50LeWNSZnmHDcHXypODSL+w9vJaEyftxsHOu8j1Xb51NVu5PPBnyPPlFp8gvOqW3vEtAFC6OLepql6vNbEO8Y8cOACIjI+/ZJy8vD9AP8R/+8AcKCgoAmDNnjoS4AXks8FkWTUwhaVcc29JXc7XsIrbW9vi3epRZUUn0DHtBr//Y/gvw9QpjY0oCX+2OQ9Fq8XD2JvyR/lWeA99RfO0ccHsShb2Z6wyWx7++U0Jcl3799VcA2rZta3R5ZWWlLqC/D7GFRe2fYXTt2pXCwkK9NmtLO5ZPOlnr79VQtQ9oT3nl9Wr1reqz6eDdjb+M+rra79v70RH0fnTEPZeH+fVi2wfGh9axw1cRO3xVtd+rJvt4N09PT9LT0x9oXbMNcWnp7auV168b/1CTkpIoKirC0dGRdu3a1WkthYWFnD17Vq/NthpHAnNSkJ/PjXtcWb6bWj+bmuxjbTLbEHt6elJcXMyBAwfo3r273rKCggKmTZsGQGhoaJ1fvPL09DRos7a0M9LTfHm1bFmjI7Ea1WQf72bsd6S6zDbEffv2JSsri4ULFxIVFUVAwO1/5qelpTFq1CiKioqA+vmSh7Fh0q1ydc6t/KBOnjhZ7TmZ1frZ1GQfa5PZhjg2NpZ///vfnDlzho4dO/LII49w48YNTp06Rb9+/fDx8WHLli1658MNzbafv+B88e1z+8ulF6i8Vc6XP/wVgOYubYnqMsqU5YkGwmxD3Lp1a/bu3cu0adPYvXs3OTk5BAUFsWzZMsaNG4efnx9Agw7xf/b/i8Ond+u1rdryLgChvj0lxAIw4xADBAYGkpycbNBeUlJCTk4OFhYWBAc3jDtRjPlwwi5TlyBUwKxDfC9HjhxBURQCAgJo2tTwSujatWsBOHr0qN5rHx8funY1nNpVCFNqlCHOzMwE7j2UHjp0qNHXo0ePZtWqVXVamxA1JSE2ojrfqxXqtefwWg6e3M6EQX/nb18O59dzR7GxssPZoTmThyyt8kmRDZHZ3gBRlfuFWJi3lP9u4Ing5wDo/9h4VsYeZ9nbh+jeMZqPvh5r2uIeQKM8Et/5XrUwT1U9HD1myFKO5KQwbdgqLJtY8Vhgf916gW0eZ+3ueBNW/mAaZYiFeavq4ejpx7cS1PYJLJtYGay34ceP6d4x2gQVP5xGOZwW5u9eD0ffd+QbegQPNuj/7+3zyC86xZh+xu89b8gkxMIsGXs4uqIopB/fQvgj/fT6fr0rnh//u555Y7/H1lp9N19IiIXZudfD0Y+d2U+bFoHY2fw2ScTa3R+xMyORheO23XeSgIZKzomF2bnXw9Gb2bvzRMfndO0XLuexLHkKXq6+TP3k9uQR1pY2LJmcWt8lPxSNIv8UNQm13qnzoCInY/K7mMbGd+SD13fed37pB1WTfaxNciQWjcanU4+YuoQ6IefEQqichFgIlZMQC6FyEmIhVE6uTpuIooC2wtRV1B8Lq2o/Fkm1n01N9rE2SYiFUDkZTguhchJiIVROQiyEykmIhVA5CbEQKichFkLlJMRCqJyEWAiVkxALoXISYiFUTkIshMpJiIVQOQmxEConIRZC5STEQqichFgIlZMQC6FyEmIhVE5CLITKSYiFUDkJsRAqJyEWQuUkxEKonIRYCJWTEAuhcv8PSMX+JMU+qREAAAAASUVORK5CYII=", + "image/png": 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\n", 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" + "
" ] }, "execution_count": 4, @@ -223,14 +224,11 @@ }, "outputs": [ { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" + "name": "stdout", + "output_type": "stream", + "text": [ + "\"The 'tweedledum' library is required to use 'PhaseOracle'. You can install it with 'pip install tweedledum'.\"\n" + ] } ], "source": [ @@ -291,9 +289,9 @@ }, { "data": { - "image/png": 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", + "image/png": 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"text/plain": [ - "
" + "
" ] }, "execution_count": 6, @@ -304,7 +302,7 @@ "source": [ "import numpy as np\n", "\n", - "# Specifying `state_preparation` \n", + "# Specifying `state_preparation`\n", "# to prepare a superposition of |01>, |10>, and |11>\n", "oracle = QuantumCircuit(3)\n", "oracle.ccz(0, 1, 2)\n", @@ -353,8 +351,8 @@ "\n", "For more advanced use, it is also possible to specify the entire Grover operator by setting the `grover_operator` argument. This might be useful if you know more efficient implementation for $\\mathcal{Q}$ than the default construction via zero reflection, oracle and state preparation.\n", "\n", - "The `qiskit.circuit.library.GroverOperator` can be a good starting point and offers more options for an automated construction of the Grover operator. You can for instance \n", - "* set the `mcx_mode` \n", + "The `qiskit.circuit.library.GroverOperator` can be a good starting point and offers more options for an automated construction of the Grover operator. You can for instance\n", + "* set the `mcx_mode`\n", "* ignore qubits in the zero reflection by setting `reflection_qubits`\n", "* explicitly exchange the $\\mathcal{S_f}, \\mathcal{S_0}$ and $\\mathcal{A}$ operations using the `oracle`, `zero_reflection` and `state_preparation` arguments" ] @@ -363,7 +361,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "For instance, imagine the good state is a three qubit state $|111\\rangle$ but we used 2 additional qubits as auxiliary qubits. " + "For instance, imagine the good state is a three qubit state $|111\\rangle$ but we used 2 additional qubits as auxiliary qubits." ] }, { @@ -375,9 +373,9 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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"text/plain": [ - "
" + "
" ] }, "execution_count": 8, @@ -409,9 +407,9 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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\n", "text/plain": [ - "
" + "
" ] }, "execution_count": 9, @@ -421,6 +419,7 @@ ], "source": [ "from qiskit.circuit.library import GroverOperator\n", + "\n", "grover_op = GroverOperator(oracle, insert_barriers=True)\n", "grover_op.decompose().draw(output='mpl')" ] @@ -439,9 +438,9 @@ "outputs": [ { "data": { - "image/png": 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\n", "text/plain": [ - "
" + "
" ] }, "execution_count": 10, @@ -693,7 +692,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.0.dev0+0f6c75e
qiskit-aer0.11.1
qiskit-optimization0.5.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Fri Nov 25 21:25:09 2022 JST
" + "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Thu Aug 17 18:12:13 2023 CEST
" ], "text/plain": [ "" @@ -705,7 +704,7 @@ { "data": { "text/html": [ - "

This code is a part of Qiskit

© Copyright IBM 2017, 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.

" + "

This code is a part of Qiskit

© Copyright IBM 2017, 2023.

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.

" ], "text/plain": [ "" @@ -718,13 +717,14 @@ "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table\n", - "%qiskit_copyright" + "%qiskit_copyright\n" ] } ], "metadata": { + "celltoolbar": "Edit Metadata", "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -738,7 +738,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.10" + "version": "3.10.2" }, "vscode": { "interpreter": { @@ -748,4 +748,4 @@ }, "nbformat": 4, "nbformat_minor": 2 -} +} \ No newline at end of file diff --git a/docs/tutorials/07_grover_examples.ipynb b/docs/tutorials/07_grover_examples.ipynb index 74bc42d7..0262a04e 100644 --- a/docs/tutorials/07_grover_examples.ipynb +++ b/docs/tutorials/07_grover_examples.ipynb @@ -6,7 +6,7 @@ "source": [ "# Grover's algorithm examples\n", "\n", - "This notebook has examples demonstrating how to use the Qiskit [Grover](https://qiskit.org/documentation/stubs/qiskit.algorithms.Grover.html) search algorithm, with different oracles." + "This notebook has examples demonstrating how to use the Qiskit Algorithms [Grover](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.Grover.html) search algorithm, with different oracles." ] }, { @@ -58,22 +58,13 @@ "cell_type": "code", "execution_count": 2, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\"The 'tweedledum' library is required to use 'classical function oracles'. You can install it with 'pip install tweedledum'.\"\n" - ] - } - ], + "outputs": [], "source": [ "import os\n", "import tempfile\n", "from qiskit.exceptions import MissingOptionalLibraryError\n", "from qiskit.circuit.library.phase_oracle import PhaseOracle\n", "\n", - "\n", "fp = tempfile.NamedTemporaryFile(mode='w+t', delete=False)\n", "fp.write(input_3sat_instance)\n", "file_name = fp.name\n", @@ -100,7 +91,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit.algorithms import AmplificationProblem\n", + "from qiskit_algorithms import AmplificationProblem\n", "\n", "problem = None\n", "if oracle is not None:\n", @@ -118,9 +109,17 @@ "cell_type": "code", "execution_count": 4, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "000\n" + ] + } + ], "source": [ - "from qiskit.algorithms import Grover\n", + "from qiskit_algorithms import Grover\n", "from qiskit.primitives import Sampler\n", "\n", "grover = Grover(sampler=Sampler())\n", @@ -143,7 +142,18 @@ "cell_type": "code", "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from qiskit.tools.visualization import plot_histogram\n", "\n", @@ -166,11 +176,14 @@ "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "\"The 'tweedledum' library is required to use 'PhaseOracle'. You can install it with 'pip install tweedledum'.\"\n" - ] + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ @@ -200,7 +213,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-ibmq-provider0.20.2
qiskit0.42.1
System information
Python version3.10.10
Python compilerGCC 12.2.1 20230201
Python buildmain, Mar 5 2023 22:26:53
OSLinux
CPUs32
Memory (Gb)125.66083908081055
Thu May 04 15:38:15 2023 EDT
" + "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Fri Aug 18 15:33:03 2023 CEST
" ], "text/plain": [ "" @@ -225,20 +238,14 @@ "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table\n", - "%qiskit_copyright" + "%qiskit_copyright\n" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { + "celltoolbar": "Edit Metadata", "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -252,7 +259,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.10" + "version": "3.10.2" }, "vscode": { "interpreter": { @@ -262,4 +269,4 @@ }, "nbformat": 4, "nbformat_minor": 2 -} +} \ No newline at end of file diff --git a/docs/tutorials/09_IQPE.ipynb b/docs/tutorials/09_IQPE.ipynb deleted file mode 100644 index b86c768c..00000000 --- a/docs/tutorials/09_IQPE.ipynb +++ /dev/null @@ -1,1046 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "feac998a", - "metadata": {}, - "source": [ - "# Iterative Quantum Phase Estimation Algorithm\n", - "\n", - "The goal of this tutorial is to understand how the Iterative Phase Estimation (IPE) algorithm works, why would we use the IPE algorithm instead of the QPE (Quantum Phase Estimation) algorithm and how to build it with Qiskit using the same circuit exploiting reset gate and the `c_if` method that allows to apply gates conditioned by the values stored in a classical register, resulting from previous measurements.\n", - "\n", - "**References**\n", - "\n", - "- [Section 2 of Lab 6: Iterative Phase Estimation (IPE) Algorithm](https://learn.qiskit.org/course/ch-labs/lab-6-iterative-phase-estimation-algorithm) \n", - "\n", - "- [Ch.3.6 Quantum Phase Estimation](https://learn.qiskit.org/course/ch-algorithms/quantum-phase-estimation)" - ] - }, - { - "cell_type": "markdown", - "id": "edf04b07", - "metadata": {}, - "source": [ - "# Conditioned gates: the ``c_if`` method" - ] - }, - { - "cell_type": "markdown", - "id": "4eb985e3", - "metadata": {}, - "source": [ - "Before starting the IPE algorithm, we will give a brief tutorial about the Qiskit conditional method, `c_if`, as it goes into building the IPE circuit.\n", - "\n", - "`c_if` is a function (actually a method of the gate class) to perform conditioned operations based on the value stored previously in a classical register. With this feature you can apply gates after a measurement in the same circuit conditioned by the measurement outcome.\n", - "\n", - "For example, the following code will execute the $X$ gate if the value of the classical register is $0$." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "8d3ed2e3", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from qiskit import QuantumCircuit\n", - "\n", - "qc = QuantumCircuit(1, 1)\n", - "qc.h(0)\n", - "qc.measure(0,0)\n", - "qc.x(0).c_if(0, 0)\n", - "qc.draw(output='mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "7bb05bbd", - "metadata": {}, - "source": [ - "We highlight that the method ``c_if`` expects as the first argument a whole classical register, not a single classical bit (or a list of classical bits), and as the second argument a value in decimal representation (a non-negative integer), not the value of a single bit, 0, or 1 (or a list/string of binary digits).\n", - "\n", - "Let's make another example. Consider that we want to perform a bit flip on the third qubit after the measurements in the following circuit, when the results of the measurement of $q_0$ and $q_1$ are both $1$." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "00b7d3a1", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from qiskit import QuantumRegister, ClassicalRegister\n", - "\n", - "q = QuantumRegister(3, 'q')\n", - "c = ClassicalRegister(3, 'c')\n", - "qc = QuantumCircuit(q, c)\n", - "\n", - "qc.h([0, 1, 2])\n", - "qc.barrier()\n", - "qc.measure(q, c)\n", - "\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "ae92e111", - "metadata": {}, - "source": [ - "We want to apply the $X$ gate, only if both the results of the measurement of $q_0$ and $q_1$ are $1$. We can do this using the ``c_if`` method, conditioning the application of $X$ depending on the value passed as argument to ``c_if``.\n", - "\n", - "We will have to encode the value to pass to the ``c_if`` method such that it will check the values 011 and 111 (in binary representation), since it does not matter what $q_2$ is measured as.\n", - "\n", - "The 2 integer values in decimal representation:\n", - "\n", - "$$\\begin{alignedat}{2}\n", - "\\left.\\begin{array}{ccc}2^2 & 2^1 & 2^0\\\\\\hline 0 & 1 & 1\\end{array}\\ \\right\\vert&\\ (0\\times2^2) + (1\\times2^1) + (1\\times2^0) = &&2 + 1 = 3 \\\\[10px]\n", - "\\left.\\begin{array}{ccc}2^2 & 2^1 & 2^0\\\\\\hline 1 & 1 & 1\\end{array}\\ \\right\\vert&\\ (1\\times2^2) + (1\\times2^1) + (1\\times2^0) = 4 + {}&&2 + 1 = 7\n", - "\\end{alignedat}$$" - ] - }, - { - "cell_type": "markdown", - "id": "25fa9853", - "metadata": {}, - "source": [ - "We can check the solutions using the ``bin()`` method in python (the prefix `0b` indicates the binary format)." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "19b565e1", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0b11\n", - "0b111\n" - ] - } - ], - "source": [ - "print(bin(3))\n", - "print(bin(7))" - ] - }, - { - "cell_type": "markdown", - "id": "c4c65c39", - "metadata": {}, - "source": [ - "So we have to apply $X$ to $q_2$ using ``c_if`` two times, one for each value corresponding to 011 and 111." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "1bbd6b37", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc.x(2).c_if(c, 3) # for the 011 case\n", - "qc.x(2).c_if(c, 7) # for the 111 case\n", - "\n", - "qc.draw(output='mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "9a50c886", - "metadata": {}, - "source": [ - "# IPE\n", - "\n", - "The motivation for using the IPE algorithm is that QPE algorithm works fine for short depth circuits but when the circuit starts to grow, it doesn't work properly due to gate noise and decoherence times.\n", - "\n", - "The detailed explanation of how the algorithm works can be found in [Iterative Phase Estimation (IPE) Algorithm](https://learn.qiskit.org/course/ch-labs/lab-6-iterative-phase-estimation-algorithm). To understand QPE in depth, you can see also [Ch.3.6 Quantum Phase Estimation](https://learn.qiskit.org/course/ch-algorithms/quantum-phase-estimation).\n", - "\n", - "## IPE example with a 1-qubit gate for $U$\n", - "\n", - "We want to apply the IPE algorithm to estimate the phase for a 1-qubit operator $U$. For example, here we use the $S$-gate.\n", - "\n", - "Let's apply the IPE algorithm to estimate the phase for $S$-gate.\n", - "Its matrix is \n", - "$$ S = \n", - "\\begin{bmatrix}\n", - "1 & 0\\\\\n", - "0 & e^\\frac{i\\pi}{2}\\\\ \n", - "\\end{bmatrix}$$\n", - "\n", - "That is, the $S$-gate adds a phase $\\pi/2$ to the state $|1\\rangle$, leaving unchanged the phase of the state $|0\\rangle$\n", - "\n", - "$$ S|1\\rangle = e^\\frac{i\\pi}{2}|1\\rangle $$\n", - "\n", - "In the following, we will use the notation and terms used in [Section 2 of lab 6](https://learn.qiskit.org/course/ch-labs/lab-6-iterative-phase-estimation-algorithm#lab-15-0).\n", - "\n", - "Let's consider to estimate the phase $\\phi=\\frac{\\pi}{2}$ for the eigenstate $|1\\rangle$, we should find $\\varphi=\\frac{1}{4}$ (where $\\phi = 2 \\pi \\varphi$). Therefore to estimate the phase we need exactly 2 phase bits, i.e. $m=2$, since $1/2^2=1/4$. So $\\varphi=0.\\varphi_1\\varphi_2$.\n", - "\n", - "Remember from the theory that for the IPE algorithm, $m$ is also the number of iterations, so we need only $2$ iterations or steps.\n", - "\n", - "First, we initialize the circuit. IPE works with only 1 auxiliary qubit, instead of $m$ counting qubits of the QPE algorithm. Therefore, we need 2 qubits, 1 auxiliary qubit and 1 for the eigenstate of $U$-gate, and a classical register of 2 bits, for the phase bits $\\varphi_1$, $\\varphi_2$." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "c82b1da1", - "metadata": {}, - "outputs": [], - "source": [ - "nq = 2\n", - "m = 2\n", - "q = QuantumRegister(nq, 'q')\n", - "c = ClassicalRegister(m, 'c')\n", - "\n", - "qc_S = QuantumCircuit(q,c)" - ] - }, - { - "cell_type": "markdown", - "id": "fead17a6", - "metadata": {}, - "source": [ - "### First step\n", - "\n", - "Now we build the quantum circuit for the first step, that is, the first iteration of the algorithm, to estimate the least significant phase bit $\\varphi_m$, in this case $\\varphi_2$. For the first step we have 3 sub-steps:\n", - "- initialization\n", - "- application of the Controlled-$U$ gates\n", - "- measure of the auxiliary qubit in X-basis\n", - "\n", - "#### Initialization\n", - "\n", - "The initialization consists of application the Hadamard gate to the auxiliary qubit and the preparation of the eigenstate $|1\\rangle$." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "b0eb6f14", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc_S.h(0)\n", - "qc_S.x(1)\n", - "qc_S.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "30757254", - "metadata": {}, - "source": [ - "#### Application of the Controlled-$U$ gates\n", - "\n", - "Then we have to apply $2^t$ times the Controlled-$U$ operators (see also in the docs [Two qubit gates](https://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html#Two-qubit-gates)), that, in this example, is the Controlled-$S$ gate ($CS$ for short).\n", - "\n", - "To implement $CS$ in the circuit, since $S$ is a phase gate, we can use the controlled phase gate $\\text{CP}(\\theta)$, with $\\theta=\\pi/2$." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "4629d696", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from math import pi\n", - "\n", - "cu_circ = QuantumCircuit(2)\n", - "cu_circ.cp(pi/2, 0, 1)\n", - "cu_circ.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "9a09a586", - "metadata": {}, - "source": [ - "Let's apply $2^t$ times $\\text{CP}(\\pi/2)$. Since for the first step $t=m-1$, and $m=2$, we have $2^t=2$." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "3e94b96d", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "for _ in range(2 ** (m - 1)):\n", - " qc_S.cp(pi/2, 0, 1)\n", - "qc_S.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "db469592", - "metadata": {}, - "source": [ - "#### Measure in X-basis\n", - "\n", - "Finally, we perform the measurement of the auxiliary qubit in X-basis. So we will define a function to perform the ``x_measurement`` and then apply it." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "aa1cd4fb", - "metadata": {}, - "outputs": [], - "source": [ - "def x_measurement(qc, qubit, cbit):\n", - " \"\"\"Measure 'qubit' in the X-basis, and store the result in 'cbit'\"\"\"\n", - " qc.h(qubit)\n", - " qc.measure(qubit, cbit)" - ] - }, - { - "cell_type": "markdown", - "id": "8e4417ce", - "metadata": {}, - "source": [ - "In this way we obtain the phase bit $\\varphi_2$ and store it in the classical bit $c_0$." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "9d767f96", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x_measurement(qc_S, q[0], c[0])\n", - "qc_S.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "99727bfd", - "metadata": {}, - "source": [ - "### Subsequent steps (2nd step)\n", - "\n", - "Now we build the quantum circuit for the other remaining steps, in this example, only the second one.\n", - "In these steps we have 4 sub-steps: the 3 sub-steps as in the first step and, in the middle, the additional step of the phase correction\n", - "- initialization with reset\n", - "- phase correction\n", - "- application of the Control-$U$ gates\n", - "- measure of the auxiliary qubit in X-basis\n", - "\n", - "#### Initialization with reset\n", - "\n", - "As we want to perform an iterative algorithm in the same circuit, we need to reset the auxiliary qubit $q_0$ after the measument gate and initialize it again as before to recycle the qubit. " - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "c69ed53a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc_S.reset(0)\n", - "qc_S.h(0)\n", - "qc_S.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "60060d00", - "metadata": {}, - "source": [ - "#### Phase correction (for step 2)\n", - "As seen in the theory, in order to extract the phase bit $\\varphi_{1}$, we perform a phase correction of $-\\pi\\varphi_2/2$.\n", - "Of course, we need to apply the phase correction in the circuit only if the phase bit $\\varphi_2=1$, i.e. we have to apply the phase correction of $-\\pi/2$ only if the classical bit $c_0$ is 1.\n", - "\n", - "So, after the reset we apply the phase gate $P(\\theta)$ with phase $\\theta=-\\pi/2$ conditioned by the classical bit $c_0$ ($=\\varphi_2$) using the `c_if` method.\n", - "So as we saw in the first part of this tutorial, we have to use the `c_if` method with a value of 1, as $1_{10} = 001_{2}$ (the subscripts $_{10}$ and $_2$ indicate the decimal and binary representations)." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "4d7b8a7b", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc_S.p(-pi/2, 0).c_if(c, 1)\n", - "qc_S.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "9b096b64", - "metadata": {}, - "source": [ - "#### Application of the Control-$U$ gates and x-measurement (for step 2)\n", - "\n", - "We apply the $CU$ operations as we did in the first step. For the second step we have $t=m-2$, hence $2^t=1$. So we apply $\\text{CP}(\\pi/2)$ once. And then we perform the X-measurement of the qubit $q_0$, storing the result, the phase bit $\\varphi_1$, in the bit $c_1$ of classical register." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "8d0b95ef", - "metadata": {}, - "outputs": [], - "source": [ - "## 2^t c-U operations (with t=m-2)\n", - "for _ in range(2 ** (m - 2)):\n", - " qc_S.cp(pi/2, 0, 1)\n", - "\n", - "x_measurement(qc_S, q[0], c[1]) " - ] - }, - { - "cell_type": "markdown", - "id": "02d9b94c", - "metadata": {}, - "source": [ - "Et voilà, we have our final circuit" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "31d410f2", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc_S.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "d5b1356c", - "metadata": {}, - "source": [ - "Let's sample the circuit with Qiskit Aer's `Sampler` primitive, a local simulator without noise that runs locally." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "1c984758", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "from qiskit.tools.visualization import plot_histogram\n", - "from qiskit_aer.primitives import Sampler\n", - "\n", - "sampler = Sampler()\n", - "\n", - "job = sampler.run(qc_S)\n", - "result = job.result()\n", - "\n", - "dist0 = result.quasi_dists[0]\n", - "\n", - "key_new = [str(key/2**m) for key in list(dist0.keys())]\n", - "dist1 = dict(zip(key_new, dist0.values()))\n", - "\n", - "fig, ax = plt.subplots(1,2)\n", - "plot_histogram(dist0, ax=ax[0])\n", - "plot_histogram(dist1, ax=ax[1])\n", - "plt.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "id": "2d830d23", - "metadata": {}, - "source": [ - "In the picture we have the same histograms but on the left we have on the x-axis the string with phase bits $\\varphi_1$, $\\varphi_2$ and on the right the actual phase $\\varphi$ in decimal representation.\n", - "\n", - "As we expected we have found $\\varphi=\\frac{1}{4}=0.25$ with a $100\\%$ probability." - ] - }, - { - "cell_type": "markdown", - "id": "2314dbb2", - "metadata": {}, - "source": [ - "## IPE example with a 2-qubit gate\n", - "\n", - "Now, we want to apply the IPE algorithm to estimate the phase for a 2-qubit gate $U$. For this example, let's consider the controlled version of the $T$ gate, i.e. the gate $U=\\textrm{Controlled-}T$ (that from now we will express more compactly with $CT$). Its matrix is\n", - "$$ CT = \n", - "\\begin{bmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0\\\\\n", - "0 & 0 & 0 & e^\\frac{i\\pi}{4}\\\\ \n", - "\\end{bmatrix} $$\n", - "That is, the $CT$ gate adds a phase $\\pi/4$ to the state $|11\\rangle$, leaving unchanged the phase of the other computational basis states $|00\\rangle$, $|01\\rangle$, $|10\\rangle$.\n", - "\n", - "Let's consider to estimate the phase $\\phi=\\pi/4$ for the eigenstate $|11\\rangle$, we should find $\\varphi=1/8$, since $\\phi = 2 \\pi \\varphi$. Therefore to estimate the phase we need exactly 3 classical bits, i.e. $m=3$, since $1/2^3=1/8$. So $\\varphi=0.\\varphi_1\\varphi_2\\varphi_3$.\n", - "\n", - "As done with the example for the 1-qubit $U$ operator we will go through the same steps but this time we will have $3$ steps since $m=3$, and we will not repeat all the explanations. So for details see the above example for 1-qubit $U$ gate.\n", - "\n", - "First, we initialize the circuit with 3 qubits, 1 for the auxiliary qubit and 2 for the 2-qubit gate, and 3 classical bits to store the phase bits $\\varphi_1$, $\\varphi_2$, $\\varphi_3$." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "c13208f6", - "metadata": {}, - "outputs": [], - "source": [ - "nq = 3 # number of qubits\n", - "m = 3 # number of classical bits\n", - "q = QuantumRegister(nq,'q')\n", - "c = ClassicalRegister(m,'c')\n", - "\n", - "qc = QuantumCircuit(q,c)" - ] - }, - { - "cell_type": "markdown", - "id": "8107bb94", - "metadata": {}, - "source": [ - "### First step\n", - "\n", - "Now we build the quantum circuit for the first step, to estimate the least significant phase bit $\\varphi_m=\\varphi_3$.\n", - "\n", - "#### Initialization\n", - "\n", - "We initialize the auxiliary qubit and the other qubits with the eigenstate $|11\\rangle$." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "982d416d", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc.h(0)\n", - "qc.x([1, 2])\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "739dbd79", - "metadata": { - "tags": [] - }, - "source": [ - "#### Application of the Controlled-$U$ gates\n", - "\n", - "Then we have to apply multiple times the $CU$ operator, that, in this example, is the Controlled-$CT$ gate ($CCT$ for short).\n", - "\n", - "To implement $CCT$ in the circuit, since $T$ is a phase gate, we can use the multi-controlled phase gate $\\text{MCP}(\\theta)$, with $\\theta=\\pi/4$." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "280518a7", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "cu_circ = QuantumCircuit(nq)\n", - "cu_circ.mcp(pi/4, [0, 1], 2)\n", - "cu_circ.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "cd174450", - "metadata": {}, - "source": [ - "Let's apply $2^t$ times $\\text{MCP}(\\pi/4)$. Since for the first step $t=m-1$ and $m=3$, we have $2^t=4$." - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "24c8f9b9", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "for _ in range(2 ** (m - 1)):\n", - " qc.mcp(pi/4, [0, 1], 2)\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "09e40686", - "metadata": {}, - "source": [ - "#### Measure in X-basis\n", - "\n", - "Finally, we perform the measurement of the auxiliary qubit in X-basis.\n", - "We can use the `x_measurement` function defined above in the example for 1-qubit gate. In this way we have obtained the phase bit $\\varphi_3$ and stored it in the classical bit $c_0$." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "6fa62739", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x_measurement(qc, q[0], c[0])\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "3ac0df28", - "metadata": {}, - "source": [ - "### Subsequent steps (2nd, 3rd)\n", - "\n", - "Now we build the quantum circuit for the other remaining steps, the second and the third ones.\n", - "As said in the first example, in these steps we have the additional sub-step of the phase correction.\n", - "\n", - "#### Initialization with reset\n" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "1520c0da", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc.reset(0)\n", - "qc.h(0)\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "f7da1b6a", - "metadata": {}, - "source": [ - "#### Phase correction (for step 2)\n", - "In order to extract the phase bit $\\varphi_{2}$, we perform a phase correction of $-\\pi\\varphi_3/2$.\n", - "\n", - "So, after the reset we apply the phase gate $P(\\theta)$ with phase $\\theta=-\\pi/2$ conditioned by the classical bit $c_0$ ($=\\varphi_3$)." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "99a64b7b", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc.p(-pi/2, 0).c_if(c, 1)\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "68be63a1", - "metadata": {}, - "source": [ - "#### Application of the Control-$U$ gates and x-measurement (for step 2)\n", - "We apply the $CU$ operations as we did in the first step. For the second step we have $t=m-2$, hence $2^t=2$. So we apply $\\text{MCP}(\\pi/4)$ $2$ times. And then we perform the X-measurement of the qubit $q_0$, storing the phase bit $\\varphi_2$ in the bit $c_1$." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "fa0d6cef", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "for _ in range(2 ** (m - 2)):\n", - " qc.mcp(pi/4, [0, 1], 2)\n", - "x_measurement(qc, q[0], c[1])\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "25949dc2", - "metadata": {}, - "source": [ - "#### All substeps of the 3rd step\n", - "For the 3rd and last step, we perform the reset and initialization of the auxiliary qubit as done in the second step.\n", - "\n", - "Then at the 3rd step we have to perform the phase correction of $-2\\pi 0.0\\varphi_{2}\\varphi_{3}= -2\\pi \\left(\\frac{\\varphi_2}{4}+\\frac{\\varphi_3}{8}\\right)=-\\frac{\\varphi_2\\pi}{2}-\\frac{ \\varphi_3\\pi}{4}$, thus we have to apply 2 conditioned phase corrections, one conditioned by $\\varphi_3$ ($=c_0$) and the other by $\\varphi_2$($=c_1$). To do this we have to apply the following:\n", - "- gate $P(-\\pi/4)$ conditioned by $c_0=1$, that is, by $c=001$ (``c_if`` with value $1$)\n", - "- gate $P(-\\pi/2)$ conditioned by $c_1=1$, that is, the gate is applied when $c=010$ (``c_if`` with values $2$)\n", - "- gate $P(-3\\pi/4)$ conditioned by $c_1=1$ and $c_0=1$ that is, the gate is applied when $c=011$ (``c_if`` with values $3$)\n", - "\n", - "Next, the $CU$ operations: we apply $2^t$ times the $\\text{MCP}(\\pi/4)$ gate and since at the 3rd step $t=m-3=0$, we apply the gate only once." - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "fee5769f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# initialization of qubit q0\n", - "qc.reset(0)\n", - "qc.h(0)\n", - "\n", - "# phase correction\n", - "qc.p(-pi/4, 0).c_if(c, 1)\n", - "\n", - "qc.p(-pi/2, 0).c_if(c, 2)\n", - "qc.p(-3*pi/2, 0).c_if(c, 3)\n", - "\n", - "# c-U operations\n", - "for _ in range(2 ** (m - 3)):\n", - " qc.mcp(pi/4, [0, 1], 2)\n", - "\n", - "# X measurement \n", - "qc.h(0)\n", - "qc.measure(0, 2)\n", - "\n", - "qc.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "id": "f32900a5", - "metadata": {}, - "source": [ - "Now, we execute the circuit with the simulator without noise." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "c6e0a06f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "result = sampler.run(qc).result()\n", - "dist0 = result.quasi_dists[0]\n", - "\n", - "key_new = [str(key/2**m) for key in list(dist0.keys())]\n", - "dist1 = dict(zip(key_new, dist0.values()))\n", - "\n", - "fig, ax = plt.subplots(1,2)\n", - "plot_histogram(dist0, ax=ax[0])\n", - "plot_histogram(dist1, ax=ax[1])\n", - "plt.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "id": "a992b916", - "metadata": {}, - "source": [ - "We have obtained $100\\%$ probability to find $\\varphi=0.125$, that is, $1/8$, as expected." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "7280b7b7", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.0.dev0+1b4fed3
qiskit-aer0.11.1
qiskit-nature0.5.0
System information
Python version3.9.13
Python compilerClang 12.0.0
Python buildmain, Oct 13 2022 16:12:30
OSDarwin
CPUs4
Memory (Gb)32.0
Fri Dec 09 16:18:07 2022 CET
" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "

This code is a part of Qiskit

© Copyright IBM 2017, 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.

" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import qiskit.tools.jupyter\n", - "%qiskit_version_table\n", - "%qiskit_copyright" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/docs/tutorials/10_pvqd.ipynb b/docs/tutorials/10_pvqd.ipynb index c44b5ca0..464cd841 100644 --- a/docs/tutorials/10_pvqd.ipynb +++ b/docs/tutorials/10_pvqd.ipynb @@ -6,7 +6,7 @@ "source": [ "# Projected Variational Quantum Dynamics\n", "\n", - "The projected Variational Quantum Dynamics (p-VQD) algorithm is a quantum algorithm for real time evolution. It's a variational algorithm that projects the state at time $t + \\Delta_t$, as calculated with Trotterization, onto a parameterized quantum circuit. \n", + "The projected Variational Quantum Dynamics (p-VQD) algorithm is a quantum algorithm for real time evolution. It's a variational algorithm that projects the state at time $t + \\Delta_t$, as calculated with Trotterization, onto a parameterized quantum circuit.\n", "\n", "For a quantum state $|\\phi(\\theta)\\rangle = U(\\theta)|0\\rangle$ constructed by a parameterized quantum circuit $U(\\theta)$ and a Hamiltonian $H$, the update rule can be written as\n", "\n", @@ -14,9 +14,9 @@ "\\theta_{n+1} = \\theta_n + \\arg\\min_{\\delta\\theta} 1 - |\\langle\\phi(\\theta_n + \\delta\\theta)|e^{-i\\Delta_t H}|\\phi(\\theta_n)\\rangle|^2,\n", "$$\n", "\n", - "where $e^{-i\\Delta_t H}$ is calculated with a Trotter expansion (using e.g. the [`PauliEvolutionGate`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.PauliEvolutionGate.html) in Qiskit!).\n", + "where $e^{-i\\Delta_t H}$ is calculated with a Trotter expansion (using e.g. the [PauliEvolutionGate](https://qiskit.org/documentation/stubs/qiskit.circuit.library.PauliEvolutionGate.html) in Qiskit!).\n", "\n", - "The following tutorial explores the p-VQD algorithm in Qiskit, which is implemented available as `qiskit.algorithms.time_evolvers.PVQD`. For details on the algorithm, see the original paper: [Barison et al. Quantum 5, 512 (2021)](https://quantum-journal.org/papers/q-2021-07-28-512/#)." + "The following tutorial explores the p-VQD algorithm, which is available as the [PVQD](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.PVQD.html) class. For details on the algorithm, see the original paper: [Barison et al. Quantum 5, 512 (2021)](https://quantum-journal.org/papers/q-2021-07-28-512/#)." ] }, { @@ -61,7 +61,7 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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\n", "text/plain": [ "
" ] @@ -121,7 +121,7 @@ "outputs": [], "source": [ "from qiskit.primitives import Sampler, Estimator\n", - "from qiskit.algorithms.state_fidelities import ComputeUncompute\n", + "from qiskit_algorithms.state_fidelities import ComputeUncompute\n", "\n", "# the fidelity is used to evaluate the objective: the overlap of the variational form and the trotter step\n", "sampler = Sampler()\n", @@ -144,7 +144,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit.algorithms.optimizers import L_BFGS_B\n", + "from qiskit_algorithms.optimizers import L_BFGS_B\n", "\n", "bfgs = L_BFGS_B()" ] @@ -162,14 +162,14 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit.algorithms.time_evolvers.pvqd import PVQD\n", + "from qiskit_algorithms import PVQD\n", "\n", "pvqd = PVQD(\n", " fidelity,\n", - " ansatz, \n", - " initial_parameters, \n", + " ansatz,\n", + " initial_parameters,\n", " estimator=estimator,\n", - " num_timesteps=100, \n", + " num_timesteps=100,\n", " optimizer=bfgs\n", ")" ] @@ -187,7 +187,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit.algorithms.time_evolvers.time_evolution_problem import TimeEvolutionProblem\n", + "from qiskit_algorithms import TimeEvolutionProblem\n", "\n", "problem = TimeEvolutionProblem(hamiltonian, time=final_time, aux_operators=[hamiltonian, observable])" ] @@ -203,9 +203,424 @@ "cell_type": "code", "execution_count": 8, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{ 'aux_ops_evaluated': array([ 0.10877508, -0.8256544 ]),\n", + " 'estimated_error': 2.4781666023709903e-06,\n", + " 'evolved_state': ,\n", + " 'fidelities': [ 1.0,\n", + " 0.999999994810878,\n", + " 0.9999999646960552,\n", + " 0.9999999987682254,\n", + " 0.99999999993364,\n", + " 0.999999997930724,\n", + " 0.99999999278486,\n", + " 0.9999999992656516,\n", + " 0.9999999984720038,\n", + " 0.9999999973540102,\n", + " 0.9999999959238208,\n", + " 0.9999999941952744,\n", + " 0.999999999206662,\n", + " 0.9999999989950918,\n", + " 0.9999999987351132,\n", + " 0.9999999984180052,\n", + " 0.9999999980339588,\n", + " 0.9999999975720132,\n", + " 0.9999999970199948,\n", + " 0.9999999963644612,\n", + " 0.9999999955906393,\n", + " 0.9999999946823838,\n", + " 0.9999999936221278,\n", + " 0.9999999926028444,\n", + " 0.9999999916365137,\n", + " 0.9999999918514156,\n", + " 0.999999990630723,\n", + " 0.9999999892521608,\n", + " 0.9999999876977836,\n", + " 0.9999999859480942,\n", + " 0.999999983982037,\n", + " 0.9999999829668812,\n", + " 0.9999999808510363,\n", + " 0.9999999785107602,\n", + " 0.9999999759237286,\n", + " 0.9999999735723598,\n", + " 0.9999999709249182,\n", + " 0.9999999682197572,\n", + " 0.9999999656644099,\n", + " 0.9999999622686514,\n", + " 0.9999999587994122,\n", + " 0.9999999558194353,\n", + " 0.9999999519966122,\n", + " 0.999999947873755,\n", + " 0.9999999440923933,\n", + " 0.9999999396397626,\n", + " 0.9999999348559656,\n", + " 0.9999999308500046,\n", + " 0.9999999259087498,\n", + " 0.9999999206337274,\n", + " 0.9999999159455149,\n", + " 0.9999999104023148,\n", + " 0.9999999060537212,\n", + " 0.9999999004854963,\n", + " 0.9999998946027308,\n", + " 0.9999998896454084,\n", + " 0.9999998837664604,\n", + " 0.9999998775898982,\n", + " 0.9999999353908055,\n", + " 0.9999999351606516,\n", + " 0.9999999702806323,\n", + " 0.9999999711201872,\n", + " 0.9999999717248588,\n", + " 0.9999999727545033,\n", + " 0.999999973714949,\n", + " 0.9999999747621942,\n", + " 0.9999999758868302,\n", + " 0.9999999770714048,\n", + " 0.9999999783325844,\n", + " 0.9999999796305166,\n", + " 0.9999999809907598,\n", + " 0.9999999823721348,\n", + " 0.9999999837950628,\n", + " 0.9999999850420018,\n", + " 0.9999999865550524,\n", + " 0.9999999878041282,\n", + " 0.9999999893175434,\n", + " 0.9999999907055506,\n", + " 0.9999999918887482,\n", + " 0.9999999932430698,\n", + " 0.9999999943095734,\n", + " 0.9999999954404026,\n", + " 0.9999999962793982,\n", + " 0.9999999971438318,\n", + " 0.999999997670787,\n", + " 0.9999999981562422,\n", + " 0.9999999982633252,\n", + " 0.9999999982553294,\n", + " 0.9999999978178036,\n", + " 0.9999999972000864,\n", + " 0.9999999960836614,\n", + " 0.9999999947055718,\n", + " 0.9999999927546424,\n", + " 0.9999999904963562,\n", + " 0.9999999875510924,\n", + " 0.9999999839950175,\n", + " 0.9999999801833134,\n", + " 0.9999999753969174,\n", + " 0.999999999876449,\n", + " 0.9999999996875087,\n", + " 0.9999999991778888],\n", + " 'observables': [ array([0.1, 2. ]),\n", + " array([0.10016308, 1.99960002]),\n", + " array([0.10065219, 1.99840036]),\n", + " array([0.10070955, 1.99640142]),\n", + " array([0.10065444, 1.993604 ]),\n", + " array([0.10048727, 1.99000921]),\n", + " array([0.10020862, 1.98561846]),\n", + " array([0.10010511, 1.98043052]),\n", + " array([0.09996625, 1.97444971]),\n", + " array([0.09979275, 1.96767845]),\n", + " array([0.09958544, 1.96011951]),\n", + " array([0.09934525, 1.95177596]),\n", + " 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array([0.83262394, 0.90528391, 0.11107046, 0.80905219, 0.73599417]),\n", + " array([0.84772926, 0.92110047, 0.11147618, 0.81397321, 0.74018839]),\n", + " array([0.86283458, 0.93691704, 0.11188189, 0.81889423, 0.74438262]),\n", + " array([0.87793911, 0.95272736, 0.11231382, 0.82380601, 0.74857453]),\n", + " array([0.89304364, 0.96853767, 0.11274575, 0.82871778, 0.75276644]),\n", + " array([0.90815653, 0.98434911, 0.11320226, 0.83363198, 0.75696584]),\n", + " array([0.92326942, 1.00016055, 0.11365877, 0.83854617, 0.76116525]),\n", + " array([0.93837987, 1.01596357, 0.11414082, 0.84345465, 0.76536605]),\n", + " array([0.95349031, 1.03176658, 0.11462287, 0.84836312, 0.76956686]),\n", + " array([0.9686059 , 1.04756715, 0.11512802, 0.85327691, 0.77377851]),\n", + " array([0.9837215 , 1.06336771, 0.11563318, 0.8581907 , 0.77799016]),\n", + " array([0.9988303 , 1.07915453, 0.11616402, 0.86310239, 0.78220794]),\n", + " array([1.0139391 , 1.09494135, 0.11669486, 0.86801407, 0.78642572]),\n", + " array([1.0290479 , 1.11072817, 0.11722571, 0.87292576, 0.7906435 ]),\n", + " array([1.04415875, 1.12650804, 0.11778728, 0.87785145, 0.79488104]),\n", + " array([1.0592696 , 1.14228792, 0.11834886, 0.88277715, 0.79911859]),\n", + " array([1.0726423 , 1.15495485, 0.11897834, 0.88944686, 0.80646734]),\n", + " array([1.08601501, 1.16762177, 0.11960783, 0.89611657, 0.81381609]),\n", + " array([1.09938771, 1.1802887 , 0.12023731, 0.90278629, 0.82116484])],\n", + " 'times': [ 0.0,\n", + " 0.01,\n", + " 0.02,\n", + " 0.03,\n", + " 0.04,\n", + " 0.05,\n", + " 0.06,\n", + " 0.07,\n", + " 0.08,\n", + " 0.09,\n", + " 0.1,\n", + " 0.11,\n", + " 0.12,\n", + " 0.13,\n", + " 0.14,\n", + " 0.15,\n", + " 0.16,\n", + " 0.17,\n", + " 0.18,\n", + " 0.19,\n", + " 0.2,\n", + " 0.21,\n", + " 0.22,\n", + " 0.23,\n", + " 0.24,\n", + " 0.25,\n", + " 0.26,\n", + " 0.27,\n", + " 0.28,\n", + " 0.29,\n", + " 0.3,\n", + " 0.31,\n", + " 0.32,\n", + " 0.33,\n", + " 0.34,\n", + " 0.35000000000000003,\n", + " 0.36,\n", + " 0.37,\n", + " 0.38,\n", + " 0.39,\n", + " 0.4,\n", + " 0.41000000000000003,\n", + " 0.42,\n", + " 0.43,\n", + " 0.44,\n", + " 0.45,\n", + " 0.46,\n", + " 0.47000000000000003,\n", + " 0.48,\n", + " 0.49,\n", + " 0.5,\n", + " 0.51,\n", + " 0.52,\n", + " 0.53,\n", + " 0.54,\n", + " 0.55,\n", + " 0.56,\n", + " 0.5700000000000001,\n", + " 0.58,\n", + " 0.59,\n", + " 0.6,\n", + " 0.61,\n", + " 0.62,\n", + " 0.63,\n", + " 0.64,\n", + " 0.65,\n", + " 0.66,\n", + " 0.67,\n", + " 0.68,\n", + " 0.6900000000000001,\n", + " 0.7000000000000001,\n", + " 0.71,\n", + " 0.72,\n", + " 0.73,\n", + " 0.74,\n", + " 0.75,\n", + " 0.76,\n", + " 0.77,\n", + " 0.78,\n", + " 0.79,\n", + " 0.8,\n", + " 0.81,\n", + " 0.8200000000000001,\n", + " 0.8300000000000001,\n", + " 0.84,\n", + " 0.85,\n", + " 0.86,\n", + " 0.87,\n", + " 0.88,\n", + " 0.89,\n", + " 0.9,\n", + " 0.91,\n", + " 0.92,\n", + " 0.93,\n", + " 0.9400000000000001,\n", + " 0.9500000000000001,\n", + " 0.96,\n", + " 0.97,\n", + " 0.98,\n", + " 0.99,\n", + " 1.0]}\n" + ] + } + ], "source": [ - "result = pvqd.evolve(problem)" + "result = pvqd.evolve(problem)\n", + "print(result)" ] }, { @@ -246,7 +661,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -287,7 +702,7 @@ " \"\"\"Get the exact values for energy and the observable.\"\"\"\n", " O = observable.to_matrix()\n", " H = hamiltonian.to_matrix()\n", - " \n", + "\n", " energ, magn = [], [] # list of energies and magnetizations evaluated at timesteps timestep\n", " times = [] # list of timepoints at which energy/obs are evaluated\n", " time = 0\n", @@ -325,7 +740,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 12, @@ -334,7 +749,7 @@ }, { "data": { - "image/png": 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dSb47a3Nq+gJatGhJvXwlOPTyMOKi//Ta1RfGmMwnYK6qMv4Vli8Pdbo/DUDS2Xh6DnqLuBXrOD52Bkc+nUq7xH94utkjPP7GK2S3mw+NMclY4TAEheag9ZsDADh/7CTbxn9L4qsvcnLafHbOXkvibZX57bp8PNqvDznDczuc1hjjNDtVZf4lW95wynVvw4rDe+kUPZ+8PR5n5m9LafPOIObe1JjDg0YQv3WX0zGNMQ6ywmFSFXxNJAVe6kDPbcuZ+/4n3FK/Hsc+mcJzN9ehfpHSHJ+1EE1MdDqmMcbP7FSVuaLsISHc3aszAIn7D3Ftl16cXrKUQ+0GcKxEYZZGleKOPl0pWv46h5Mak3Fd6Fb9gpYtW9K3b1+vbDs6Opq9e/fSpEkTr2zPCofxSPaiBen97Xg0MZEz85axa8Qknvr8Q1pM/ob3nu5KnmceJUeFa5yOaUyGk1qXI94QHR3NqlWrvFY47FSVuSqSPTu5mtSjwqwR/P7Dj/R6rA2nvv2Jxbc+Qr0ipVk7/hu7pNeYdDp+/Djly5dny5YtgOsO8tGjRwPQuXNnoqKiqFSpEgMGDLj4mpUrV3LrrbdSuXJlatasyfHjx+nfv//Fu8inTJmS/mCqmukf1atXV+N7iUeO69QOz2uZkFz6W/5bdFe9J3XrqEkaf/qM09GMuaxNmzb9a7p+/fr6xRdfqKrquXPntH79+vrll1+qqurp06e1fv36OnnyZFVVPXbsmNavX1+nTZumqqqxsbFav359nTlzpqqq7tu3L00ZgoKCtHLlyhcfF7Y/b948rVWrlk6aNEnvvvvui+sfPnxYVVUTExO1fv36unbtWo2Pj9eyZcvq77//rqqqx48f14SEBP3iiy+0a9euad5/VVVglabymWqnqozXZMsXwSOj3uPhYYM5NX0Bxz6eRIeuXYjt0Zlfho4i4okHCAq1HnuNSUlqp6oaNmzI119/TdeuXVm7du3F+VOnTmXUqFEkJiayb98+Nm3ahIhQrFgxatSoAUBERIRPslrhMF4XlDMHEa2aEN6iMd3e/IBdX8/h8MvDODpkPN9XLcbj775KvhLFnI5pTKoWL1588XlwcPC/psPCwv41nSdPnn9NFyxY8F/TRYsWTVeWpKQkNm/eTGhoKEeOHCEyMpLt27fz3nvvsXLlSvLly0fbtm2Ji4tLdYwOb7M2DuMzEhREs5d70yN6AcW/G87fkXnoPmk0w6vexdH3x3H+xCmnIxoT8IYMGUKFChWYNGkS7dq1IyEhgRMnTpArVy7y5MnDgQMHmDNnDgA33HADe/fuZeXKlQCcPHmSxMREwsPDOXnypNcyWeEwfhF6axUazf+KZRO+4Yk77+HIW58xrnwDXmj0IKcPHnI6njGOuzAC4IVH3759+euvv/jss894//33qVu3LvXq1eP111+ncuXKVK1alUqVKtGuXTvq1KkDQEhICFOmTKFbt25UrlyZhg0bEhcXx+23386mTZu81jhuveMaR8Sv3ULv1m354c+1/Fi2PgWfbU1Eu2ZkC8/ldDSTBVnvuNY7rskAclQuz/ANy1n5y6/kjrqRg6+NpGaRkox+ugcaf87peMaYy7DCYRxVoHY1ik16l5wTBpMrd26Sps5nV63HOPzlTBLi452OZ4xJgRUOExBK312fJQd38fjMcWQrlJ9hnXtSKX8Rdn0zx24kNH6RVf+dXc1+W+EwASVXgxqU+PFTbur1NFG5CnCu02D2PtidPYuXOx3NZGI5c+bk8OHDWa54qCqHDx8mp4fDR1vjuAlYmpDIiS9nsf2tkdyxdSFda95O/6/HE1wyfdfFG3OphIQEYmJiiIuLczqK3+XMmZPIyEiCg4P/Nd/GHLfCkaGd3H+QVx9rxx0bY7khODdB7ZqSr3ML8hQr4nQ0YzItu6rKZGjhRQvz3sLvabRmJrkeaMCr775N+VJl2DPmGzQpyel4xmQ5VjhMhpG9RBGKfPIK7Ua+T8drqxL3wofsadyJrbMXOB3NmCwloAqHiIwRkYMisiGV5Q1E5LiIRLsf/f2d0TivbpuWvLp5KYVHvMKW7f9Q8d6GDLmjGYkHjzgdzZgsIaAKBzAWaHyFdX5R1SruxyA/ZDIBSEQIb96IGr9Monv9e7h140F213qM7UO+4NzZs07HMyZTC6jCoapLAPvaaNIsomhh3lv8A1WXTiJH9Yp06Nub2kVKcXp5tNPRjMm0AqpwpFFtEVkrInNEpFJqK4lIRxFZJSKrYmNj/ZnPOCDkulIUm/o+7Xv3pEWeUux/oBsHn3uL47v2OB3NmEwnoxWONUBpVa0MDAdmpLaiqo5S1ShVjSpUqJC/8hkHiQitBvej9+ZfyPtsK+aNn0SZsmVZPPjDLHdjlzG+lKEKh6qeUNVT7uezgWARKehwLBNggnKHUWBAF24a/y53FC1DoSFT2NusB2e3bHc6mjGZQoYqHCJSVNzDW4lITVz5DzubygSqyvc14pvdf1Lyg76cWb+F2jdV4c0HW6PnEpyOZkyGFlCFQ0QmAcuB8iISIyLtRaSTiHRyr9Ic2CAia4FhQEu1cxDmMiQoiIgnH6DAvE+5tlQpIhauIeaup4lbtdHpaMZkWNbliMlSTs9bSmyfD/h6+wa2XF+EYT9+R1iBfE7HMibgWJcjxrjlalSHUku/ZN+NpVi/di0HGnXkzBL7UmGMJ6xwmCwnKHcYHyybz/wFP5Ete3b+ataNZ2s04GjMXqejGZMhWOEwWVZEvRpELh7LuoY3MWrVEn6+43HOLF7pdCxjAp4VDpOlBYXm4MnJo9j8/XyqFSjGvkd6Memh9hzbu9/paMYELCscxgDX3nsnkQvHcK7NvTw1fSzPVanL2aV/OB3LmIBkhcMYt6DQHFR4ry9zR43luRI3svfB7mzp9QanDh91OpoxAcUKhzGXaNDhCW7+dSIR7R6i00fvUbv0dZxZs8npWMYEDCscxqQgKFcohd7uyfNvDKJtvrLsu7cLRz8YT1KC3XVuTJoKh4jkE5EnRWS6iGwUke9FpIOI2KDPJlO7r/ezPLd+Ebnvb8B3r77DLYVLsut3a/swWdsVC4eIfAt8CxQGXlDVSkAXICfwpYgs9mlCYxyWLW84RUYNJEen5ujZeE41782JSbOtx12TZV2xyxERyauqx652eSCwLkeMt5zbvZ/YZwdzcukaRkQG8cqMCRQsU8rpWMZ4Xbq6HLlSUQj0omGMN4WULErxb4fyT6sGjFi7lG9vb8HZZdFOxzLGrzxuHBeRhiIyWkSquKc7ej2VMQFMsmXj3uGDWf/9PBoXKsPeZj1Y0mMgCXFxTkczxi+u5qqqLkAf4HERuQOo4tVExmQQ5e+9i8iFn3PuvjrcO/x1Ot5Qg4SYA07HMsbnrqZwxKrqMVXtDTQCang5kzEZRlDuMCp8/gYf9ezLU4n5iGnQlhOzFjsdyxifuprC8cOFJ6raFxjvvTjGZExt3n+d2r9MIrhsJO0faUm7ardx/qydujKZU1ouxz0kIvdemFbV75IvV9XhvghmTEYTXLYExWZ9RNFqNxL65y72NunCuX92Ox3LGK9LyxFHAjBCRJ6+dIF7qFdjjFu2nDkYvuwn3p4+icQ9B/ip7qOM7tHX6VjGeFVaCsc+oB7QW0QGXrKsvNcTGZMJ5L67DiUXjWF8tmP0+2gI2559jaS4eKdjGeMVaWrjUNUdQB2gkYh8JiLWx5UxV5C9RBG+/OsPZj37MjplHjGNO7FjmQ0UZTK+tBQAAVDVw8AduLoemSkiYReWGWNSFhyak5of9qfohLcZv2klN95Wm1WfjHM6ljHpkpbCcbFHN1WNAx4E9gCLgQifpDImk8nV6FYe+3487creTJ7+ozn0ynA0IdHpWMZclbR0OdLukukkVX0G12W5ZX0VzJjM5pqa1fhw82/k69CcHZ9M4P5S5dm2co3TsYzx2FW3Vajqq1jhMMYjEhJMwTef41DPR1l+cDfrHunBmV9WOx3LGI+kq5FbVXeKyAveCmNMVtG4Xy+2ro6mWonS7Gveix97DuT8+fNOxzImTa6mk8OpyR5fA/+5v8MYc2X5qlQk8sdR7Lr1BpoMfZXXbmlE0snTTscy5oqu5ojjhKo+6n48AvzkrTAiMkZEDorIhlSWi4gME5GtIrJORKp5672NcUJQ7jDqTxvBR0925qFd54hp2IH4P7c5HcuYy/K4yxFg8CWrvOzFPGOBxpdZfg9Qzv3oCIzw4nsb44igoCA6j/uEcjOGc+74SRpXvYVxffo7HcuYVHnc5Yiqbr+wQEQmqeoRb4VR1SXA5bbXFBivLiuAvCJSzFvvb4yTQm+tQsS09zkdmp3YkVM4PGgkau0eJgBltC5HSgDJe42Lcc/7DxHpKCKrRGRVbGysX8IZk16FK17Psj3badOpA8eGT2DmXa3Z/9c/Tscy5l8yWpcjKd2pnuKg6ao6SlWjVDWqUKFCPo5ljPdkD81JoXd7E/7Wc3RYMp0natYlfuNWp2MZc1FG63IkBiiZbDoS2OvnDMb4ReH2DzN97Hj6F7mRPU06c3LGQqcjGQNkvC5HZgJPuq+uqgUcV9V9fs5gjN/UeaIFtX+eSEil6+jc6nG61W1EUqJ1VWKcFVBdjrjH91gOlBeRGBFpLyKdRKSTe5XZwDZgKzAa1/jnxmRq2YsWpNi0IYSUL0P86k0cePIlzp845XQsk4WJaopNBP+/gkiQqialsqw0sDu15YEiKipKV61a5XQMY9JFVTn+xXQOvzyMmKIR5H2rB5XvvtPpWCaTEpHVqhqV0rLsaXj9fBE5BMwAflDVE+72jcZAM+BGoKq3whpjUiYi5G33EDnKl6V1w7vYf98C1s2eR0TDOk5HM1lMWk5V3Qm8CpQBfhCRFcAC4GZgiKpa0TDGj0LrVGXiwh8ZdlMDYh9/iWMjp5CUFNAH/SaTueKpqv+8QCSnu5E8w7BTVSYzSjp1hoPPDuazb6awNjKcL39fQs6IcKdjmUzicqeqPL4fI6MVDWMyq6DcYRQZ8xrn6lbm8LadHGzZh8TYo07HMlmAjR1uTAYmQUEMmjON6RMnk7j+bzbf9RQrp81yOpbJ5KxwGJMJ5GneiOKzPub1XX9w5yMPEfP1HKcjmUzMCocxmUTOKjfwwZI5fHBTA+K7vsnRjybiaRumMWmR5sZxEckBPIzr6qqLl/Gq6iCfJPMiaxw3WUnSmTgOdnuDRdNmMLN4MGNWLCbUGs2Nh7zVOP4drm7NE4HTyR7GmAASFJaTIqMHsv22iqz8azPbW/Ti/JHjTscymYgnRxwbVPVGH+fxCTviMFnVwYnfc+p/Q5BiBYl/uxs33HGb05FMBuGtI45lInKTlzIZY/yg8GP3UXz6hwzbEU2Nhrez5ZsfnI5kMoG0dDlywW1AWxHZDsTj6lJdVfVmnyQzxnhFzho30m3WBHK16kT2bu9yIh4iWt975RcakwpPTlWVTmm+qu70aiIfsFNVxsD5E6c40L4/fy/4hVk3F+at+TPIHhzsdCwToLxyqspdIPIC97sfeTNC0TDGuGSLyE2xSe+w6OYijF7yI3+06knS2XinY5kMKM2FQ0R6ABNwjQBYGPhKRLr5Kpgxxvske3YGLJrF8sHDyL9kHXubdefY9l1OxzIZjCeN4+2BW1S1v6r2B2oBHXwTyxjjKyJCxRe7UOSL15m88lcqlb+BLQt+cTqWyUA8KRwCnE82fR7/jzlujPGS3PfWo+7Hr3FLWAGk4+uc/XWN05FMBuFJ4fgC+E1EBorIQGAF8LlPUhlj/OKWlg8xZd3v5CxWmL+b9+DLni87HclkAJ40jn8AtAOOAEeBp1R1qI9yGWP8JLhUMUr88AkTCpyn7dA3WNHnDevjylyWJ/dxoKqrgdU+ymKMcUi2POG8vnIBtR/vTqGxc4iNg0Lv90FC7HJd819XPOIQkV/dP0+KyIlkj5MicsL3EY0x/hAcFkrTaaPI90I7lnw5hdtLXkfsDrviyvxXWsYcv839M1xVI5I9wlU1wvcRjTH+IiLk7/0U8e0fYO+RQ+xp2YfEPQecjmUCjCf3cbydlnnGmIyv9fuvserHBeQ5eJxddz/Dxu/nOx3JBBBPrqpqmMK8e7wVxBgTWCLuqEXx7z9m1OF/qPFAY9Z9+Y3TkUyAuGLjuIh0BroA14jIumSLwoFlvgpmjHFejorX0u3HyWRr1oawPsM5kT2MiFZNnI5lHHbFTg5FJA+QD3gT6Jts0UlVPeLDbF5jnRwakz5JJ0+z/6l+bF+4lB9rl2bAzMlky5bN6VjGh9LVyaGqHlfVHaraCjgBFAFKAzeKSD0vB20sIltEZKuI9E1heQMROS4i0e5Hf2++vzEmZUHhuSg28R1mX5+XD+ZMZ02Hl9DERKdjGYd40jj+NLAE+BF41f1zoLeCiEg24GNc7SYVgVYiUjGFVX9R1SruR8CPd25MZiEhwby2bC4/9xpE/lnL2P/kS5w7ftLpWMYBnjSO9wBqADtV9XagKhDrxSw1ga2quk1VzwGTcY1xbowJEEFBQVR/7yUKvtebqT/MolpkWfZs3OJ0LONnnhSOOFWNAxCRHKr6J1Dei1lKALuTTce4512qtoisFZE5IlIptY2JSEcRWSUiq2JjvVnfjDF52jSl7AsdKZwIp57sR8K2GKcjGT/ypHDEiEheYAYwX0S+A/Z6MUtKPe1e2nK/BiitqpWB4e4sKVLVUaoapapRhQoV8l5KYwwAD7zUk9m//kzI6bNsvacjyyZ87XQk4yeedHLYTFWPqepA4BVcPeN681RSDFAy2XQklxQmVT2hqqfcz2cDwSJS0IsZjDEeyFm9EiV++IT3j23lzida8s/kWU5HMn7gSeP4AhFpAqCqP6vqTFyN2d6yEignImVFJARoCcy8JENRERH385q48h/2YgZjjIdCri3F4J9n817FevDc+5yY+IPTkYyPeXKqqizwgogMSDYvxWt8r4aqJgLP4rpaazMwVVU3ikgnEenkXq05sEFE1gLDgJZq/T8b47giN1xH5xU/EFq3Gou69uOFRg+SlJTkdCzjI1e8AfDiiiJrcF35NAzXKaXHgUWqWs138bzDbgA0xj/0XAI9at3JtLW/s7DLS1w/9GXEbhTMkNJ1A2Dy7ahqoqp2AaYBvwKFvRHQGJM5SEgwQ1cuYmHvQWSfPJ/97fpz5thxp2MZL/OkcIy88ERVxwJtgXlezmOMyeCCsmWj/Nv/o8Br3Xjnm6+4tcz1HNvtzQswjdM8uarq00umV6tqO+9HMsZkBnk7PUqt7u2plJCdE4/1JXGf3U+VWdgIgMYYn2nxZn9Gz51JYswBou9qy6qZs52OZLzARgA0xvhUWN3qlPhuOC/tWkOThx7i6C92oUpGZyMAGmN8LsfN1/PpvFl8eN2tHG3dl9PzljodyaSDjQBojPGLsrWjeOSXaYRcX4YvH32G99p2uvKLTEBKSxtHZxFZD5QXkXXJHtuB9b6PaIzJLLIXykfxGcOYE57AVxMmcvCDsdg9vBnPFYeOBSYCc8jAIwAaYwJHUO4wvtkSzfYur3Lyzc9JjD1CoVefJTgkxOloJo3SPAIg0BqoC7RR1Z1Abnd/UcYY45HgsFDKjXmDiKcfpvOQt2havjLn4+KdjmXSyJM2jo+B2kAr9/RJvNvJoTEmC5GgIAq+0YM6991DpYNnOfDEiySdOuN0LJMGnhSOW1S1KxAHoKpHATu2NMZcNRHhf9+M45VRH3N2yWp+btSG3Rs2OR3LXEFa2jguSHCPC64AIlIIsO4vjTHpFtH6Xsibm7sfbEKe2otZvnEdIaWKOR3LpMKTI45hwHSgiIgMxtXJ4Rs+SWWMyXIi7q3PuFGf8Vqe8uy9twvxm7c5HcmkwpO+qiYA/8NVLPYCD6qqjRVpjPGaOk+14s5540CVN+rey/fDPr3yi4zfeXLneA6gGpAHKAA8IiL9fRXMGJM15ah4LQWnD+Wbs/v57MWBnJ63zOlI5hKenKr6DtcY44nA6WQPY4zxqtzlyrBkXTTv39KY/U++xOEJNpZ5IPGkcTxSVRv7LIkxxiRT4NrS5Jv5Mdtb96FR29Y0ntyYwbOmOh3L4NkRxzIRuclnSYwx5hJBucMoNfFdKl5zHcV/Xs/hQSOsi5IA4EnhuA1YLSJb3H1VrReRdb4KZowxAMG5whi/aSWPPtOeY8Mn8lOrbsSdtrPkTvLkVJX1hGuMcYRky0bBd57nSGh2mr3em0f+WM7n0csICs3hdLQsKc2Fw90/lTHGOEJEKD/oOT4+uJvy3yxl36PPU/SrN8mWJ9zpaFlOmguHiPRKYfZxYLWqRnstkTHGXEabke9z8u6fONDldXpXrkvXr8dwXY1qTsfKUjxp44gCOgEl3I+OQANgtIj8z/vRjDEmZeHN7iLhg+f4YvdGPm/2FAnb9zgdKUvxpHAUAKqp6vOq+jyuQlIIqAe09UE2Y4xJVYVWD7Jq1lw6hEWy594unIn+0+lIWYYnhaMUcC7ZdAJQWlXPAtaRvjHG765rcieRP3xCrCRQtWYNpr833OlIWYInhWMisEJEBojIAGApMElEcgFe6QdZRBq7L/fdKiJ9U1guIjLMvXydiNiJTWOyuJBypYmc9C4FQnMh74zn9JxfnI6U6XnSyeFrQAfgGK5G8U6qOkhVT6tq6/QGcXfZ/jGuy34rAq1EpOIlq90DlHM/OgIj0vu+xpiMr9jNlViy7U+iqlVjf9t+LHvzI6cjZWqeHHEAbAOWA2uAMBGp58UsNYGtqrpNVc8Bk3H1jZVcU2C8uqwA8oqIddpvjCF7gbwU/2YI6ysW5baXujHiiU5OR8q0POkd92lgCfAj8Kr750AvZikB7E42HeOe5+k6AIhIRxFZJSKrYmNjvRjTGBOognKHcd/scQys1Yh6c9ZxaMDHaJKNN+dtnhxx9ABqADtV9XagKuDNT2RJYd6lndKkZR3XTNVRqhqlqlGFChVKdzhjTMaQPTQnryydQ+H2j3Dw44n0rd2QMydOOh0rU/GkcMSpahy4xuZQ1T+B8l7MEgOUTDYdiWvAKE/XMcZkcRIURMG3nmPDgzV57/eFTG/ajqQzcU7HyjQ8KRwxIpIXmAHMF5Hv8O6H9kqgnIiUFZEQoCUw85J1ZgJPuq+uqgUcV9V9XsxgjMkkRIRHPxvCyjc/otbGA+x79HkSj51wOlam4MlVVc1U9ZiqDgReAT7jv43XV01VE4FncbWdbAamqupGEekkIhdauWbjaqDfCowGunjr/Y0xmVO1vl0pMmogf/z2O1VLlmXLipVOR8rwJK1924tIFPAyUBpXH1cCqKre7Lt43hEVFaWrVq1yOoYxxkG/jBxH5+7dGF2+HlHfjST4mkinIwU0EVmtqlEpLfPkVNUE4AvgYeB+4D73T2OMCXh1O7Vh5YoVFD0HMfd2ZuOseU5HyrA8KRyxqjpTVber6s4LD58lM8YYLwutVpES33/MxFN7qPbAPfw2dorTkTIkTwZyGiAinwELSNY3lap+6/VUxhjjIyHlSvP0nIkcu7cl+V8ayamCRcl9X32nY2UonhxxPAVUARrjOkV14XSVMcZkKEVuvIG3opcQWuUGNj/1IkPadraxzD3gyRFHZVW9yWdJjDHGj7Lli6D41x8wrFZDho0bRf3i11B1cG9EUrrP2CTnyRHHihQ6HTTGmAwrKFcob65ayJxHO5Fn9EwOvzyMpPPnnY4V8DwpHLcB0e5uz9eJyHoRWeerYMYY4w/ZcoTQYNJw8nR6lOkfj+Luaypw8shRp2MFNE9OVTX2WQpjjHGQBAVRYNCzxP+zntivJ7Ov3Svk+uodgnKHOR0tIHly5/jOlB6+DGeMMf4iIjw7cRSLxnxFtuXr2dmsO7s3bHY6VkDydDwOY4zJ1PI98QBFx75O/+VzqVm9OrEbtjgdKeBY4TDGmEvkuqcu3UcOpUN4aU636kv85m1ORwooVjiMMSYFNR5vzstLvgdVltzdhm8/sOFoL7DCYYwxqchR8VpKzB7BB6d20PV/vTn03QKnIwUEKxzGGHMZwaWKMXnNMibWvJ/jHQdx4qvvnY7kOCscxhhzBXnKlKT+vHGE1qvOu52680zdRpzPwjcKWuEwxpg0CModRrEJb3PoumLs/H0NsS8ORbNo8bDCYYwxaSQhwXyy5hfG9nmF01/M4K82L3I89pDTsfzOkzvHjTEmy5OgIIq+3oOjRQtxX68unJ09nt+2/UVw3gino/mNHXEYY8xVyPfsYzzfuzdtk/Kz/8EeJO7POkceVjiMMeYqPfRGP56e9gUJ2/fwdb3mLJs+y+lIfmGFwxhj0iHszlso+u0QXtv1B90ee5Kzqzc6HcnnrHAYY0w6hVWvxNzFC/mk3G3se+g5Ts1f7nQkn7LCYYwxXlCqVnWqzx9L9msieabpw/Rv0cbpSD5jhcMYY7wke5ECFJ3+IXGF8nBw1kKOfjA+U45lboXDGGO8KCRvBFO3RDOwTQeOvDmatZ37c+bUKadjeZUVDmOM8bJsOXNQ5ON+hHV+lIc+e5+HKlQj6Wy807G8JiAKh4jkF5H5IvK3+2e+VNbb4R7rPFpEVvk7pzHGpJUEBVFsUDcGtO9M+1Nh7Hv4Oc4fOe50LK8IiMIB9AUWqGo5YIF7OjW3q2oVVY3yTzRjjLl6bT59n3vGDSF+3V8Mq9mY32fPczpSugVK4WgKjHM/Hwc86FwUY4zxrtwP3E7er95gyM61DGr1FPFrM/ZwtIFSOIqo6j4A98/CqaynwDwRWS0iHS+3QRHpKCKrRGRVbGysl+MaY4xn8je4hSULFvJO6RrsadqNE/OXOh3pqvmtcIjITyKyIYVHUw82U0dVqwH3AF1FpF5qK6rqKFWNUtWoQoUKpTu/McakV5l6tbh+3mdoqaI0ue/+DHuvh98Kh6repao3pvD4DjggIsUA3D8PprKNve6fB4HpQE1/5TfGGG/IXrQgJaZ/SPFixcg9ezlH3hmT4e71CJRTVTOBC6W3DfDdpSuISC4RCb/wHGgEbPBbQmOM8ZKcBfIx+a9o2rZpw9F3v2BBq26cOHLU6VhpFiiF4y2goYj8DTR0TyMixUVktnudIsCvIrIW+B34QVXnOpLWGGPSKSgkmELDXyK4W0taTB3Fk1Vqk3TytNOx0kQy2iHS1YiKitJVq+y2D2NMYPr2f4Mo8MVsrqlUgWKT3iF7MefbZUVkdWq3PQTKEYcxxmRZD73TnxpTPiRhxx56VqnL3DFfOR3psqxwGGNMAAi74xYiJr/N/OP7+KZnP878HLhnSaxwGGNMgChYqyrL1/1Bvyr12NeyNztGTgrIK66scBhjTADJd/01lPp+BEm1buSuZ9vT8dY7A654WOEwxpgAExSei2unDOHRmnW5ffMhDnZ+DY0/53Ssi6xwGGNMAAoKCWbw0rncM7APp6bNZ3Sdpvy1OtrpWIAVDmOMCVgiQr7nniDXsP/R74+F9GnUlHP/7HY6lhUOY4wJdEVb3c/CKdMYlP8G9tzTiVO/rnE0jxUOY4zJAG5sfh8V542B/BE8cFcjBrR6yrEsVjiMMSaDCC5bgqIzP6JA4UJkm/ULR976zJErrqxwGGNMBhJauABT/l5Lp/ZPc/T9cfz00DMc2BXj1wxWOIwxJoMJyhFCoaEvkPvFp2kzczwtqtcm8eAR/72/397JGGOM14gIRXq1YcI7Q+iXPZI9d3ckftM/fnlvKxzGGJOB3f58Z+rOHYsmnuf5Wxsy9dW3ff6eVjiMMSaDy1G5PMXmjCAuIozrh3/HsRGTfdpoboXDGGMygRyRRRm1eSVF77+Dw/0/Jva5t9FzCT55LyscxhiTSQTlCqXI54PI16sNJyf+wN7mPUk6dcbr75Pd61s0xhjjGAkKIv+LTxN8fWnO/rIayRXq9fewwmGMMZlQ+MMNCX+4oU+2baeqjDHGeMQKhzHGGI9Y4TDGGOMRKxzGGGM8YoXDGGOMR6xwGGOM8YgVDmOMMR6xwmGMMcYj4sToUf4mIrHAzqt8eUHgkBfjZAS2z5lfVttfsH32VGlVLZTSgixRONJDRFapapTTOfzJ9jnzy2r7C7bP3mSnqowxxnjECocxxhiPWOG4slFOB3CA7XPml9X2F2yfvcbaOIwxxnjEjjiMMcZ4xAqHMcYYj1jhAESksYhsEZGtItI3heUiIsPcy9eJSDUncnpTGva5tXtf14nIMhGp7EROb7rSPidbr4aInBeR5v7M5wtp2WcRaSAi0SKyUUR+9ndGb0vDv+08IjJLRNa69/kpJ3J6i4iMEZGDIrIhleXe//xS1Sz9ALIB/wDXACHAWqDiJes0AeYAAtQCfnM6tx/2+VYgn/v5PVlhn5OttxCYDTR3Orcf/s55gU1AKfd0Yadz+2GfXwLedj8vBBwBQpzOno59rgdUAzakstzrn192xAE1ga2quk1VzwGTgaaXrNMUGK8uK4C8IlLM30G96Ir7rKrLVPWoe3IFEOnnjN6Wlr8zQDdgGnDQn+F8JC37/BjwraruAlDVjL7fadlnBcJFRIDcuApHon9jeo+qLsG1D6nx+ueXFQ4oAexONh3jnufpOhmJp/vTHtc3lozsivssIiWAZsBIP+bypbT8na8H8onIYhFZLSJP+i2db6Rlnz8CKgB7gfVAD1VN8k88R3j98yt7uuJkDpLCvEuvUU7LOhlJmvdHRG7HVThu82ki30vLPg8FXlDV864voxleWvY5O1AduBMIBZaLyApV/cvX4XwkLft8NxAN3AFcC8wXkV9U9YSPsznF659fVjhc1bdksulIXN9EPF0nI0nT/ojIzcBnwD2qethP2XwlLfscBUx2F42CQBMRSVTVGX5J6H1p/bd9SFVPA6dFZAlQGciohSMt+/wU8Ja6GgC2ish24Abgd/9E9Duvf37ZqSpYCZQTkbIiEgK0BGZess5M4En31Qm1gOOqus/fQb3oivssIqWAb4EnMvC3z+SuuM+qWlZVy6hqGeAboEsGLhqQtn/b3wF1RSS7iIQBtwCb/ZzTm9Kyz7twHWEhIkWA8sA2v6b0L69/fmX5Iw5VTRSRZ4EfcV2RMUZVN4pIJ/fykbiusGkCbAXO4PrGkmGlcZ/7AwWAT9zfwBM1A/csmsZ9zlTSss+qullE5gLrgCTgM1VN8bLOjCCNf+fXgLEish7XaZwXVDXDdrcuIpOABkBBEYkBBgDB4LvPL+tyxBhjjEfsVJUxxhiPWOEwxhjjESscxhhjPGKFwxhjjEescBhjjPGIFQ5jjDEescJhjDHGI1Y4jEknEckrIl2STS/z0ftEikgLX2zbGE9Y4TAm/fICFwuHqt7qo/e5E9e4C8Y4ygqHMen3FnCtexS9d0XkFICIlBGRP0XkMxHZICITROQuEVkqIn+LSM0LGxCRx0Xkd/c2PhWRbMnfQERuAz4AmrvXKevXPTQmGetyxJh0EpEywPeqeqN7+pSq5nbP3wpUBTbi6oBvLa5u6h8AnlLVB0WkAvAO8JCqJojIJ8AKVR1/yfvMBXpn5L6kTOaQ5Ts5NMbHtqvqegAR2QgsUFV1d7BXxr3OnbjGxFjp7lAylJRHICwPbPF5YmOuwAqHMb4Vn+x5UrLpJP7//58A41T1xdQ2IiIFcHWHneCTlMZ4wNo4jEm/k0B4Ol6/AFfbRWEAEckvIqUvWacsGXvwMJOJWOEwJp3coyMudTeAv3sVr98E9APmicg6YD5Q7JLV/sQ13sIGEfHVVVvGpIk1jhtjjPGIHXEYY4zxiBUOY4wxHrHCYYwxxiNWOIwxxnjECocxxhiPWOEwxhjjESscxhhjPPJ/hVvWqP67XJgAAAAASUVORK5CYII=\n", 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\n", 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" ] @@ -375,7 +790,7 @@ " \\theta_{k+1} = \\theta_{k} - \\eta_k \\nabla\\ell(\\theta_k).\n", "$$\n", "\n", - "Here we're using a learning rate of \n", + "Here we're using a learning rate of\n", "\n", "$$\n", " \\eta_k = 0.1 k^{-0.602}\n", @@ -391,7 +806,7 @@ }, "outputs": [], "source": [ - "from qiskit.algorithms.optimizers import GradientDescent\n", + "from qiskit_algorithms.optimizers import GradientDescent\n", "\n", "maxiter = 80\n", "learning_rate = 0.1 * np.arange(1, maxiter + 1) ** (-0.602)\n", @@ -416,7 +831,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -436,7 +851,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -445,13 +860,13 @@ "Text(0.5, 1.0, 'Energy over time')" ] }, - "execution_count": 26, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -483,8 +898,12 @@ }, { "cell_type": "code", - "execution_count": 27, - "metadata": {}, + "execution_count": 18, + "metadata": { + "tags": [ + "nbsphinx-thumbnail" + ] + }, "outputs": [ { "data": { @@ -492,13 +911,13 @@ "Text(0.5, 1.0, 'Magnetization over time')" ] }, - "execution_count": 27, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -536,7 +955,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.0.dev0+d814ad4
qiskit-aer0.11.1
qiskit-ignis0.7.1
qiskit-ibmq-provider0.19.2
qiskit-nature0.6.0
qiskit-finance0.3.4
qiskit-optimization0.6.0
qiskit-machine-learning0.6.0
System information
Python version3.10.4
Python compilerClang 12.0.0
Python buildmain, Mar 31 2022 03:38:35
OSDarwin
CPUs4
Memory (Gb)32.0
Tue May 09 13:16:11 2023 CEST
" + "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Fri Aug 18 15:40:38 2023 CEST
" ], "text/plain": [ "" @@ -561,11 +980,12 @@ "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table\n", - "%qiskit_copyright" + "%qiskit_copyright\n" ] } ], "metadata": { + "celltoolbar": "Edit Metadata", "kernelspec": { "display_name": "Python 3", "language": "python", @@ -581,9 +1001,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.4" + "version": "3.10.2" } }, "nbformat": 4, "nbformat_minor": 4 -} +} \ No newline at end of file diff --git a/docs/tutorials/11_VarQTE.ipynb b/docs/tutorials/11_VarQTE.ipynb index 790eb07e..2dc2eb9a 100644 --- a/docs/tutorials/11_VarQTE.ipynb +++ b/docs/tutorials/11_VarQTE.ipynb @@ -1,928 +1,958 @@ { - "cells": [ - { - "cell_type": "markdown", - "source": [ - "# Variational Quantum Time Evolution\n", - "This notebook demostrates how to use Qiskit’s implementation of the Variational Quantum Time Evolution (VarQTE) algorithm for computing the time evolving state under a given Hamiltonian. Specifically, it introduces variational quantum imaginary and real time evolution based on McLachlan's variational principle, and shows how this can be leveraged using the `algorithms.time_evolvers.variational` sub-module." - ], - "metadata": { - "id": "lTiEsmieVAf-" - } - }, - { - "cell_type": "markdown", - "metadata": { - "id": "Zw5nQ9h0xVqF" - }, - "source": [ - "## Introduction\n", - "`VarQTE` is a quantum algorithm that simulates the time evolving state under given Hamiltonian ([Yuan et al. Quantum 3, 191](https://quantum-journal.org/papers/q-2019-10-07-191/)). For a quantum closed system's Hamiltonian $H$, the time evolving $\\rho$ density matrix follows the equation below\n", - "\n", - "$$\\frac{d\\rho}{dt}=\\mathcal{L}\\left(\\rho\\right)$$\n", - "\n", - "where $\\mathcal{L}\\left(\\rho\\right)=-i[H,\\rho]$ for real time dynamics and $\\mathcal{L}\\left(\\rho\\right)=-[H,\\rho]$ for imaginary time dynamics. The corresponding state $\\psi[\\theta(t)]$ is parameterized by time dependent $\\theta(t)$. Using McLachlan variational principle, the algorithm updates the parameters by minimizing the distance between the right hand side and left hand side of the equation above. This is called the McLachlan's distance $L$ , and defined as\n", - "\n", - "$$L\\equiv\\left\\Vert \\sum_{i}\\frac{\\partial\\rho\\left[\\theta\\right]}{\\partial\\theta_{i}}\\dot{\\theta}_{i}-\\mathcal{L}\\left(\\rho\\right)\\right\\Vert _{F}$$\n", - "\n", - "where $\\left\\Vert M\\right\\Vert _{F}=\\sqrt{M^{\\dagger}M}$ is the Frobenius norm of the matrix $M$. The equivalent way is to minimize the squared distance\n", - "\n", - "$$\\left\\Vert \\sum_{i}\\frac{\\partial\\rho\\left[\\theta\\right]}{\\partial\\theta_{i}}\\dot{\\theta}_{i}-\\mathcal{L}\\left(\\rho\\right)\\right\\Vert _{F}^{2}=\\sum_{i,j}F_{ij}\\dot{\\theta}_{i}\\dot{\\theta}_{j}-2\\sum_{i}V_{i}\\dot{\\theta}_{i}+\\text{Tr}\\left[\\mathcal{L}^{2}\\left(\\rho\\right)\\right]$$\n", - "\n", - "where\n", - "\n", - "$$F_{ij}=2\\text{Re}\\left[\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}\\frac{\\partial\\left|\\psi\\left[\\theta\\right]\\right\\rangle }{\\partial\\theta_{j}}+\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}\\left|\\psi\\left[\\theta\\right]\\right\\rangle \\left\\langle \\psi\\left[\\theta\\right]\\right|\\frac{\\partial\\left|\\psi\\left[\\theta\\right]\\right\\rangle }{\\partial\\theta_{j}}\\right]$$,\n", - "\n", - "and\n", - "\n", - "$$V_{i}=\\begin{cases}\n", - "2\\text{Im}\\left[\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}H\\left|\\psi\\left[\\theta\\right]\\right\\rangle +\\left\\langle \\psi\\left[\\theta\\right]\\right|\\frac{\\partial\\left|\\psi\\left[\\theta\\right]\\right\\rangle }{\\partial\\theta_{i}}\\left\\langle H\\right\\rangle _{\\theta}\\right] & \\text{Real time}\\\\\n", - "2\\text{Re}\\left[\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}H\\left|\\psi\\left[\\theta\\right]\\right\\rangle \\right] & \\text{Imaginary time}\n", - "\\end{cases}$$.\n", - "\n", - "Minimizing $L^2$ with respect to $\\dot{\\theta}$ can lead to the equation of motion for $\\theta$\n", - "\n", - "$$\\sum_{ij}F_{ij}\\dot{\\theta}_{i}=V_{j}$$\n", - "\n", - "Solving this equation is equivalent to minimizing $L^2$, a variational approach that is more stable in simulation ([Yuan et al. Quantum 3, 191](https://quantum-journal.org/papers/q-2019-10-07-191/)). $F_{i,j}$ and $V_{j}$ can be calculated using a quantum circuit (more details in [Zoufal et al.](https://arxiv.org/abs/2108.00022) and [Yao et al.](https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.030307)), and the classical computer can minimize $L^2$ to get the variational parameters for the next time step.\n", - "In this tutorial, we focus on how to use Qiskit's implementation of the `VarQTE` algorithm.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "source": [ - "## Running VarQTE" - ], - "metadata": { - "id": "caoBgyluhQ3L" - } - }, - { - "cell_type": "markdown", - "source": [ - "In this tutorial, we will use two Qiskit classes that extend `VarQTE`, `VarQITE` ([Variational Quantum Imaginary Time Evolution](https://qiskit.org/documentation/stubs/qiskit.algorithms.VarQITE.html#qiskit.algorithms.VarQITE)) and `VarQRTE` ([Variational Quantum Real Time Evolution](https://qiskit.org/documentation/stubs/qiskit.algorithms.VarQRTE.html#qiskit.algorithms.VarQRTE)) for time evolution.\n", - "We can use a simple Ising model on a spin chain to illustrate this. Let us consider the following Hamiltonian:\n", - "\n", - "$$H = -J\\sum_{i=0}^{L-2}Z_{i}Z_{i+1} - h\\sum_{i=0}^{L-1}X_i$$\n", - "\n", - "where $J$ stands for the interaction energy, and\n", - "$h$ represents an external field which is orthogonal to the transverse direction. $Z_i$ and $X_i$ are the Pauli operators on the spins. Taking $L=2$, $J=0.2$, and $h =1$, the Hamiltonian and the magnetization $\\sum_i Z_i$ can be constructed using `SparsePauliOp` as follows:" - ], - "metadata": { - "id": "WG-18slyLnVM" - } - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "id": "6B0nZEDh0EqI" - }, - "outputs": [], - "source": [ - "from qiskit.quantum_info import SparsePauliOp\n", - "\n", - "hamiltonian = SparsePauliOp(['ZZ', 'IX', 'XI'],\n", - " coeffs=[-0.2 , -1, -1])\n", - "\n", - "magnetization = SparsePauliOp([ 'IZ', 'ZI'], coeffs=[1, 1])" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "Y_9Jskw4m8nF" - }, - "source": [ - "# Imaginary Time Evolution\n", - "\n", - "Imaginary time evolution can be used, for example, to find the ground state or calculate the finite temperature expectation value of the system. Here, we will use the `VarQITE` class from `algorithms.time_evolvers.variational` to compute a ground state energy. Firstly, we need to choose an ansatz. We can use `EfficientSU2` to easily construct an ansatz, setting the number of repetitions using `reps`." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 191 - }, - "id": "0fyXDwr10KqA", - "outputId": "8df79033-2b4e-40cc-96a4-081300d579a9" - }, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "
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\n" - }, - "metadata": {}, - "execution_count": 3 - } - ], - "source": [ - "from qiskit.circuit.library import EfficientSU2\n", - "\n", - "ansatz = EfficientSU2(hamiltonian.num_qubits, reps=1)\n", - "ansatz.decompose().draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "TZEbbCfg_JLq" - }, - "source": [ - "Here, we prepare a dictionary to store the initial parameters we set up, which determine the initial state." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "id": "Ju2SO4sZ0R3P" - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "\n", - "init_param_values={}\n", - "for i in range(len(ansatz.parameters)):\n", - " init_param_values[ansatz.parameters[i]]=np.pi/2" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "2VzjiBc0EeRb" - }, - "source": [ - "Note that the initial state should be in overlap with the ground state.\n", - "\n", - "Next, we choose `ImaginaryMcLachlanPrinciple` as the variational principle we'll use later." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "id": "zK934ZfdEJtG" - }, - "outputs": [], - "source": [ - "from qiskit.algorithms.time_evolvers.variational import ImaginaryMcLachlanPrinciple\n", - "\n", - "var_principle = ImaginaryMcLachlanPrinciple()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "4gOIKzLYFaCP" - }, - "source": [ - "We set a target imaginary time $t=5$, and set the Hamiltonian as an auxiliary operator. We create a `TimeEvolutionProblem` instance with `hamiltonian`, `time`, and `aux_operators` as arguments." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "id": "_4LN_OIB0Vn0" - }, - "outputs": [], - "source": [ - "from qiskit.algorithms import TimeEvolutionProblem\n", - "\n", - "time = 5.0\n", - "aux_ops = [hamiltonian]\n", - "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "bhGjcZzsGcFa" - }, - "source": [ - "We now use the `VarQITE` class to calculate the imaginary time evolving state. We can use `VarQITE.evolve` to get the results. Note this cell may take around $1.5$ minutes to finish." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "id": "T2jv73lRGbHt" - }, - "outputs": [], - "source": [ - "from qiskit.algorithms import VarQITE\n", - "from qiskit.primitives import Estimator\n", - "\n", - "var_qite = VarQITE(ansatz, init_param_values, var_principle, Estimator()) \n", - "# an Estimator instance is necessary, if we want to calculate the expectation value of auxiliary operators.\n", - "evolution_result = var_qite.evolve(evolution_problem)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "5oFggUXMktgG" - }, - "source": [ - "## Exact Classical Solution\n", - "In order to check whether our calculation using `VarQITE` is correct or not, we also call `SciPyImaginaryEvolver` to help us calculate the exact solution.\n", - "\n", - "Firstly, we can use `qiskit.quantum_info.Statevector` to help us get the statevector from the quantum circuit." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "id": "nF6lJqEZkz2f" - }, - "outputs": [], - "source": [ - "from qiskit.quantum_info import Statevector\n", - "\n", - "init_state = Statevector(ansatz.assign_parameters(init_param_values))" - ] - }, - { - "cell_type": "markdown", - "source": [ - "Then we can set up the evolving problem using `SciPyImaginaryEvolver`. Here we set number of time steps as $501$." - ], - "metadata": { - "id": "SUWse0TNkfky" - } - }, - { - "cell_type": "code", - "source": [ - "from qiskit.algorithms import SciPyImaginaryEvolver\n", - "\n", - "evolution_problem = TimeEvolutionProblem(hamiltonian, time, initial_state=init_state, aux_operators=aux_ops)\n", - "exact_evol = SciPyImaginaryEvolver(num_timesteps=501)\n", - "sol = exact_evol.evolve(evolution_problem)" - ], - "metadata": { - "id": "ZX89FSpmkhd7" - }, - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "afbae447lVAR" - }, - "source": [ - "## Results and Comparison\n", - "\n", - "We use `evolution_result.observables` to get the variation over time of the expectation values of the Hamiltonian." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 449 - }, - "id": "cCWhV-2y765c", - "outputId": "5562be51-75fa-4a4e-a4dc-292c2d9b22f6" - }, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
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\n" - }, - "metadata": {} - } - ], - "source": [ - "import pylab\n", - "\n", - "h_exp_val = np.array([ele[0][0] for ele in evolution_result.observables])\n", - "\n", - "exact_h_exp_val = sol.observables[0][0].real\n", - "\n", - "times = evolution_result.times\n", - "pylab.plot(times, h_exp_val, label= \"VarQITE\")\n", - "pylab.plot(times, exact_h_exp_val , label= \"Exact\", linestyle='--')\n", - "pylab.xlabel(\"Time\")\n", - "pylab.ylabel(r\"$\\langle H \\rangle$ (energy)\")\n", - "pylab.legend(loc=\"upper right\");" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "-2uSBEO83vU3", - "outputId": "369b4864-f0b0-4096-8a59-4d104bf841b1" - }, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Ground state energy -2.0097479079521197\n" - ] - } - ], - "source": [ - "print(\"Ground state energy\", h_exp_val[-1])" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "8dp41GBm3TIS" - }, - "source": [ - "As the above figure indicates, we have obtained the converged ground state energy." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "zSGo5QcUlePi" - }, - "source": [ - "## Efficient classical calculation of gradients with VarQITE\n", - "\n", - "You can use classically efficient gradient calculations to speed up the time evolution simulation by setting `qgt` to `ReverseQGT()` and `gradient` to `ReverseEstimatorGradient()`." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "id": "6PzxWQyIld-T" - }, - "outputs": [], - "source": [ - "from qiskit.algorithms.gradients import ReverseEstimatorGradient, ReverseQGT\n", - "\n", - "var_principle = ImaginaryMcLachlanPrinciple(qgt = ReverseQGT() , gradient = ReverseEstimatorGradient())\n", - "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)\n", - "var_qite = VarQITE(ansatz, init_param_values, var_principle, Estimator())\n", - "evolution_result_eff = var_qite.evolve(evolution_problem)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "S8mtNpT5NirQ" - }, - "source": [ - "In this example, it takes only $1$ minute to calculate imaginary time evolution. The execution time is reduced by about 33% (this may vary for each execution, but generally results in a speedup)." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 449 - }, - "id": "pvmRXMXxBz2H", - "outputId": "11962fe6-96d6-4aa4-c4b4-6fcbbf65515d" - }, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ], - "source": [ - "h_exp_val_eff = np.array([ele[0][0] for ele in evolution_result_eff.observables])\n", - "\n", - "exact_h_exp_val_eff = sol.observables[0][0].real\n", - "\n", - "times = evolution_result_eff.times\n", - "pylab.plot(times, h_exp_val_eff, label= r\"VarQITE$_{eff}$\")\n", - "pylab.plot(times, exact_h_exp_val_eff , label= \"Exact\", linestyle='--')\n", - "pylab.xlabel(\"Time\")\n", - "pylab.ylabel(r\"$\\langle H \\rangle$ (energy)\")\n", - "pylab.legend(loc=\"upper right\");" - ] - }, - { - "cell_type": "markdown", - "source": [ - "We can also get a converged result, which is consistent with the previous one." - ], - "metadata": { - "id": "3yZ_CTqK0-Oy" - } - }, - { - "cell_type": "code", - "source": [ - "print(\"Ground state energy\", h_exp_val_eff[-1])" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "_OxkX7wv03db", - "outputId": "04a87fdc-e2e0-4cb6-eb96-1c6e9057d28f" - }, - "execution_count": 14, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Ground state energy -2.0097479079521183\n" - ] - } - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "ed9_4HhXLE_A" - }, - "source": [ - "\n", - "\n", - "Let us compare the performance of different methods. The error is defined as the difference between the results and exact solution for each method." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 449 - }, - "id": "PpDLxpZdpFhA", - "outputId": "7d7acfef-27f8-47fa-c464-4ab0e15a4267" - }, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ], - "source": [ - "pylab.plot(times, (h_exp_val-exact_h_exp_val), label= \"VarQITE\")\n", - "pylab.plot(times, (h_exp_val_eff-exact_h_exp_val_eff), label= r\"VarQITE$_{eff}$\", linestyle='--')\n", - "pylab.xlabel(\"Time\")\n", - "pylab.ylabel(r\"$\\Delta \\langle H \\rangle$\")\n", - "pylab.legend(loc=\"upper right\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "ejlBv7Qi0C1-" - }, - "source": [ - "In this task, the accuracies of `VarQITE` with both gradient methods are very close, but `ReverseEstimatorGradient()` takes a considerably shorter time to run. \n", - "\n", - "We can do the same comparison for `VarQRTE` for simulating the magnetization of the Ising model." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "m-tp9kdHmy55" - }, - "source": [ - "# Real Time Evolution\n", - "Real time evolution is more suitable for tasks such as simulating quantum dynamics. For example, one can use `VarQRTE` to get time evolving expectation values of the magnetization.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "TPGhF7xfodnT" - }, - "source": [ - "## VarQRTE\n", - "Again, the first step is to select an ansatz." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 191 - }, - "id": "l7hz6wSLnZx3", - "outputId": "b23ea3f0-d19c-4def-a494-72fa0d5d40cf" - }, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {}, - "execution_count": 16 - } - ], - "source": [ - "ansatz = EfficientSU2(hamiltonian.num_qubits, reps=1)\n", - "ansatz.decompose().draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "source": [ - "We set all initial parameters as $\\frac{\\pi}{2}$." - ], - "metadata": { - "id": "Hil3c_xfubIw" - } - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "id": "thWw2mahnipB" - }, - "outputs": [], - "source": [ - "init_param_values = {}\n", - "\n", - "for i in range(len(ansatz.parameters)):\n", - " init_param_values[ansatz.parameters[i]] = np.pi/2 # initialize the parameters which also decide the initial state" - ] - }, - { - "cell_type": "markdown", - "source": [ - "We also define an initial state:" - ], - "metadata": { - "id": "i18irpxD4ETl" - } - }, - { - "cell_type": "code", - "source": [ - "init_state = Statevector(ansatz.assign_parameters(init_param_values))\n", - "print(init_state)" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "4AsVk0Gj3-KQ", - "outputId": "60460d22-a873-4c1c-a034-a5b62c305526" - }, - "execution_count": 18, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Statevector([-5.00000000e-01+0.00000000e+00j,\n", - " -5.00000000e-01-5.55111512e-17j,\n", - " 0.00000000e+00-5.00000000e-01j,\n", - " 1.66533454e-16+5.00000000e-01j],\n", - " dims=(2, 2))\n" - ] - } - ] - }, - { - "cell_type": "markdown", - "source": [ - "In order to use the real time McLachlan principle, we instantiate the `RealMcLachlanPrinciple` class." - ], - "metadata": { - "id": "-ee7tApy4lsp" - } - }, - { - "cell_type": "code", - "source": [ - "from qiskit.algorithms.time_evolvers.variational import RealMcLachlanPrinciple\n", - "\n", - "var_principle = RealMcLachlanPrinciple()" - ], - "metadata": { - "id": "U8ytm_9g4kkx" - }, - "execution_count": 19, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "qknpQG8LFRdX" - }, - "source": [ - "We also set the target time as $t=10$, and set the auxiliary operator to be the magnetization operator. The following steps are similar to `VarQITE`.\n" - ] - }, - { - "cell_type": "code", - "source": [ - "aux_ops = [magnetization]" - ], - "metadata": { - "id": "Yh7vyZr62ubD" - }, - "execution_count": 20, - "outputs": [] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "id": "-o2B3533nqsU" - }, - "outputs": [], - "source": [ - "from qiskit.algorithms import VarQRTE\n", - "\n", - "time = 10.0\n", - "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)\n", - "var_qrte = VarQRTE(ansatz, init_param_values,var_principle, Estimator())\n", - "evolution_result_re = var_qrte.evolve(evolution_problem)" - ] - }, - { - "cell_type": "markdown", - "source": [ - "We can also obtain the exact solution with `SciPyRealEvolver`. We first create the corresponding initial state for the exact classical method." - ], - "metadata": { - "id": "ByiDyBuia1fN" - } - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "id": "yDWL-Zd5oQwH" - }, - "outputs": [], - "source": [ - "init_circ = ansatz.assign_parameters(init_param_values)" - ] - }, - { - "cell_type": "markdown", - "source": [ - "`SciPyRealEvolver` can help us get the classical exact result." - ], - "metadata": { - "id": "SimuqpjpbHuU" - } - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "id": "ac4twWUqonXm" - }, - "outputs": [], - "source": [ - "from qiskit.algorithms import SciPyRealEvolver\n", - "\n", - "evolution_problem = TimeEvolutionProblem(hamiltonian, time, initial_state = init_circ, aux_operators=aux_ops)\n", - "rtev = SciPyRealEvolver(1001)\n", - "sol = rtev.evolve(evolution_problem)" - ] - }, - { - "cell_type": "markdown", - "source": [ - "We can compare the results, where $m_z$ represents the magnetization." - ], - "metadata": { - "id": "M2hl_f2Y67tu" - } - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 449 - }, - "id": "02oeqzHDotYT", - "outputId": "2b95d596-f9be-43cc-f1f0-18c1f13dc47d" - }, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ], - "source": [ - "mz_exp_val_re = np.array([ele[0][0] for ele in evolution_result_re.observables])\n", - "exact_mz_exp_val_re = sol.observables[0][0].real\n", - "times = evolution_result_re.times\n", - "pylab.plot(times, mz_exp_val_re, label= \"VarQRTE\")\n", - "pylab.plot(times, exact_mz_exp_val_re , label= \"Exact\", linestyle='--')\n", - "pylab.xlabel(\"Time\")\n", - "pylab.ylabel(r\"$\\langle m_z \\rangle$\")\n", - "pylab.legend(loc=\"upper right\");" - ] - }, - { - "cell_type": "markdown", - "source": [ - "## Efficient Way to run VarQRTE\n", - "\n", - "Similarly, we can set `qpt` as `ReverseQGT()` and `gradient` as `ReverseEstimatorGradient()` to speed up the calculation." - ], - "metadata": { - "id": "korN4ZZv8j_8" - } - }, - { - "cell_type": "code", - "source": [ - "var_principle = RealMcLachlanPrinciple(qgt = ReverseQGT() , gradient = ReverseEstimatorGradient())\n", - "time = 10.0\n", - "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)\n", - "var_qrte = VarQRTE(ansatz, init_param_values,var_principle, Estimator())\n", - "evolution_result_re_eff = var_qrte.evolve(evolution_problem)" - ], - "metadata": { - "id": "gnBS19NQ85cn" - }, - "execution_count": 27, - "outputs": [] - }, - { - "cell_type": "code", - "source": [ - "mz_exp_val_re_eff = np.array([ele[0][0] for ele in evolution_result_re_eff.observables])\n", - "pylab.plot(times, mz_exp_val_re_eff, label= r\"VarQRTE$_{eff}$\")\n", - "pylab.plot(times, exact_mz_exp_val_re , label= \"Exact\", linestyle='--')\n", - "pylab.xlabel(\"Time\")\n", - "pylab.ylabel(r\"$\\langle m_z \\rangle$\")\n", - "pylab.legend(loc=\"upper right\");" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 449 - }, - "id": "IriOFWu89iTX", - "outputId": "1160c308-3d08-490f-a595-325433794117" - }, - "execution_count": 28, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "markdown", - "source": [ - "Again, the accuracies of `VarQRTE` with both gradient methods are very similar, while the `ReverseEstimatorGradient()` shows a speedup of about $21\\%$ in this execution." - ], - "metadata": { - "id": "-IHBehQVAfZm" - } + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "lTiEsmieVAf-" + }, + "source": [ + "# Variational Quantum Time Evolution\n", + "This notebook demonstrates how to use the Variational Quantum Time Evolution (VarQTE) algorithm for computing the time evolving state under a given Hamiltonian. Specifically, it introduces variational quantum imaginary and real time evolution based on McLachlan's variational principle, and shows how this can be leveraged using the `time_evolvers.variational` sub-module." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Zw5nQ9h0xVqF" + }, + "source": [ + "## Introduction\n", + "The time evolution of a quantum state $|\\Psi\\rangle$ is governed by the Schrödinger equation (here with $\\hbar \\equiv 1$)\n", + "\n", + "$$\n", + " \\frac{d}{dt} |\\Psi(t)\\rangle = -i H |\\Psi(t)\\rangle,\n", + "$$\n", + "\n", + "\n", + "or without the factor $i$ for imaginary time dynamics.\n", + "\n", + "In VarQTE, the time evolution of the _state_ $|\\Psi(t)\\rangle$ is replaced by the evolution of _parameters_ $\\theta(t)$ in a variational ansatz $|\\psi[\\theta(t)]$ ([Yuan et al. Quantum 3, 191](https://quantum-journal.org/papers/q-2019-10-07-191/)). Using the McLachlan variational principle, the algorithm updates the parameters by minimizing the distance between the right-hand side and left-hand side of the equation above, that is\n", + "\n", + "$$\n", + "\\dot\\theta(t) = \\mathrm{argmin} \\Bigg\\| \\left(\\frac{d}{dt} + i H\\right)|\\psi[\\theta(t)]\\rangle \\Bigg\\|,\n", + "$$\n", + "\n", + "with the norm $\\| |\\psi\\rangle \\| = \\sqrt{\\langle\\psi | \\psi\\rangle}$. This is equivalent to solving the following linear system of equations\n", + "\n", + "$$\n", + "\\sum_{ij}F_{ij}\\dot{\\theta}_{i}=V_{j}\n", + "$$\n", + "\n", + "where\n", + "\n", + "$$F_{ij}=\\text{Re}\\left[\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}\\frac{\\partial\\left|\\psi\\left[\\theta\\right]\\right\\rangle }{\\partial\\theta_{j}}+\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}\\left|\\psi\\left[\\theta\\right]\\right\\rangle \\left\\langle \\psi\\left[\\theta\\right]\\right|\\frac{\\partial\\left|\\psi\\left[\\theta\\right]\\right\\rangle }{\\partial\\theta_{j}}\\right]$$,\n", + "\n", + "and\n", + "\n", + "$$V_{i}=\\begin{cases}\n", + "\\text{Im}\\left[\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}H\\left|\\psi\\left[\\theta\\right]\\right\\rangle +\\left\\langle \\psi\\left[\\theta\\right]\\right|\\frac{\\partial\\left|\\psi\\left[\\theta\\right]\\right\\rangle }{\\partial\\theta_{i}}\\left\\langle H\\right\\rangle _{\\theta}\\right] & \\text{Real time}\\\\\n", + "-\\text{Re}\\left[\\frac{\\partial\\left\\langle \\psi\\left[\\theta\\right]\\right|}{\\partial\\theta_{i}}H\\left|\\psi\\left[\\theta\\right]\\right\\rangle \\right] & \\text{Imaginary time}\n", + "\\end{cases}$$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "caoBgyluhQ3L" + }, + "source": [ + "\n", + "## Running VarQTE" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "WG-18slyLnVM" + }, + "source": [ + "In this tutorial, we will use two classes that extend `VarQTE`, `VarQITE` ([Variational Quantum Imaginary Time Evolution](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.VarQITE.html#qiskit_algorithms.VarQITE)) and `VarQRTE` ([Variational Quantum Real Time Evolution](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.VarQRTE.html)) for time evolution.\n", + "We can use a simple Ising model on a spin chain to illustrate this. Let us consider the following Hamiltonian:\n", + "\n", + "$$H = -J\\sum_{i=0}^{L-2}Z_{i}Z_{i+1} - h\\sum_{i=0}^{L-1}X_i$$\n", + "\n", + "where $J$ stands for the interaction energy, and\n", + "$h$ represents an external field which is orthogonal to the transverse direction. $Z_i$ and $X_i$ are the Pauli operators on the spins. Taking $L=2$, $J=0.2$, and $h =1$, the Hamiltonian and the magnetization $\\sum_i Z_i$ can be constructed using `SparsePauliOp` as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "6B0nZEDh0EqI" + }, + "outputs": [], + "source": [ + "from qiskit.quantum_info import SparsePauliOp\n", + "\n", + "hamiltonian = SparsePauliOp(['ZZ', 'IX', 'XI'],\n", + " coeffs=[-0.2 , -1, -1])\n", + "\n", + "magnetization = SparsePauliOp([ 'IZ', 'ZI'], coeffs=[1, 1])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Y_9Jskw4m8nF" + }, + "source": [ + "## Imaginary Time Evolution\n", + "\n", + "Imaginary time evolution can be used, for example, to find the ground state or calculate the finite temperature expectation value of the system. Here, we will use the `VarQITE` class from `time_evolvers.variational` to compute a ground state energy. Firstly, we need to choose an ansatz. We can use `EfficientSU2` to easily construct an ansatz, setting the number of repetitions using `reps`." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 191 + }, + "id": "0fyXDwr10KqA", + "outputId": "8df79033-2b4e-40cc-96a4-081300d579a9" + }, + "outputs": [ + { + "data": { + "image/png": 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IH70BJ0fnak4H5yvwqIUtcnLhWhZ4ulXN/ksj86NqGbbIALy9vYstz87OJiUlhT59+hQtCw8Pr9B7ODg42LTd/HHJhAX0qNB7VFZKymbaD+9ZodfaI/dHX8eRdfM6b34SXbSscf1gJj31XpmvqUzme3UaMpuOg14ttqzw7mRZylp/793MwOBHuHr2cCXS3aFqjug4P+D+cufb+LyMIYvMy8sLgLS0NPr27Vu0fN68eZw7d87QF/rLM/3pBNURbDZh8CImDF6k7P3zbpfyGSQ7yb2VXWX7rgyZHxVjyCLz9/cnNDSU+Ph4PD098fHxITExkfXr1wPYpchsbfpdq9R9b1NERA/yF1fsYo6q3JXJfK8fT8GyLcWXlfWcmC3PkRVydoRrF9Ix2ekKsY5jreu8LoshL/abTCZWr15NSEgIMTExjBw5Ei8vL8aPH4/ZbC660C8ebE3qVc1+fT2wW4kJYzDkERlAUFAQycnJxZY9++yztGjRgpo1aypKJapTXVfw8yr4eJE9tW5q3/0J9bT6e2nXrl0lTitnzZqFr68vO3fuZOzYsfj6+nL06FFFCYW9dbHzx/pqOEJ7f/vuU6hn2COye2VmZpKWlkZsbGyx5XFxccTFxSlKVWDp+pf5KX07Ic264Fs/mFXJc5k05H1CmoUz5d3uHD9/gCWT9+HjFUh2TibT3++FT71A/hr1kSFzN/MO4dUP+2M2O1HLpQ4zn/kEiyVPSe42TQue7k+301FZ3zBwcbLPvu5HWWMdFhDBgFl1CGzUGoDXnltDbVdPZi7rR2b2NRaO31b9YcvJXMulDouTJgFw8eoJBnWbyOBuk5Rm1uaIzM3Njby8PF544QXVUYo5fj6VrJs3eCt2Czd++5Wbt7IYGvEiYQERmE2OzI7+jG6tniravmYNN2aMWKUwcQFrud1qevB27DbeikkhyKct3x5cpyy3yQTDO4OT2fp2kz4u/0J/QAPoFmy/bLayNtYAft6tij6zWPhE/5xR66o/6F2sZQ70ebQor99DoXR8pJ/yzNoUmVGlHt9Gu6CCD/e2af4HTKY7/8c5ODjg4d5QVTSrrOU2m8yYfr8anpefh49XcyUZCzWsDX+JKL/MrPHxgFHdwWTb44N2ZW2sAU5ePMTkd7vxwfq/2nw3vaqVlxkg+1YWVzPOG+KTCNqcWhpVxm9XWLdzCZ9ufZvM7GtEhA2jrlsD1bHKVV7uwye/53//G4uzowtDu09VmLRA8EMwvlfBN8T+mnl/rw1rAn/qCK6KHj4vb6wTXjqCe00P/vHpOHYe/D/CQ/qrCXoXW+b1D4c30C44UlHC4qTIKsnd1ZPnev+d8JD+fHtwHZeu6/HLAsvL/XCTDrw7cRerUxbwxQ/LGNK95MfFqlszL5j+BHx1ALYfKf87yrzrQGQreFTxXcryxrrwdDK85UB+ObPXEEVmy7zenvpfhvWYriBdSXJqWUkt/bpy4FjBU5v7j27GYslTnMg21nLfzr1V9HMtl9o4OxnncZcajvBka5g9GKI6Q3hgwfNmXm5Q3x2CvaFXCPxPL3jpCfUlBtbHOvtWFnm///NP6dtpVC9AScZ7lTevc/Nuc/LiIQIahamIV4IckVWSn3dLHM1OTF3cgxZNO+PiXIs8y51v7otbPozU9G2cuXyEP/WYTnjLAQrT3mEt99Gz+3j/8xcxOZhwr+nJS8OXl7O36lfDETr4F/wxOmtjfebSERasHkVNZze8Pf348x9nK05boLx5vfeXb3g04DGFCYuTIrOD0X3nFv285cdEViW/gY9Xc8ICIpj17H+KbZudk8kbK58huHH76o5ZgrXcb8WkFNvWSLl1ZG2sF0/aU2L7mcv64Vn7oeqMWIK1zO2De9M+uHex7VVmdsg3ym0Sg1L5mbS6vtDu6Yq9VlXuymTWlY5jreu8LosckZXDXeENyMq8t6rcKsdLFR3HWtd5XRY5IhNCaE/uWgohtCdFJoTQnhSZEEJ7UmRCCO1JkQkhtCdFJoTQnhSZEEJ7UmRCCO1JkQkhtCdFJoTQnhSZEEJ7UmRCCO1JkQkhtCdFJoTQnhSZEEJ7UmRCCO1JkQkhtCdFJoTQ3v8D7uqZcu+yQGsAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.circuit.library import EfficientSU2\n", + "\n", + "ansatz = EfficientSU2(hamiltonian.num_qubits, reps=1)\n", + "ansatz.decompose().draw('mpl')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "TZEbbCfg_JLq" + }, + "source": [ + "Here, we prepare a dictionary to store the initial parameters we set up, which determine the initial state." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "id": "Ju2SO4sZ0R3P" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "init_param_values={}\n", + "for i in range(len(ansatz.parameters)):\n", + " init_param_values[ansatz.parameters[i]]=np.pi/2" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "2VzjiBc0EeRb" + }, + "source": [ + "Note that the initial state should be in overlap with the ground state.\n", + "\n", + "Next, we choose `ImaginaryMcLachlanPrinciple` as the variational principle we'll use later." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "id": "zK934ZfdEJtG" + }, + "outputs": [], + "source": [ + "from qiskit_algorithms.time_evolvers.variational import ImaginaryMcLachlanPrinciple\n", + "\n", + "var_principle = ImaginaryMcLachlanPrinciple()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4gOIKzLYFaCP" + }, + "source": [ + "We set a target imaginary time $t=5$, and set the Hamiltonian as an auxiliary operator. We create a `TimeEvolutionProblem` instance with `hamiltonian`, `time`, and `aux_operators` as arguments." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "id": "_4LN_OIB0Vn0" + }, + "outputs": [], + "source": [ + "from qiskit_algorithms import TimeEvolutionProblem\n", + "\n", + "time = 5.0\n", + "aux_ops = [hamiltonian]\n", + "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "bhGjcZzsGcFa" + }, + "source": [ + "We now use the `VarQITE` class to calculate the imaginary time evolving state. We can use `VarQITE.evolve` to get the results. Note this cell may take around $1.5$ minutes to finish." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "id": "T2jv73lRGbHt" + }, + "outputs": [], + "source": [ + "from qiskit_algorithms import VarQITE\n", + "from qiskit.primitives import Estimator\n", + "\n", + "var_qite = VarQITE(ansatz, init_param_values, var_principle, Estimator())\n", + "# an Estimator instance is necessary, if we want to calculate the expectation value of auxiliary operators.\n", + "evolution_result = var_qite.evolve(evolution_problem)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5oFggUXMktgG" + }, + "source": [ + "### Exact Classical Solution\n", + "In order to check whether our calculation using `VarQITE` is correct or not, we also call `SciPyImaginaryEvolver` to help us calculate the exact solution.\n", + "\n", + "Firstly, we can use `qiskit.quantum_info.Statevector` to help us get the statevector from the quantum circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "id": "nF6lJqEZkz2f" + }, + "outputs": [], + "source": [ + "from qiskit.quantum_info import Statevector\n", + "\n", + "init_state = Statevector(ansatz.assign_parameters(init_param_values))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "SUWse0TNkfky" + }, + "source": [ + "Then we can set up the evolving problem using `SciPyImaginaryEvolver`. Here we set number of time steps as $501$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "id": "ZX89FSpmkhd7" + }, + "outputs": [], + "source": [ + "from qiskit_algorithms import SciPyImaginaryEvolver\n", + "\n", + "evolution_problem = TimeEvolutionProblem(hamiltonian, time, initial_state=init_state, aux_operators=aux_ops)\n", + "exact_evol = SciPyImaginaryEvolver(num_timesteps=501)\n", + "sol = exact_evol.evolve(evolution_problem)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "afbae447lVAR" + }, + "source": [ + "### Results and Comparison\n", + "\n", + "We use `evolution_result.observables` to get the variation over time of the expectation values of the Hamiltonian." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "cCWhV-2y765c", + "outputId": "5562be51-75fa-4a4e-a4dc-292c2d9b22f6" + }, + "outputs": [ + { + "data": { + 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import pylab\n", + "\n", + "h_exp_val = np.array([ele[0][0] for ele in evolution_result.observables])\n", + "\n", + "exact_h_exp_val = sol.observables[0][0].real\n", + "\n", + "times = evolution_result.times\n", + "pylab.plot(times, h_exp_val, label= \"VarQITE\")\n", + "pylab.plot(times, exact_h_exp_val , label= \"Exact\", linestyle='--')\n", + "pylab.xlabel(\"Time\")\n", + "pylab.ylabel(r\"$\\langle H \\rangle$ (energy)\")\n", + "pylab.legend(loc=\"upper right\");" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "-2uSBEO83vU3", + "outputId": "369b4864-f0b0-4096-8a59-4d104bf841b1" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ground state energy -2.0097479079521197\n" + ] + } + ], + "source": [ + "print(\"Ground state energy\", h_exp_val[-1])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8dp41GBm3TIS" + }, + "source": [ + "As the above figure indicates, we have obtained the converged ground state energy." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zSGo5QcUlePi" + }, + "source": [ + "### Efficient classical calculation of gradients with VarQITE\n", + "\n", + "You can use classically efficient gradient calculations to speed up the time evolution simulation by setting `qgt` to `ReverseQGT()` and `gradient` to `ReverseEstimatorGradient()`." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "id": "6PzxWQyIld-T" + }, + "outputs": [], + "source": [ + "from qiskit_algorithms.gradients import ReverseEstimatorGradient, ReverseQGT\n", + "\n", + "var_principle = ImaginaryMcLachlanPrinciple(qgt=ReverseQGT() , gradient=ReverseEstimatorGradient())\n", + "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)\n", + "var_qite = VarQITE(ansatz, init_param_values, var_principle, Estimator())\n", + "evolution_result_eff = var_qite.evolve(evolution_problem)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "S8mtNpT5NirQ" + }, + "source": [ + "In this example, it takes only $1$ minute to calculate imaginary time evolution. The execution time is reduced by about 33% (this may vary for each execution, but generally results in a speedup)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "pvmRXMXxBz2H", + "outputId": "11962fe6-96d6-4aa4-c4b4-6fcbbf65515d" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "h_exp_val_eff = np.array([ele[0][0] for ele in evolution_result_eff.observables])\n", + "\n", + "exact_h_exp_val_eff = sol.observables[0][0].real\n", + "\n", + "times = evolution_result_eff.times\n", + "pylab.plot(times, h_exp_val_eff, label= r\"VarQITE$_{eff}$\")\n", + "pylab.plot(times, exact_h_exp_val_eff , label= \"Exact\", linestyle='--')\n", + "pylab.xlabel(\"Time\")\n", + "pylab.ylabel(r\"$\\langle H \\rangle$ (energy)\")\n", + "pylab.legend(loc=\"upper right\");" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3yZ_CTqK0-Oy" + }, + "source": [ + "We can also get a converged result, which is consistent with the previous one." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "_OxkX7wv03db", + "outputId": "04a87fdc-e2e0-4cb6-eb96-1c6e9057d28f" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ground state energy -2.0097479079521183\n" + ] + } + ], + "source": [ + "print(\"Ground state energy\", h_exp_val_eff[-1])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ed9_4HhXLE_A" + }, + "source": [ + "\n", + "\n", + "Let us compare the performance of different methods. The error is defined as the difference between the results and exact solution for each method." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "PpDLxpZdpFhA", + "outputId": "7d7acfef-27f8-47fa-c464-4ab0e15a4267" + }, + "outputs": [ + { + "data": { + "image/png": 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sVNVfHaCvnzn/vhqZ0wqPz/1H8UzTt3ggb3Cn9ynz9SNxd9scbkzvVVBQQGlpKW7eTj+c+f1+CgoKurSPJxKQqraIyE3AW4SGYT+lqstF5EfAQlWdRSiZ/ElESoBdhJIUTruZwApCI99uVNWAiJwKXAV8JiKLnUPdrapvEEo8M0XkWmADcGnUTvYQrGvK5F3fqaSkpHZ6n+rEfHLqvohgVMb0LHFxcQwadPC5FE10eSIBATiJ4Y02ZT9otd0AtDM9Lajq/cD9bcr+DcgB2pcD47sZctQk7/iEM5LrCF3UdU5TSiF9a+agwSDSwewJxhjjBvvN1AOcu+0P3BJ4ukv7rB3+DU5ofIRd9i6QMcajLAH1ACkt5dQn5HRpn+w+eVSSypaqxghFZYwx3WMJqAfIDFbQ7O/aMPDChAa+HTuT2vULIhSVMcZ0jyUgj2tpbiKN3QSTsru0X9+0OG6O/Rsxm+Z13NgYY1xgCcjjqneFXlGKScrq0n5ZOXk0aBxaZUOxjTHeZAnI43YFE7mk8V4qB07o0n4SE8POmBzidtuyDMYYb7IE5HGVjcInOpzE7MKOG7fdN64vyQ3bIhCVMcZ0nyUgj2vY8QUXxXxIdmxDl/etT+xHcktl+IMyxpgwsATkcfGlc3g4/nEyZXeX9/3oyHs4o+EhWgLBCERmjDHdYwnI4wK7ywFIy+7T5X37ZGYQVGFHjb0LZIzxHktAXle3i2b1kZyS0eVdB/u28VDc79m1bnHYwzLGmO6yBORxMQ0VVEvqIc3n1i85him+f9GwZVkEIjPGmO6xBORxcU2V1MR0fhbs1rL7h5ZvaNm1qYOWxhgTfZ6ZDdu07/+Sb8CfVMdvDmHf1PQsajQRqu1lVGOM99gVkMeta0ylIa3zC9G1tdPXhwR7GdUY40GWgDzunJpXOVZXHvL+O/0DaGi2YdjGGO+xBORhGgxyS+Bpjqmff8h9vDzkAW4MfieMURljTHhYAvKw3bVVxEsASco85D7yM/zs2t1EQ3MgjJEZY0z3WQLysD0zYfuSu7YUQ2ujAqt4Pu5+yjatCVdYxhgTFpaAPGx3ZSgBxaYcegLKTYJTfMup2vJ5uMIyxpiwsATkYQ1VZQD407u2GmprGX0HAVBXtiEsMRljTLhYAvKwdaljGdfwKPGFYw+5j5z8UAIKVJaGKyxjjAkLS0AeVtEAO8gkPS3tkPvwJyazizRiauxdIGOMt1gC8rC0zR9ws+9lMvzdm7BiVdwodrQkhSkqY4wJD88kIBGZKCKrRaRERO5spz5BRF506ueJSFGruruc8tUiMqFV+VMiskNElrXp6z4R2Swii52v/4royR2i/js+5Lq4N4iN9XWrn6cKfsKjMVeEKSpjjAkPTyQgEfEBjwLnASOBaSIysk2za4EKVR0CPAw86Ow7EpgKjAImAo85/QE87ZS152FVHeN8vRHO8wkXX2MlNXJoE5G21j/Dz5bK+jBEZIwx4eOJBASMA0pUda2qNgEzgElt2kwCnnG2XwLGi4g45TNUtVFV1wElTn+o6r+AXdE4gUiIb6pkty+92/2c2vABrwRvYXdNZfeDMsaYMPFKAsoHWq8ZUOqUtdtGVVuAKiC7k/u25yYRWercpmt3qgERuV5EForIwrKyss6dSRgltlTRENv9BJSVGMsRMVvZuWV994Myxpgw8UoCirbHgSOAMcBW4JftNVLVJ1S1WFWLc3MP/V2cQ5UYqKEpPqP7/eQMAKB6+7pu92WMMeHilQS0GShs9bnAKWu3jYjEAulAeSf33YeqblfVgKoGgT/g3LLzmvODv+atI+7qdj8Z/ULvAtXvtIXpjDHe4ZUEtAAYKiKDRCSe0KCCWW3azAKucbanAO+pqjrlU51RcoOAocBBp48WkbxWHy8CPLdmdXMgSFVjkNSUQ38HaI+c/gMBexnVGOMtnkhAzjOdm4C3gJXATFVdLiI/EpELnWbTgWwRKQG+Ddzp7LscmAmsAP4B3KiqAQAReQGYAwwXkVIRudbp6+ci8pmILAXOAm6Lyol2QdWuMn4a+yRDmw59LaA9EvxJvCcnUBo49Fm1jTEm3DyzJLczFPqNNmU/aLXdAHzlAPveD9zfTvm0A7S/qlvBRsHunZu4PPY9PgmeH5b+Hs76AVm++Pa/gcYY4wJPXAGZ/dVVhkbdJaTmhKW/vHQ/W6vsXSBjjHd45grI7KuhphwAf3p4EtDUuj8zuvJlYH1Y+jPGmO6yKyCPaq7ZCUBKZp+w9JeUlEwfqaCmqse+l2uMOcxYAvKoxoY6GjWWtKzwJKDYrNBI9fKt68PSnzHGdJclII/6d9ZFHBX4E4lJ3R+GDZC092XU9WHpzxhjussSkEdV7m4mMykeiQnPf6I9L6M27NwYlv6MMaa7bBCCR524+Y8cI7uBL4Wlv5y8gfw1cBoazPXmtA/GmF7HEpBHDa+dDyJh6y8+wc/P/LdytvRhSth6NcaYQ2e34DwqKVBFY1xGWPvsn5ZAeYWNgjPGeINdAXlUSrCGHQkZYe3z+40PkVvxBR6c+s4Y0wvZFZAHaTBIutYQ8GeFtd9AYi45gZ1h7dMYYw6VJSAPqq2tZqtmEUzJ67hxF2haPilST7W9jGqM8QBLQB5U2RLP6U2/YcuwK8Pab9yel1E3rw1rv8YYcygsAXlQRV0TAJlJ8WHtN8V5GbXGXkY1xniAJSAPCmyYx7NxD9CvJbwrmKYVjOC3LZPZpOGZ4NQYY7rDEpAHBXat53TfZ6T5wztIMbdfAQ8HLmV1oH9Y+zXGmENhCciDWmpDSzGkZvYNa79xvhiGpDRRV7YhrP0aY8yhsPeAPEjrdhFUIS0zN+x9P6IP0LQhCTgn7H0bY0xX2BWQB8XU76JGkvDFhv/vg90JfUlrLgt7v8YY01WWgDyoXFNZ7RsWkb6bkvPIDZShwWBE+jfGmM6yW3Ae9ELS5dTEXMrfItF5Wn+SdjRSVbmL9CwbDWeMcY9dAXlQZV0zmUlxEel778uo2+xlVGOMuywBedD3K+7hK3UvRqTvuIHjuKv5WrY0pUakf2OM6axOJSARyRSRq0XkFRFZLiJ/F5FviEifcAUiIhNFZLWIlIjIne3UJ4jIi079PBEpalV3l1O+WkQmtCp/SkR2iMiyNn1lichsEVnj/JsZrvMIh9GBVWRJTUT6zskfwguB8WxsTI5I/8YY01kdJiAReRl4GegD3KGqo4D/AfzAcyLyQXeDEBEf8ChwHjASmCYiI9s0uxaoUNUhwMPAg86+I4GpwChgIvCY0x/A005ZW3cC76rqUOBd57MnNDU2kCwNaGJkcmKf1ARGxmykYduqiPRvjDGd1ZkroK+r6lmq+pCqfg6gqhtV9Xeqei4wOQxxjANKVHWtqjYBM4BJbdpMAp5xtl8CxouIOOUzVLVRVdcBJU5/qOq/gPamfm7d1zNhOoewqN61HYCY5OyI9B/ri+Hp+J9z1NrpEenfGGM6qzMJqK/zi75dqloZhjjygdYTn5U6Ze22UdUWoArI7uS+bfVV1a3O9jYgvFMOdENtxQ4AYlPCuxZQaxWxfUhs2Bax/o0xpjM6Mwz7JWCgiHwOLAU+2/Ovqu6IZHDRoKoqItpenYhcD1wPMGDAgKjEU9UQ5KPAKFKyiiJ2jFp/X/rsXhOx/o0xpjM6vAJS1aOAXOCbwAXAYOBuYKmIhOvP6M1AYavPBU5Zu21EJBZIB8o7uW9b20Ukz+krD2g3karqE6parKrFubnhnxanPVvjB3JF8z3EDjg+YsdoTs4jJ7jTXkY1xriqU6PgnOcrC4BaVf2Wqo5X1X7AkWGKYwEwVEQGiUg8oUEFs9q0mQVc42xPAd5TVXXKpzqj5AYBQ4H5HRyvdV/XAK+G4RzCojJCawHtIy2fRGmiusKm5DHGuKer7wHtc6tKVSvCEYTzTOcm4C1gJTBTVZeLyI9E5EKn2XQgW0RKgG/jjFxT1eXATGAF8A/gRlUNAIjIC8AcYLiIlIrItU5fPwPOEZE1wJecz55Q8PmzfBB/G5nx7d4VDIu6wRP5atN32bL7gI/2jDEm4jp8BiQijwKLnK+I/cZS1TeAN9qU/aDVdgPwlQPsez9wfzvl0w7QvhwY3514IyW2dgv9ZBf+pKSIHSOrYBgfBMu4slbDdglrjDFd1ZlBCEuAMcDVQKqIrACWE7riWKGqkXllv5eKaaigWlLxR/AY+WnxnB2ziN0bY2HkhI53MMaYCOgwAanqE60/i0gBcBRwNKFBCZaAwiiuqZLamDTCNsVEO3JS/Twa91uWrLsEsARkjHFHZ27Bxajq3uFSqlpK6F2bN9urN93jb66kPjY9oseQmBh2+PoQX9vRYEFjjImcztyCmy0iO4G/Aa+rarWIJBGa4uYiQldDYyIWYS+zWEaQlJrJqAgfpyo+j9SGLRE+ijHGHFhnbsGNd+ZbmwS87gyTDhIasfYrVf00wjH2Kg8FLmdCQb/95iEKt/rkfArLbT44Y4x7Ovse0ApVfUBVTwPOVNWTCE3ieV1Eo+tlVJXK+sitBdRaML2QTGqoramM+LGMMaY9XXoPSESOBX4oIhuAh4ArIxJVL1VdWc6yuGs4seK1yB9r2BTObXyQzTWRe9/IGGMOpjPLMQwTkXtFZDXwJKHpb85U1RNof6Zpc4hqK7aTKE34/YkRP1Zu/4F8roVsrm6K+LGMMaY9nRmEsIrQVDlTVPWzNnX253MY7a4MTY0Tl5oT8WMVpMVypW82jWubYcTkiB/PGGPa6swtuIuBdcDbIvInEblARCL/kKIXqq8KJaDE9MgnoNy0ZL4f+xyZG9+O+LGMMaY9nZkN+2+qOhUYQujdn+uBUhH5I5AW4fh6leaanQAkpUfyNdSQ/7wLtKnjxsYYEwGdHoSgqrtV9c+qegEwgtAkn0sjFlkvtC2mLy+0nEVqTv+oHK8yvh+pDVs7bmiMMRHQ1dmwgdAs2M5aOWeHO6De7PP4UdwT+AZp6ZFZjrut+qR8slu2R+VYxhjT1iElIBMZNbW1ZPh9xMREZ5mEYHohWVRTV1sVleMZY0xrloA85MvrfszL3B614+068iqObvgDm3fb/wbGmOiz3zweEt9USYMvNWrH69e3H9UkU1pZH7VjGmPMHpaAPCSxpZqGuMjOhN1aQarw3dgZBNa8F7VjGmPMHpaAPCQlUE1zfEbUjpebnso3fG+QvPnDqB3TGGP2sATkIWlaTcCfGbXjxfh8bI/pQ0KNvQtkjIk+S0Ae0djcwh8C51PW5+SoHrciIZ+0+tKoHtMYY8ASkGdU1LXwcMsUagvPjOpx61MK6RPYigZtUVtjTHRZAvKIXVVV5FBFZqIvqsfVzEGIKlUV5VE9rjHGWALyiOD6OSz0f5MBu9tOOB5Zu4+5lqMan2Td7s5MjG6MMeFjCcgjGqp3AJCc0Teqxx3YJw0QNu6qi+pxjTHGMwlIRCaKyGoRKRGRO9upTxCRF536eSJS1KruLqd8tYhM6KhPEXlaRNaJyGLna0ykz68jgZrQUgxp2f2ietyCjER+Gfc4ictfjOpxjTHGE/ddRMQHPAqcA5QCC0RklqquaNXsWqBCVYeIyFTgQeAyERkJTAVGAf2Bd0RkmLPPwfr8rqq+FPGT6yTdXU5QhbTM3Kge1x8fy6m+FWzcEflVWI0xpjWvXAGNA0pUda2qNgEzgElt2kwCnnG2XwLGi4g45TNUtVFV1wElTn+d6dMzpL6cKknFFxv9vwnK4/uTWmdDsY0x0eWVBJQPtH4bstQpa7eNqrYAVUD2QfbtqM/7RWSpiDwsIgntBSUi14vIQhFZWFZW1vWz6oK5/lN4JuHyiB7jQGqTB5DTvMWVYxtjei+vJKBou4vQonrHA1nAHe01ctY8KlbV4tzcyN4am6NH8XHm5Ige40CCGUXkUEltdYUrxzfG9E5eSUCbgcJWnwucsnbbiEgskA6UH2TfA/apqls1pBH4I6Hbda5Krf6CAQm1rhw7tu+RfB7MZ+tWuwoyxkSPVxLQAmCoiAwSkXhCgwpmtWkzC7jG2Z4CvKeq6pRPdUbJDQKGAvMP1qeI5Dn/CjAZWBbJk+uMB2rv4Ss1z7pybP9RF3Ju0y8oacpy5fjGmN7JE6PgVLVFRG4C3gJ8wFOqulxEfgQsVNVZwHTgTyJSAuwilFBw2s0EVgAtwI2qGgBor0/nkM+LSC4gwGLghiidars0GCBDqwkmupMABmYnAbC+3N4FMsZEjycSEICqvgG80absB622G4CvHGDf+4H7O9OnU352d+MNp+rKXaRLEEnKduX4qf44nkh8hPhlA+HM37sSgzGm9/FMAurNqsu3kg7Epkb3HaDW8uNqiKla4trxjTG9j1eeAfVquyu2AxDvYgLanTKIfs22LpAxJnosAXnA9tj+3N50A7H5R7sWQzB7KJnUUFG21bUYjDG9iyUgD9geSOOvwdNJyy1wLYbE/iMA2LZ2qWsxGGN6F0tAHtBcVsJY+ZyspDjXYsgpOoZ/Bo5mc1WTazEYY3oXS0AecMTGv/B8/E9JjHdvTEi/gcP4ht7N/JYhrsVgjOldLAF5gK++nCpJI/RerEsxxAiDc5JZu73atRiMMb2LDcP2gPimCmp96W6HwZ06naKNC4HlHbY1xpjusisgD0hsrqAuLsPtMEhIzaIguIWmxga3QzHG9AKWgDwgJVBJU3ym22EQ12cYsRJk67oVHTc2xphusgTkMlXljpb/ZmnhlW6HQnrhKADK19tQbGNM5NkzIJdVN7TwYfORnN73SLdDoWDYsQRVaNxiz4C8LNDSQkNdDU2SQAs+Ao01BGt2Egg0E2xuIhBoIdDSRG3aEbTE+JHqzSRUlqCBAKpBIIgGlfI+JxLwJeKvXk9q9WoIBgkqQBA0yJZ+4wn6EkitXEVq1WrQIKqKaBBUWZt/ARoTR3bFEtJrS/aLc23hJQDk7vqE1Np1+9QFY2JZVzAZgL4755JS959ZOFQh4POzPv8CAPLK/k1S/b4vSDfHpbIhbwIA+dvfJ7Fx5z71jfEZbOp3DgCFW98moalyn/p6fy6lfc4CoGjLG8S1/GcpFAV2J+axJfc0AAaXvkpscN/b0tVJA9mWcyIAQza9RExo/uO9KlOOYEdWMagybNPM/b43FanDKcscQ0ywmSGlL+9XX54+ivL00cS21DF4y2v71ZdljKEibTjxzdUUbX1zv/rtWcVUpRyBv7GcAdvf2a9+a/aJ1CQPJLFhO4U7PtivfnPOqexOyie5bjPZ1StIHXsJYweE/y6NJSCXlZdt47yYeRQkFHbcOMISk1N5IX4Su5oHcpLbwRymAi0tVOzYTOWOjWwlhx2BVIIV6ynY+CrSUImvsZrY5mriW2p4JvEaljCc0Q0LuavxN8TThF8biZcAycDXGv+X+Xokk2P+za/jH9vvWOc33s9yHcQVvne4P+6p/erPbPwl6zWP632vcXfcC/vV39DwGGVkcFvsX7gl9pX96q9ZUEgdfr4f+zzXxe7/S/DSBcMAeCD2GcbHvr9PXY0mMnX+EQD8Lm46Z/vm7lO/TTO5fH4RANPjnuAE36f71H8RzOPKptACxy/GP84JMav2qV8aHMTVTXkA/D3+EUbHrN+nfk5gJN9vDk199X78wwyK2b5P/ezAWP63OfQLd0HCQ+RK1T71fwuczP82pwCwPOFBkqVxn/rnW8bzvy1+QFnv32+eZJ5oOZ+ftsSSQh3L2ql/uPkSfhOAvuxiXjv1P26+gumB8zlCNvNuwv71dzZfx4zA2Rwla3mtnfpvNd3Ea8GTOSlmOS/E71//9abv8F5wLF+K+YQbY1/lrYRTI5KAJLSkjulIcXGxLly4MOz9Lvvo74yefQXLvvQco0+9IOz9d9V//2kha7bX8t53znQ7lB5Jg0HKd2ymbMMK1jaksqw+i/otK7li80/ICJSTpZX4JPQzd3vTDfw1eDpj5XNeTriPWk2kVlKoi0mmwZfCy5nXUpp6DIMC6zir+m8EYxPRWD/EJSFxfjbmTaQpuT8Z9aX0rVqExMQhsbHE+OKQmDhq+o1D/Bn4G8pIqdsIMT5EYpAYHyJCY+ZwiPMT27CTuLqdxMQAEhNqI0JzxmDEF0tsQwW+pmpn39Bd+5iYGIKp/ZGYGKShCmnevd/3IpjaHwBpqERa6hFav2YgBFP6OfUVSMu+v8AlJoZgcp/Qdv0uJLDvC9Ia40OTcpG99c371vti0cRsZ/9yJBig9eE1Jg5NDP1Clbqdoau61nwJqD9jbz1t62P9aEKaU18Wumzbpz4RTUgF1VB9W3FJaHwKaDDUfxsalwTxKRAMIPXl+9fHJ0NcMgRbkPpd7dSnQFwSBJqRhv1XOtaENIj1Q6AJaahspz4dYhOgpQFprsefnkNKwqFdr4jIJ6pa3F6dXQG5rKEitAppak6+y5GEDO+byvIVy2hoqMfvT3Q7HM/bWdvIki82k7zgERLLPyO//nNyqCQHeLN5Cn/QSxid6ePiuAwqUodRktKPmLR+xGfk87XC47i5zwDS4s+mxX8jKXHxpLTqe+TereMIrcG4rxP3bg0ETjlIlDnAwW7xpgNHHKQ+5SB1QHoH/590WJ938Pq0/t2s7+BnK7WDKbBSu7l/Wgd3NzqqT086SGUCpCcfvP6g//0SgNQO6iP3ioglIJe1VG0DIKOP+7fgAM4MzuHbCbewZtURDB1zmtvheE5D/W5Wz3md+tXv8llVIvdXnkMMQZYk/Jmdvj6sSz+Rkr5HkZQ3gkuPGMvN+UXE+mKAC90O3RjPsQTktpptNGocaRnuLEbXVs7gMTAXKtYtBktAADQHgiz74C8ElsxkRNVHHCP1NGoc9Snj+e6E4Zw4OIvYPusYlJjIILeDNaYHsQTkMl99Gbskg7wYb4yIzx88mgaNI7jNRsJt37qR5z+r54UFm7in4WnO9C1lRdbZ+I++mGEnTOSspBTOcjtIY3owS0Auey7xamJjzueXbgfi8MXGsi52AMmVq90OxTWb1ixh299/wrGV7/B28085algxmWN+TfLIIsbFJ7gdnjGHDUtALltZn0ZRdgcPYaOsImUoRVXz3A4j6nZu28jaGXdwXMWb5BDHwn6XMv38CeQPGOx2aMYcliwBuezM6llk9D0RaHeUoiu2HnEpz84dwg9rG8lKOfz/4m8JBPnTR2s4/90JjKGaBf0uY8hF3+fEft4YGGLM4coSkIuaGhu4W59kToMP+Irb4eyVM/IMXvvYz6VbqzltaK7b4URU6aYN3PJaKZ9srGR3wY1MmnAuJw49xu2wjOkVLAG5qGzzOvKB2AxvvAO0x6j8dMZICVtXBmGo+y/HRsrC1/6PIxf+gCFyPVdddgOTxvyXq2syGdPbWAJyUcXWEvKBpNwit0PZR3piHI/4H2fH6iHA4ZeAgoEA8568lZO2PsuK+NHcdtXV9BvgrT8CjOkNvDH2FxCRiSKyWkRKROTOduoTRORFp36eiBS1qrvLKV8tIhM66lNEBjl9lDh9xkf8BNtRt2M9ABn9D/YWuju2pxxJ/92rOm7YwzTU1bLkl1/mpK3PMi97MkO/+x79Bgx1OyxjeiVPJCAR8QGPAucRmoFkmoiMbNPsWqBCVYcADwMPOvuOBKYCo4CJwGMi4uugzweBh52+Kpy+oy6wayMAufneS0DNfY+hH2WUby91O5SwqW8K8Mj0Jzl69xzmDr+DcTf+kTgbVm2MazyRgIBxQImqrlXVJmAGMKlNm0nAM872S8B4Cd2wnwTMUNVGVV0HlDj9tduns8/ZTh84fU6O1Imt3lbDL95aRVVd8351r6Z8hUviHiHeg3OupQ4eB0DpijkuRxIedY3NfO3p+Ty6ZSjvnP06J067e+/EmsYYd3jlJzAf2NTqc6lT1m4bVW0BqoDsg+x7oPJsoNLp40DHAkBErheRhSKysKysnRltO2FXyTzO/Ogqtq3ZfybtDVVBNNOb75gMGHUiQRXq1od/BvBoa25qZMWvJxGz/kMevnQME8442MSdxpho8UoC8iRVfUJVi1W1ODf30IYj56YmcnzM5+zesv/zlPFlT3NO3GfdDTMiUtOzuCn5QZ6X890OpVs0GOTTx75Kcf1H3HJcApOPtcEGxniFVxLQZqD1W38FTlm7bUQkltAc4eUH2fdA5eVAhtPHgY4VNrkFQwBoKt+wT3kwEODqppmMCXp3zrX4AeNYsKWJnrxm1Lw//5BxlW8wt+BaTrjkFrfDMca04pUEtAAY6oxOiyc0qGBWmzazgGuc7SnAexr6zTgLmOqMkhsEDAXmH6hPZ5/3+c8CK9cAr0bqxNIyc9mtfqRq0z7lO7dtJF4CxGR69237U3PruLLuT2wtXet2KIdk+cdvULzmtyxKPp0Tvv6Q2+EYY9rwRAJynsfcBLwFrARmqupyEfmRiOxZSGU6kC0iJcC3gTudfZcDM4EVwD+AG1U1cKA+nb7uAL7t9JXt9B0REhPDDl9f4ndv2ad81+YSAPw5RZE6dLcdmxvDt2L/xpZP33Y7lC4rq2lkyezn2OLLY+j1z9iAA2M8yDMvoqrqG8Abbcp+0Gq7gQPMV6Oq9wP7LWzeXp9O+VpCo+SiYl3yMVQ1Kse2KqveHHomlDXgYCtVuqto5PHU/DWRwIY5wDfdDqfTVJW7X/mMfzZfyevX/YzU9Cy3QzLGtMP+LIyCOSPu4o66KwgE//Mspb58I40aR97A4S5GdnC+2FjWJY6mb8Uit0Ppko/e/DNfrPyU700YwdCiAW6HY4w5AEtAUTA4N4WmliBbKuv3lv0p7jKmpP+Z2DhXJmHotLp+4ygKbqJy5za3Q+mUnds2cvT87/Cr1D/z9VNsfVJjvMwSUBSMjt3MvxNuZtfSN/eWleyoobCvN5bhPpi04adRrYmsWbHY7VA6Zd0Lt+PXJrK/8mtiYmxiUWO8zBJQFBQOGESB7KR+0xIAqip2ck/1j/hSsvdHlw0eO55xLdN5p3ag26F0aMWcNzm+6m0+KbiKQltSwRjPswQUBRk5/dgifYjfvhiATcs/5hzfIoZm+twNrBP8CfGMKshk7rpdbodyUMFAAP/sO9lGLmMu/7Hb4RhjOsESUJRsSz6SvNoVANSWzAWgcNTJbobUaVdkr+Hn2//b08+B/v7pet5uGs3G4+8mMTnV7XCMMZ1gCShKmvJPII8ySks+I33z+5T4jiAjp5/bYXXKyEH5DI/ZxBfz/u52KO1qagnyi/c28FqfGyg+72tuh2OM6SRLQFEy8OQpPNcynjc/XsSwppXszDvT7ZA6bciY06kimcCad90OpV0fv/YUgyrn8r0Jw23ggTE9iCWgKMkbOJy3Bt3B31bWsIzBFE34H7dD6rTYuHi+SCmmqHIuGgy6Hc4+mhobOHLJT7kz+XVOH5rjdjjGmC6wBBRFD15yNKOOO42dU9+kX+EQt8PpksDg8fRhF+tXLnA7lH0sfuMP9KWclpNvs+l2jOlhPDMVT2/QPyORn0/pmcODB5xwAbM+fZOG9ZUMGuV2NCHBQIC+n/2eL3yDOOqMi90OxxjTRfYno+mUvvmDeTznHl7c6J0RZkvefYGBwVIqxt5oVz/G9ED2U2s67ctH51G+cQXbtkVs+aQu+dfKzXwqIxlz7jUdNzbGeI4lINNpFw5s4YOE21n/3lNuh0LJjhoe3jqaj0//k+fn0zPGtM8SkOm0wsEj+MI3mIy1r7sdCu++9zbJvgCXHe/dBf2MMQdnCch0yY4B5zGiZSXbNq5xLYbdNZVcvvJG/pA7k5yUBNfiMMZ0jyUg0yUDTrsCgHUfPOtaDMvfeZZUqSfrpKtdi8EY032WgEyX5A8exYq40eSun4WqdrxDBCSv/AubpD/Dj/+SK8c3xoSHJSDTZaWnPsDFdXczZ2151I+9dcNqRjUtpXTAhTb02pgezn6CTZedfvIp4M/gubkbon7skn/NBGDgmTbpqDE9nSUg02X+OB+3jq7nhtXXsWXtiqgdNxhU7t1+Krfn/J7+g0ZE7bjGmMiwBGQOyQUnj2GEbGDTG7+IyvHqdlfz6JP/x9qddZxy8mlROaYxJrJsLjhzSHL7FzE/ayJjyl5j26aSiE6uum1TCbVPX8r1LRvIHP93Ljo2P2LHMsZEj10BmUNWOPleBGXjX/83YsdYtfBdYqePp1/LFlad8ThXnnMSIrbmjzGHA9cTkIhkichsEVnj/Jt5gHbXOG3WiMg1rcqPE5HPRKRERH4rzm+nA/UrImeKSJWILHa+fhCdMz385A0czqJ+Uziu4k0+Xzo/7P0vePUxBr92KQ3ip3zq6xxz9qVhP4Yxxj2uJyDgTuBdVR0KvOt83oeIZAH3AicA44B7WyWqx4FvAEOdr4md6PdDVR3jfP0oAufUaxw59X5+FvvffPv9eloC4VmsrjkQ5Cd/X8EH8z9lTcIoUm78JwOPPC4sfRtjvMMLCWgS8Iyz/QwwuZ02E4DZqrpLVSuA2cBEEckD0lR1robeiny21f6d6dd0U3pmDmMn38qyrbU88uaibve3dcNq7v3dkzz573XUHn8zw74zm4ycfmGI1BjjNV5IQH1VdauzvQ3o206bfGBTq8+lTlm+s922vKN+TxKRJSLypogccHk1EbleRBaKyMKysrLOn1Evc95Redw+uo6vLriQT99+7pD7+fStZ0j641ncUPEQj087mh9OPoq4eJvrzZjDVVQSkIi8IyLL2vma1LqdcxUT9vld2vS7CBioqscAvwP+dpD9nlDVYlUtzs3NDXdYh5VvXHweO+LyGfnRrXz2r1e7tO/OLRtY9Isvc+ycm9nhy8N39cucd4zNcm3M4S4qCUhVv6Sqo9v5ehXY7txKw/l3RztdbAZa/0YqcMo2O9ttyzlQv6paraq1zvYbQJyI5ITtZHspf1IKfW54jS2+fEa8+zXmvfgzgoHAQffZ3djCH1//kIT/O4GRtXOZM/hmiu74mPwjRkcpamOMm7xwC24WsGdU2zVAe38+vwWcKyKZzuCDc4G3nFts1SJyojP67epW+7fbr4j0azVSbhyh70H0JzU7DGXk9CPrW++yInEsJ6x8gEd+81P+sWwbdU0te9s01O9mxdx/8PJTv+CkB97lhx9W8UHmFMqufJeTrv6x3XIzphcRt2Y03huASDYwExgAbAAuVdVdIlIM3KCq1zntvg7c7ex2v6r+0SkvBp4GEoE3gW+pqh6k35uAbwItQD3wbVX9uKM4i4uLdeHCheE67cNaMBBg3uvT+e6ygZRWt3Bz7CtcHvsBQRFygruIlxaqNYn7hr3CVacN59gB7Y68N8YcBkTkE1UtbrfO7QTUU1gC6rqWQJCPvihn97xnyd05D9Egzcl5+AedwODiCaRn2XM1Yw53B0tANhWPiZhYXwxnDMuFYbe7HYoxxoO88AzIGGNML2QJyBhjjCssARljjHGFJSBjjDGusARkjDHGFZaAjDHGuMISkDHGGFdYAjLGGOMKmwmhk0SkjNCUPociB9gZxnB6Ajvn3qG3nXNvO1/o/jkPVNV2pz2xBBQFIrLwQFNRHK7snHuH3nbOve18IbLnbLfgjDHGuMISkDHGGFdYAoqOJ9wOwAV2zr1Dbzvn3na+EMFztmdAxhhjXGFXQMYYY1xhCcgYY4wrLAFFmIhMFJHVIlIiIne6HU+kichTIrJDRJa5HUs0iEihiLwvIitEZLmI3OJ2TJEmIn4RmS8iS5xz/qHbMUWLiPhE5FMR+bvbsUSDiKwXkc9EZLGIhH1JaHsGFEEi4gM+B84BSoEFwDRVXeFqYBEkIqcDtcCzqjra7XgiTUTygDxVXSQiqcAnwOTD/L+xAMmqWisiccC/gVtUda7LoUWciHwbKAbSVPXLbscTaSKyHihW1Yi8fGtXQJE1DihR1bWq2gTMACa5HFNEqeq/gF1uxxEtqrpVVRc52zXASiDf3agiS0NqnY9xztdh/5esiBQA5wNPuh3L4cISUGTlA5tafS7lMP/l1JuJSBFwLDDP5VAizrkVtRjYAcxW1cP+nIFfA98Dgi7HEU0KvC0in4jI9eHu3BKQMWEgIinAX4FbVbXa7XgiTVUDqjoGKADGichhfbtVRL4M7FDVT9yOJcpOVdWxwHnAjc4t9rCxBBRZm4HCVp8LnDJzGHGeg/wVeF5VX3Y7nmhS1UrgfWCiy6FE2inAhc4zkRnA2SLynLshRZ6qbnb+3QG8QuixQthYAoqsBcBQERkkIvHAVGCWyzGZMHIeyE8HVqrqr9yOJxpEJFdEMpztREKDbFa5GlSEqepdqlqgqkWEfo7fU9UrXQ4rokQk2RlYg4gkA+cCYR3dagkoglS1BbgJeIvQw+mZqrrc3agiS0ReAOYAw0WkVESudTumCDsFuIrQX8SLna//cjuoCMsD3heRpYT+yJqtqr1iWHIv0xf4t4gsAeYDr6vqP8J5ABuGbYwxxhV2BWSMMcYVloCMMca4whKQMcYYV1gCMsYY4wpLQMYYY1xhCcgYjxGR7FZDureJyGZnu1ZEHnM7PmPCxYZhG+NhInIfUKuqD7kdizHhZldAxvQQInLmnnVoROQ+EXlGRD4UkQ0icrGI/NxZu+UfzvRAiMhxIvJPZzLJt5zlI4zxBEtAxvRcRwBnAxcCzwHvq+pRQD1wvpOEfgdMUdXjgKeA+90K1pi2Yt0OwBhzyN5U1WYR+QzwAXumSfkMKAKGA6OB2aEp6/ABW12I05h2WQIypudqBFDVoIg0638e6AYJ/WwLsFxVT3IrQGMOxm7BGXP4Wg3kishJEFo2QkRGuRyTMXtZAjLmMOUsAz8FeNCZ0XgxcLKrQRnTig3DNsYY4wq7AjLGGOMKS0DGGGNcYQnIGGOMKywBGWOMcYUlIGOMMa6wBGSMMcYVloCMMca44v8Byd+T1MLStjUAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "pylab.plot(times, (h_exp_val-exact_h_exp_val), label=\"VarQITE\")\n", + "pylab.plot(times, (h_exp_val_eff-exact_h_exp_val_eff), label=r\"VarQITE$_{eff}$\", linestyle='--')\n", + "pylab.xlabel(\"Time\")\n", + "pylab.ylabel(r\"$\\Delta \\langle H \\rangle$\")\n", + "pylab.legend(loc=\"upper right\");" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ejlBv7Qi0C1-" + }, + "source": [ + "In this task, the accuracies of `VarQITE` with both gradient methods are very close, but `ReverseEstimatorGradient()` takes a considerably shorter time to run.\n", + "\n", + "We can do the same comparison for `VarQRTE` for simulating the magnetization of the Ising model." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "m-tp9kdHmy55" + }, + "source": [ + "## Real Time Evolution\n", + "Real time evolution is more suitable for tasks such as simulating quantum dynamics. For example, one can use `VarQRTE` to get time evolving expectation values of the magnetization.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "TPGhF7xfodnT" + }, + "source": [ + "### VarQRTE\n", + "Again, the first step is to select an ansatz." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 191 + }, + "id": "l7hz6wSLnZx3", + "outputId": "b23ea3f0-d19c-4def-a494-72fa0d5d40cf" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ansatz = EfficientSU2(hamiltonian.num_qubits, reps=1)\n", + "ansatz.decompose().draw('mpl')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Hil3c_xfubIw" + }, + "source": [ + "We set all initial parameters as $\\frac{\\pi}{2}$." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "id": "thWw2mahnipB" + }, + "outputs": [], + "source": [ + "init_param_values = {}\n", + "\n", + "for i in range(len(ansatz.parameters)):\n", + " init_param_values[ansatz.parameters[i]] = np.pi/2 # initialize the parameters which also decide the initial state" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "i18irpxD4ETl" + }, + "source": [ + "We also define an initial state:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "4AsVk0Gj3-KQ", + "outputId": "60460d22-a873-4c1c-a034-a5b62c305526" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Statevector([-5.00000000e-01+0.00000000e+00j,\n", + " -5.00000000e-01-5.55111512e-17j,\n", + " 0.00000000e+00-5.00000000e-01j,\n", + " 1.66533454e-16+5.00000000e-01j],\n", + " dims=(2, 2))\n" + ] + } + ], + "source": [ + "init_state = Statevector(ansatz.assign_parameters(init_param_values))\n", + "print(init_state)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-ee7tApy4lsp" + }, + "source": [ + "In order to use the real time McLachlan principle, we instantiate the `RealMcLachlanPrinciple` class." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "id": "U8ytm_9g4kkx" + }, + "outputs": [], + "source": [ + "from qiskit_algorithms.time_evolvers.variational import RealMcLachlanPrinciple\n", + "\n", + "var_principle = RealMcLachlanPrinciple()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "qknpQG8LFRdX" + }, + "source": [ + "We also set the target time as $t=10$, and set the auxiliary operator to be the magnetization operator. The following steps are similar to `VarQITE`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "id": "Yh7vyZr62ubD" + }, + "outputs": [], + "source": [ + "aux_ops = [magnetization]" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "id": "-o2B3533nqsU" + }, + "outputs": [], + "source": [ + "from qiskit_algorithms import VarQRTE\n", + "\n", + "time = 10.0\n", + "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)\n", + "var_qrte = VarQRTE(ansatz, init_param_values,var_principle, Estimator())\n", + "evolution_result_re = var_qrte.evolve(evolution_problem)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ByiDyBuia1fN" + }, + "source": [ + "We can also obtain the exact solution with `SciPyRealEvolver`. We first create the corresponding initial state for the exact classical method." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "id": "yDWL-Zd5oQwH" + }, + "outputs": [], + "source": [ + "init_circ = ansatz.assign_parameters(init_param_values)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "SimuqpjpbHuU" + }, + "source": [ + "`SciPyRealEvolver` can help us get the classical exact result." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "id": "ac4twWUqonXm" + }, + "outputs": [], + "source": [ + "from qiskit_algorithms import SciPyRealEvolver\n", + "\n", + "evolution_problem = TimeEvolutionProblem(hamiltonian, time, initial_state = init_circ, aux_operators=aux_ops)\n", + "rtev = SciPyRealEvolver(1001)\n", + "sol = rtev.evolve(evolution_problem)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "M2hl_f2Y67tu" + }, + "source": [ + "We can compare the results, where $m_z$ represents the magnetization." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "02oeqzHDotYT", + "outputId": "2b95d596-f9be-43cc-f1f0-18c1f13dc47d" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "mz_exp_val_re = np.array([ele[0][0] for ele in evolution_result_re.observables])\n", + "exact_mz_exp_val_re = sol.observables[0][0].real\n", + "times = evolution_result_re.times\n", + "pylab.plot(times, mz_exp_val_re, label= \"VarQRTE\")\n", + "pylab.plot(times, exact_mz_exp_val_re , label= \"Exact\", linestyle='--')\n", + "pylab.xlabel(\"Time\")\n", + "pylab.ylabel(r\"$\\langle m_z \\rangle$\")\n", + "pylab.legend(loc=\"upper right\");" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "korN4ZZv8j_8" + }, + "source": [ + "### Efficient Way to run VarQRTE\n", + "\n", + "Similarly, we can set `qpt` as `ReverseQGT()` and `gradient` as `ReverseEstimatorGradient()` to speed up the calculation." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "id": "gnBS19NQ85cn" + }, + "outputs": [], + "source": [ + "from qiskit_algorithms.gradients import DerivativeType\n", + "\n", + "var_principle = RealMcLachlanPrinciple(qgt=ReverseQGT() , gradient=ReverseEstimatorGradient(derivative_type=DerivativeType.IMAG))\n", + "time = 10.0\n", + "evolution_problem = TimeEvolutionProblem(hamiltonian, time, aux_operators=aux_ops)\n", + "var_qrte = VarQRTE(ansatz, init_param_values,var_principle, Estimator())\n", + "evolution_result_re_eff = var_qrte.evolve(evolution_problem)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "IriOFWu89iTX", + "outputId": "1160c308-3d08-490f-a595-325433794117", + "tags": [ + "nbsphinx-thumbnail" + ] + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "mz_exp_val_re_eff = np.array([ele[0][0] for ele in evolution_result_re_eff.observables])\n", + "pylab.plot(times, mz_exp_val_re_eff, label= r\"VarQRTE$_{eff}$\")\n", + "pylab.plot(times, exact_mz_exp_val_re , label= \"Exact\", linestyle='--')\n", + "pylab.xlabel(\"Time\")\n", + "pylab.ylabel(r\"$\\langle m_z \\rangle$\")\n", + "pylab.legend(loc=\"upper right\");" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-IHBehQVAfZm" + }, + "source": [ + "Again, the accuracies of `VarQRTE` with both gradient methods are very similar, while the `ReverseEstimatorGradient()` shows a speedup of about $21\\%$ in this execution." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "ESuUu7jILMQn", + "outputId": "e3f76d34-ef66-47d8-f4a4-9f20713ba8e7" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "pylab.plot(times, (mz_exp_val_re-exact_mz_exp_val_re), label= \"VarQRTE\")\n", + "pylab.plot(times, (mz_exp_val_re_eff-exact_mz_exp_val_re), label= r\"VarQRTE$_{eff}$\", linestyle='--')\n", + "pylab.xlabel(\"Time\")\n", + "pylab.ylabel(r\"$\\Delta \\langle m_z \\rangle$\")\n", + "pylab.legend(loc=\"upper right\");" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 555 }, + "id": "tFR-8_hIvuwz", + "outputId": "d9c1cc74-52e6-47be-e57c-26e032104636" + }, + "outputs": [ { - "cell_type": "code", - "execution_count": 29, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 449 - }, - "id": "ESuUu7jILMQn", - "outputId": "e3f76d34-ef66-47d8-f4a4-9f20713ba8e7" - }, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } + "data": { + "text/html": [ + "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Fri Aug 18 16:53:22 2023 CEST
" ], - "source": [ - "pylab.plot(times, (mz_exp_val_re-exact_mz_exp_val_re), label= \"VarQRTE\")\n", - "pylab.plot(times, (mz_exp_val_re_eff-exact_mz_exp_val_re), label= r\"VarQRTE$_{eff}$\", linestyle='--')\n", - "pylab.xlabel(\"Time\")\n", - "pylab.ylabel(r\"$\\Delta \\langle m_z \\rangle$\")\n", - "pylab.legend(loc=\"upper right\");" + "text/plain": [ + "" ] + }, + "metadata": {}, + "output_type": "display_data" }, { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 555 - }, - "id": "tFR-8_hIvuwz", - "outputId": "d9c1cc74-52e6-47be-e57c-26e032104636" - }, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "" - ], - "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.1
qiskit-aer0.12.0
qiskit-ibmq-provider0.20.2
qiskit0.43.1
System information
Python version3.10.12
Python compilerGCC 9.4.0
Python buildmain, Jun 7 2023 12:45:35
OSLinux
CPUs1
Memory (Gb)12.678398132324219
Fri Jun 16 00:10:15 2023 UTC
" - ] - }, - "metadata": {} - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "" - ], - "text/html": [ - "

This code is a part of Qiskit

© Copyright IBM 2017, 2023.

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.

" - ] - }, - "metadata": {} - } + "data": { + "text/html": [ + "

This code is a part of Qiskit

© Copyright IBM 2017, 2023.

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.

" ], - "source": [ - "import qiskit.tools.jupyter\n", - "%qiskit_version_table\n", - "%qiskit_copyright" + "text/plain": [ + "" ] + }, + "metadata": {}, + "output_type": "display_data" } - ], - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "display_name": "Python 3", - "name": "python3" - }, - "language_info": { - "name": "python" - } + ], + "source": [ + "import qiskit.tools.jupyter\n", + "%qiskit_version_table\n", + "%qiskit_copyright\n" + ] + } + ], + "metadata": { + "celltoolbar": "Edit Metadata", + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" }, - "nbformat": 4, - "nbformat_minor": 0 -} + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} \ No newline at end of file diff --git a/docs/tutorials/12_gradients_framework.ipynb b/docs/tutorials/12_gradients_framework.ipynb index 174a15ee..71e9863d 100644 --- a/docs/tutorials/12_gradients_framework.ipynb +++ b/docs/tutorials/12_gradients_framework.ipynb @@ -1,7 +1,6 @@ { "cells": [ { - "attachments": {}, "cell_type": "markdown", "metadata": { "collapsed": true, @@ -10,11 +9,11 @@ } }, "source": [ - "# Qiskit Gradient Framework using Primitives\n", - "This tutorial demonstrates the use of the `qiskit.algorithms.gradients` module to evaluate quantum gradients using the [Qiskit Primitives](https://qiskit.org/documentation/apidoc/primitives.html).\n", + "# Gradient Framework\n", + "This tutorial demonstrates the use of the `qiskit_algorithms.gradients` module to evaluate quantum gradients using the [Qiskit Primitives](https://qiskit.org/documentation/apidoc/primitives.html).\n", "\n", "## Introduction\n", - "The gradient frameworks allows the evaluation of quantum gradients (see [Schuld et al.](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.032331) and [Mari et al.](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.012405)). \n", + "The gradient frameworks allows the evaluation of quantum gradients (see [Schuld et al.](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.032331) and [Mari et al.](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.012405)).\n", "Besides gradients of expectation values of the form\n", "$$ \\langle\\psi\\left(\\theta\\right)|\\hat{O}\\left(\\omega\\right)|\\psi\\left(\\theta\\right)\\rangle $$\n", "and sampling probabilities of the form\n", @@ -23,7 +22,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -37,13 +35,12 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "## The `algorithms.gradients` Framework\n", + "## The `qiskit_algorithms.gradients` Framework\n", "\n", - "The `algorithms.gradients` module contains tools to compute both circuit gradients and circuit metrics. The gradients extend the `BaseEstimatorGradient` and `BaseSamplerGradient` base classes. These are abstract classes on top of which different gradient methods have been implemented. The methods currently available in this module are:\n", + "The `qiskit_algorithms.gradients` module contains tools to compute both circuit gradients and circuit metrics. The gradients extend the `BaseEstimatorGradient` and `BaseSamplerGradient` base classes. These are abstract classes on top of which different gradient methods have been implemented. The methods currently available in this module are:\n", "- Parameter Shift Gradients\n", "- Finite Difference Gradients\n", "- Linear Combination of Unitaries Gradients\n", @@ -52,7 +49,7 @@ "Additionally, the module offers reverse gradients for efficient classical computations.\n", "\n", "The metrics available are based on the notion of the Quantum Geometric Tensor (QGT). There is a `BaseQGT` class (`Estimator`-based) on top of which different QGT methods have been implemented:\n", - "- Linear Comination of Unitaries QGT\n", + "- Linear Combination of Unitaries QGT\n", "- Reverse QGT (classical)\n", "As well as a Quantum Fisher Information class (QFI) that is initialized with a reference QGT implementation from the above list." ] @@ -73,11 +70,10 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "
The outline of the qiskit.algorithms.gradients framework
" + "
The outline of the qiskit_algorithms.gradients framework
" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "slideshow": { @@ -113,11 +109,10 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "## Gradient Evaluation of Quantum Circuits \n", + "## Gradient Evaluation of Quantum Circuits\n", "- Let's say that we want to use one of our `Estimator` gradients classes, then we need a quantum state $\\vert\\psi(\\theta)\\rangle$ and a Hamiltonian H acting as an observable. For the Sampler gradients, we just need a quantum state." ] }, @@ -130,14 +125,14 @@ }, { "cell_type": "code", - "execution_count": 65, + "execution_count": 1, "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -175,7 +170,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -183,15 +177,15 @@ "\n", "#### Using Estimator\n", "Given a Hermitian operator $g$ with two unique eigenvalues $\\pm r$ which acts as generator for a parameterized quantum gate $$G(\\theta)= e^{-i\\theta g}.$$\n", - "Then, quantum gradients can be computed by using eigenvalue $r$ dependent shifts to parameters. \n", + "Then, quantum gradients can be computed by using eigenvalue $r$ dependent shifts to parameters.\n", "All [standard, parameterized Qiskit gates](https://github.com/Qiskit/qiskit-terra/tree/master/qiskit/circuit/library/standard_gates) can be shifted with $\\pi/2$, i.e.,\n", - " $$ \\frac{\\partial\\langle\\psi\\left(\\theta\\right)|\\hat{O}\\left(\\omega\\right)|\\psi\\left(\\theta\\right)\\rangle}{\\partial\\theta} = \n", + " $$ \\frac{\\partial\\langle\\psi\\left(\\theta\\right)|\\hat{O}\\left(\\omega\\right)|\\psi\\left(\\theta\\right)\\rangle}{\\partial\\theta} =\n", " \\frac{\\langle\\psi\\left(\\theta+\\pi/2\\right)|\\hat{O}\\left(\\omega\\right)|\\psi\\left(\\theta+\\pi/2\\right)\\rangle -\\langle\\psi\\left(\\theta-\\pi/2\\right)|\\hat{O}\\left(\\omega\\right)|\\psi\\left(\\theta-\\pi/2\\right)\\rangle }{ 2}.$$" ] }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -204,7 +198,7 @@ ], "source": [ "from qiskit.primitives import Estimator\n", - "from qiskit.algorithms.gradients import ParamShiftEstimatorGradient\n", + "from qiskit_algorithms.gradients import ParamShiftEstimatorGradient\n", "\n", "#Define the estimator\n", "estimator = Estimator()\n", @@ -218,7 +212,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -229,17 +222,17 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 3, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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\n", 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" ] }, - "execution_count": 62, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -261,7 +254,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -274,7 +267,7 @@ ], "source": [ "from qiskit.primitives import Sampler\n", - "from qiskit.algorithms.gradients import ParamShiftSamplerGradient\n", + "from qiskit_algorithms.gradients import ParamShiftSamplerGradient\n", "\n", "param_vals = [[np.pi/4, np.pi/2]]\n", "sampler = Sampler()\n", @@ -284,15 +277,13 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "> **Note:** All the following methods in this tutorial are explained using the `Estimator` class to evaluate the gradients, but, in an analogous way to the Parameter Shift gradients just introduced, the method explanation can also be applied to `Sampler`-based gradients. Both versions are available in `algorithms.gradients`." + "> **Note:** All the following methods in this tutorial are explained using the `Estimator` class to evaluate the gradients, but, in an analogous way to the Parameter Shift gradients just introduced, the method explanation can also be applied to `Sampler`-based gradients. Both versions are available in the gradients module." ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "slideshow": { @@ -301,8 +292,8 @@ }, "source": [ "### Linear Combination of Unitaries Gradients\n", - "Unitaries can be written as $U\\left(\\omega\\right) = e^{iM\\left(\\omega\\right)}$, where $M\\left(\\omega\\right)$ denotes a parameterized Hermitian matrix. \n", - "Further, Hermitian matrices can be decomposed into weighted sums of Pauli terms, i.e., $M\\left(\\omega\\right) = \\sum_pm_p\\left(\\omega\\right)h_p$ with $m_p\\left(\\omega\\right)\\in\\mathbb{R}$ and $h_p=\\bigotimes\\limits_{j=0}^{n-1}\\sigma_{j, p}$ for $\\sigma_{j, p}\\in\\left\\{I, X, Y, Z\\right\\}$ acting on the $j^{\\text{th}}$ qubit. Thus, the gradients of \n", + "Unitaries can be written as $U\\left(\\omega\\right) = e^{iM\\left(\\omega\\right)}$, where $M\\left(\\omega\\right)$ denotes a parameterized Hermitian matrix.\n", + "Further, Hermitian matrices can be decomposed into weighted sums of Pauli terms, i.e., $M\\left(\\omega\\right) = \\sum_pm_p\\left(\\omega\\right)h_p$ with $m_p\\left(\\omega\\right)\\in\\mathbb{R}$ and $h_p=\\bigotimes\\limits_{j=0}^{n-1}\\sigma_{j, p}$ for $\\sigma_{j, p}\\in\\left\\{I, X, Y, Z\\right\\}$ acting on the $j^{\\text{th}}$ qubit. Thus, the gradients of\n", "$U_k\\left(\\omega_k\\right)$ are given by\n", "\n", "$$\\frac{\\partial U_k\\left(\\omega_k\\right)}{\\partial\\omega_k} = \\sum\\limits_pi \\frac{\\partial m_{k,p}\\left(\\omega_k\\right)}{\\partial\\omega_k}U_k\\left(\\omega_k\\right)h_{k_p}$$\n", @@ -312,7 +303,7 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -324,7 +315,7 @@ } ], "source": [ - "from qiskit.algorithms.gradients import LinCombEstimatorGradient\n", + "from qiskit_algorithms.gradients import LinCombEstimatorGradient\n", "\n", "# Evaluate the gradient of the circuits using linear combination of unitaries\n", "state_grad = LinCombEstimatorGradient(estimator)\n", @@ -352,7 +343,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -364,7 +355,7 @@ } ], "source": [ - "from qiskit.algorithms.gradients import FiniteDiffEstimatorGradient\n", + "from qiskit_algorithms.gradients import FiniteDiffEstimatorGradient\n", "\n", "state_grad = FiniteDiffEstimatorGradient(estimator, epsilon = 0.001)\n", "\n", @@ -374,7 +365,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -385,7 +375,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -397,7 +387,7 @@ } ], "source": [ - "from qiskit.algorithms.gradients import SPSAEstimatorGradient\n", + "from qiskit_algorithms.gradients import SPSAEstimatorGradient\n", "\n", "state_grad = SPSAEstimatorGradient(estimator, epsilon = 0.001, batch_size=10, seed=50)\n", "\n", @@ -407,7 +397,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "slideshow": { @@ -416,11 +405,11 @@ }, "source": [ "## Circuit Quantum Geometric Tensor (QGTs)\n", - "[Quantum Geometric Tensor](https://arxiv.org/abs/1012.1337) is a metric in geometric quantum computing and can be regarded as a metric measuring the geodesic distance of points lying on the Bloch sphere. Its real and imaginary parts give different informations about the quantum state. \n", + "[Quantum Geometric Tensor](https://arxiv.org/abs/1012.1337) is a metric in geometric quantum computing and can be regarded as a metric measuring the geodesic distance of points lying on the Bloch sphere. Its real and imaginary parts give different information about the quantum state.\n", "\n", "The entries of the QGT for a pure state is given by\n", "\n", - "$$QGT_{kl}(\\theta) = \\langle\\partial_k\\psi(\\theta)|\\partial_l\\psi(\\theta)\\rangle-\\langle\\partial_k\\psi(\\theta)|\\psi(\\theta)\\rangle\\langle\\psi(\\theta)|\\partial_l\\psi(\\theta)\\rangle.$$ \n", + "$$QGT_{kl}(\\theta) = \\langle\\partial_k\\psi(\\theta)|\\partial_l\\psi(\\theta)\\rangle-\\langle\\partial_k\\psi(\\theta)|\\psi(\\theta)\\rangle\\langle\\psi(\\theta)|\\partial_l\\psi(\\theta)\\rangle.$$\n", "\n", "### Linear Combination QGT\n", "This method employs a linear combination of unitaries, as explained in the **Gradients** section." @@ -428,7 +417,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -442,7 +431,7 @@ } ], "source": [ - "from qiskit.algorithms.gradients import DerivativeType, LinCombQGT\n", + "from qiskit_algorithms.gradients import DerivativeType, LinCombQGT\n", "\n", "qgt = LinCombQGT(estimator, derivative_type=DerivativeType.COMPLEX)\n", "\n", @@ -455,13 +444,12 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### Quantum Fisher Information (QFI)\n", "\n", - "[Quantum Fisher Information](https://quantum-journal.org/papers/q-2020-05-25-269/) is a metric tensor which is representative for the representation capacity of a \n", + "[Quantum Fisher Information](https://quantum-journal.org/papers/q-2020-05-25-269/) is a metric tensor which is representative for the representation capacity of a\n", "parameterized quantum state $|\\psi\\left(\\theta\\right)\\rangle = V\\left(\\theta\\right)|\\psi\\rangle$ with input state $|\\psi\\rangle$, parametrized Ansatz $V\\left(\\theta\\right)$.\n", "\n", "The QFI can thus be evaluated from QGT as\n", @@ -475,7 +463,7 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -489,7 +477,7 @@ } ], "source": [ - "from qiskit.algorithms.gradients import QFI\n", + "from qiskit_algorithms.gradients import QFI\n", "\n", "#Define the QFI metric for the QGT\n", "qfi = QFI(qgt)\n", @@ -519,7 +507,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "slideshow": { @@ -527,26 +514,29 @@ } }, "source": [ - "Let's see an application of these gradient classes in a gradient-based optimization. We will use the Variational Quantum Eigensolver (VQE) algorith. First, the Hamiltonian and wavefunction ansatz are initialized." + "Let's see an application of these gradient classes in a gradient-based optimization. We will use the Variational Quantum Eigensolver (VQE) algorithm. First, the Hamiltonian and wavefunction ansatz are initialized." ] }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" - } + }, + "tags": [ + "nbsphinx-thumbnail" + ] }, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "
" + "
" ] }, - "execution_count": 61, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -555,9 +545,9 @@ "from qiskit.circuit import ParameterVector\n", "\n", "# Instantiate the system Hamiltonian\n", - "h2_hamiltonian = SparsePauliOp.from_list([('II', -1.05), \n", - " ('IZ', 0.39), \n", - " ('ZI', -0.39), \n", + "h2_hamiltonian = SparsePauliOp.from_list([('II', -1.05),\n", + " ('IZ', 0.39),\n", + " ('ZI', -0.39),\n", " ('ZZ', -0.01)])\n", "\n", "# This is the target energy\n", @@ -582,7 +572,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -600,7 +590,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 12, "metadata": { "slideshow": { "slide_type": "subslide" @@ -611,14 +601,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Result of Estimator VQE: -1.8199999998468706 \n", + "Result of Estimator VQE: -1.819999999752812 \n", "Reference: -1.85727503\n" ] } ], "source": [ - "from qiskit.algorithms.optimizers import CG\n", - "from qiskit.algorithms.minimum_eigensolvers import VQE, SamplingVQE\n", + "from qiskit_algorithms.optimizers import CG\n", + "from qiskit_algorithms import VQE, SamplingVQE\n", "\n", "#Conjugate Gradient algorithm\n", "optimizer = CG(maxiter=50)\n", @@ -643,19 +633,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can also use a classical optimizer to optimize the VQE. We'll use the `minimize` function from SciPy. " + "We can also use a classical optimizer to optimize the VQE. We'll use the `minimize` function from SciPy." ] }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Result of classical optimizer: -1.8199999999831082 \n", + "Result of classical optimizer: -1.819999999951288 \n", "Reference: -1.85727503\n" ] } @@ -672,7 +662,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 14, "metadata": { "slideshow": { "slide_type": "notes" @@ -682,7 +672,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.0
qiskit-aer0.12.0
qiskit-ignis0.7.1
qiskit-ibmq-provider0.20.2
qiskit0.43.0
System information
Python version3.8.10
Python compilerGCC 9.4.0
Python builddefault, Mar 13 2023 10:26:41
OSLinux
CPUs4
Memory (Gb)3.842151641845703
Tue May 30 19:13:50 2023 UTC
" + "

Version Information

SoftwareVersion
qiskit0.44.0
qiskit-terra0.25.0
qiskit_algorithms0.2.0
System information
Python version3.9.17
Python compilerClang 14.0.6
Python buildmain, Jul 5 2023 16:17:03
OSDarwin
CPUs8
Memory (Gb)64.0
Thu Aug 17 18:15:27 2023 CEST
" ], "text/plain": [ "" @@ -707,13 +697,14 @@ "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table\n", - "%qiskit_copyright" + "%qiskit_copyright\n" ] } ], "metadata": { + "celltoolbar": "Edit Metadata", "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -727,9 +718,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.10.2" } }, "nbformat": 4, "nbformat_minor": 1 -} +} \ No newline at end of file diff --git a/requirements-dev.txt b/requirements-dev.txt index f8c068a4..8264b70b 100644 --- a/requirements-dev.txt +++ b/requirements-dev.txt @@ -7,7 +7,7 @@ stestr>=2.0.0 pylatexenc>=1.4 ddt>=1.2.0,!=1.4.0,!=1.4.3 reno>=3.4.0 -Sphinx>=5.0 +Sphinx>=5.0,<7.2 #remove pin once issue is fixed nbsphinx qiskit-sphinx-theme~=1.14.0rc1 sphinx-design>=0.2.0 @@ -15,3 +15,11 @@ sphinxcontrib-spelling jupyter-sphinx discover rustworkx>=0.13 +qiskit-aer>=0.12 +networkx>=2.2 + +# Tweedledum is unmaintained and its existing Mac wheels are unreliable. If you +# manage to get a working install on a Mac the functionality should still work, +# but as a convenience this file won't attempt the install itself. +tweedledum; python_version<'3.11' and platform_system!="Darwin" +