Add MidMeasureMP C++ implementation

[tomlqc]

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Context:
Native-execution of circuits with mid-measurements is enabled via the dynamic-one-shot transform. To support the transform, a device must implement methods to apply MidMeasureMP.

MidMeasureMP is a special kind of operation where a sample is drawn from the state vector probability distribution and a projector is applied to the state vector accordingly. It may also support options like reset and post-selection.

The most straightforward way to deal with the requirements is to enhance the state vector class StateVectorLQubit.

Description of the Change:

• Add method to obtain the probability in the z-basis on a given wire.
• Add RNG attribute.
• Add method to init the RNG attribute with a given seed.
• Add method to sample from a binomial distribution.
• Add method to collapse the state vector onto a given branch.
• Add method which implements the MidMeasureMP workflow.
• Add bindings to the MidMeasureMP method.

Benefits:

Possible Drawbacks:

Related GitHub Issues:

Related Shortcut Story:
[sc-57704]

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.71%. Comparing base (6c758e4) to head (9e76d5d).
Report is 1 commits behind head on master.

Additional details and impacted files

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[AmintorDusko]

Beautiful! You have my approval already, but please check my suggestions.

[dime10]

Looks good from my side 💯 So on the Catalyst side we move to just calling the sample and collapse function ourselves here (similar to what lightningqubit.py is doing) ?

[dime10]

Nice! So the seed has to be set on each measurement object right?

[tomlqc]

That's the current way in LQubit or GPU implementations (set randomly).