Create and diagonalize mid-circuit measurements in conditionals

[lillian542]

Context:

• Currently, we can't correctly execute mid-circuit measurements inside Conditionals, so we need to get rid of those before we get to execution.
• The wrapper created in qml.cond doesn't return anything (so its not suitable for conditionally applying functions that return a MeasurementValue), and would need different handling for measurement functions than for an Operator or qfunc. We've decided to continue limiting it Operator and qfunc, and make a separate function just for measurements. It will be restricted in its inputs and outputs to make sure that what it returns is up-to-date with our current ability to process conditional MCMs, and it will be part of the ftqc module.

Description of the Change:

• We add cond_meas, with a call signature condition, true_fn, false_fn, to match qml.cond. Limitation on inputs will be informed by our limitations on what we can process for execution, and will currently be:

  • both true_fn and false_fn are required, and should create a MidMeasureMP (likely a parametrized one from the ftqc module) and return a MeasurementValue
  • the measurements on both branches must be applied to the same wire, and they must have the same reset and postselect attributes. Effectively this means only the measurement basis is conditional.

• We update the diagonalize_mcms transform to assume any Conditional containing a mid-circuit measurement is accompanied by its corresponding false_fn Conditional on the tape, and to diagonalize pairs of Conditionals together. The transform "factors out" the measurement as a Z-basis measurement, so it's no longer conditional, and applies conditional diagonalizing gates.

Benefits:

We can add a measurement to a circuit whose measurement basis is conditional on a previous measurement outcome, and retrieve the measurement value.

Possible Drawbacks:
It's restrictive, and it's limited to devices where we want to diagonalize the MCMs - but for now, it does what we need it to do.

[sc-84499]

[lillian542]

There's currently only support for conditional having two measurement outcomes, so this test and the previous test became the same test

[github-actions]

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[codecov]

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