Add support for mid-circuit measurement program capture

[mudit2812]

Context:
This PR is following up on the new program capture effort by adding support for capturing mid-circuit measurements. Currently, mid-circuit measurements can be captured, classically processed, and executed, with specific constraints, but cannot be used with qml.cond

Description of the Change:

• Add primitive for capturing qml.measure. This primitive's concrete implementation is basically the same as the original, where it queues a MidMeasureMP and returns a MeasurementValue, but its abstract eval returns a boolean integer tracer. Follow up work will take advantage of this.

Benefits:

• Mid-circuit measurements can be captured
• Arbitrary classical processing of MCMs can be captured. This includes functionality that is already available, as well as new functionality such as operations like jnp.sin(m), jnp.array([m1, m2]), and even jnp.max(jnp.array([m1, m2])! All of this can be captured, but not executed.
• Using mid-circuit measurements as gate parameters, eg. qml.RX(m, 0), can be captured, but not executed.
• Circuits containing mid-circuit measurements can be executed with qml.capture.enable(). This only works when the circuit does not classically process MCMs or applies qml.cond with MCMs in the predicate.
• Circuits collecting statistics on mid-circuit measurements or sequences of mid-circuit measurements can be captured and executed.

[mudit2812]

[sc-66783] [sc-69204] [sc-69668] [sc-69206] [sc-70055]

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.66%. Comparing base (0b0e212) to head (2959d55).
Report is 2 commits behind head on master.

Additional details and impacted files

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##           master    #6015      +/-   ##
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+ Coverage   99.52%   99.66%   +0.13%     
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  Files         430      430              
  Lines       41835    41452     -383     
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- Hits        41637    41312     -325     
+ Misses        198      140      -58     

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[PietropaoloFrisoni]

Seems pretty good! Just a few questions for my own understanding

[PietropaoloFrisoni]

LGTM

[dime10]

Nice work 💯

I'm guessing you abandoned cond(m, fun)()?

I also vaguely remember at the start you told me that other primitives that have been implemented didn't work with measure yet because it didn't exist, and that you would need to update those. Was that just the measurement processes of mcms or do you remember if there was anything else?

[mudit2812]

I'm guessing you abandoned cond(m, fun)()?

@dime10 That's in a different PR #6058 (though that needs to be updated as well)

I also vaguely remember at the start you told me that other primitives that have been implemented didn't work with measure yet because it didn't exist, and that you would need to update those. Was that just the measurement processes of mcms or do you remember if there was anything else?

It was just the measurement processes of MCMs, which is working in this PR.