Add CancelInversesInterpreter for transforming plxpr

[mudit2812]

[sc-72846]

Context:
This PR adds a CancelInversesInterpreter to apply the cancel_inverses transform natively to plxpr.

Description of the Change:

• Add CancelInversesInterpreter to transform plxpr
• Note that the interpreter may reorder some primitives with disjoint wires. This does not impact the correctness of the circuit, and is a consequence of the implementation used.
• Currently, inner jaxpr of transform primitives will not be transformed.

Benefits:
cancel_inverses can be applied natively to plxpr.

Possible Drawbacks:
Potential operator reordering may confuse users.

Related GitHub Issues:

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.62%. Comparing base (579e70d) to head (4e75f95).
Report is 3 commits behind head on master.

Additional details and impacted files

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  Coverage   99.62%   99.62%            
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  Files         476      478     +2     
  Lines       44733    44973   +240     
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+ Hits        44564    44804   +240     
  Misses        169      169            

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[PietropaoloFrisoni]

Looks very good!

One question from me. Why isn't the operation canceled if I have a nested adjoint operation? Something like:

@CancelInversesInterpreter()
def f():
    qml.adjoint(qml.adjoint(qml.adjoint(qml.PauliX(0))))
    qml.PauliX(0)

>>> jaxpr = jax.make_jaxpr(f)()

{ lambda ; . let
    a:AbstractOperator() = PauliX[n_wires=1] 0
    b:AbstractOperator() = Adjoint a
    c:AbstractOperator() = Adjoint b
    _:AbstractOperator() = Adjoint c
    _:AbstractOperator() = PauliX[n_wires=1] 0
  in () }

If this is too much trouble to implement I am perfectly fine with postponing nested adjoint operators : )

[mudit2812]

@PietropaoloFrisoni the same also doesn't work with program capture disabled:

>>> print(qml.transforms.cancel_inverses(qml.tape.QuantumScript([qml.X(0), qml.adjoint(qml.adjoint(qml.adjoint(qml.X(0))))]))[0][0].circuit)
[X(0), Adjoint(Adjoint(Adjoint(X(0))))]

There are many cases in which cancel_inverses misses cancellations, but that is a separate issue 😅 . For now, we're at feature parity with program capture enabled and disabled, so it should be fine.

[PietropaoloFrisoni]

@mudit2812 I agree. This can probably be fixed automatically by ensuring that the adjoint of an adjoint operator returns the operator itself

[PietropaoloFrisoni]

🚀

[lillian542]

🚀