Support joint measurement statistics for mid-circuit measurements

[mudit2812]

Context:
Adding support for advanced statistics for mid-circuit measurements. Users can now collect statistics on multiple measurement values. This can be done in two ways:

1. Using arithmetic operators to collect measurement values into a composite value. Eg: m0 * m1 - 2 * m3 or m1 > m0 or ~m0 & m1, etc. Available for qml.expval, qml.var, qml.sample, qml.counts.
2. Putting values in a list. This will give wire-like results. Eg: [m0, m1, m2]. Available for qml.sample, qml.probs, qml.counts.

Composite vs single MeasurementValues:
Composite MeasurementValues refers to MeasurementValues created by applying arithmetic/boolean operators to MeasurementValues as shown in the first point above. A single MeasurementValue is the output of qml.measure. Applying arithmetic/boolean operators to MeasurementValues also returns MeasurementValues.

Description of the Change:

• Add __repr__ to MeasurementValue and update MeasurementProcess.__repr__ appropriately.
• Update MeasurementProcess.eigvals to return outcomes of composed MeasurementValues when in use. If a list of MeasurementValues is given, the eigenvalues are just range(2**num_wires).
• Update QubitDevice to use the correct eigenvalues for composite MeasurementValues, and treat a list of MeasurementValues as wires.
• Update qml.expval and qml.var to disallow using lists of MeasurementValues, and allow composite MeasurementValue`s.
• Update qml.sample and qml.counts to allow both lists of MeasurementValues as well as composite MeasurementValues.
• Update qml.defer_measurements to disallow using qml.probs with composite MeasurementValues. This is done because the wire order of the composite value is not deterministic as the sorting is determined by the ID of the mid-circuit measurements, which are generated randomly. There isn't really a way to go around this at the moment, so I just blocked users from being able to do it. Besides, the results should be the same as when they use a list of MeasurementValues.

TODO: Add docs.

Benefits:

• Advanced mid-circuit statistics are now supported! And in multiple ways 😄

Possible Drawbacks:

Related GitHub Issues:

[github-actions]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (f435f87) 99.66% compared to head (16f5fac) 99.65%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4888      +/-   ##
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- Coverage   99.66%   99.65%   -0.02%     
==========================================
  Files         388      388              
  Lines       35379    35158     -221     
==========================================
- Hits        35262    35038     -224     
- Misses        117      120       +3     

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[mudit2812]

[sc-48303]

[timmysilv]

looks great, super comprehensive testing! got a few questions first but very nice 😎

[mudit2812]

Smol breaking change: qml.counts with a single MeasurementValue used to return strings for the keys, but now it returns integers. This is because of potentially having to process measurement values if unary operators are applied to it (eg. ~m0). I'm not very worried about this though since mid-circuit measurement support for qml.counts has only been out for 1 release. Thanks @timmysilv for catching this.

[timmysilv]

🎉

[albi3ro]

Impressive amount of work and an exciting new feature!