Commutation dag

[rmoyard]

Context:

This PR adds a

1. Function is_commuting checks if two operations commute, it does not use matrices multiplications but a truth table. It also uses some matrix multiplication for edge cases.

commutation = qml.is_commuting(qml.CNOT(wires=[0, 1]), qml.Toffoli(wires= [0, 1, 2]))

2. A DAG that represents the pairwise commutation structure of the quantum circuit.

def circuit():
    qml.CNOT(wires=[0, 1])
    qml.CNOT(wires=[0, 2])
    qml.PauliZ(wires=[0])
    qml.CNOT(wires=[2, 0])

dag = qml.transforms.commutation_dag(circuit)()

Benefits:
A commutation function that does not use matrices multiplication and takes any two operations as inputs. A new DAG that represents the commutation structure of quantum circuits and is useful for quantum circuits optimization.

[github-actions]

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[codecov]

Codecov Report

Merging #1712 (00c9af7) into master (d4931e7) will increase coverage by 0.05%.
The diff coverage is 99.68%.

@@            Coverage Diff             @@
##           master    #1712      +/-   ##
==========================================
+ Coverage   99.22%   99.27%   +0.05%     
==========================================
  Files         231      232       +1     
  Lines       18392    18708     +316     
==========================================
+ Hits        18249    18573     +324     
+ Misses        143      135       -8     

Impacted Files	Coverage Δ
pennylane/__init__.py	100.00% <ø> (ø)
pennylane/operation.py	95.99% <ø> (ø)
pennylane/templates/subroutines/qpe.py	100.00% <ø> (ø)
pennylane/transforms/commutation_dag.py	99.67% <99.67%> (ø)
pennylane/transforms/__init__.py	100.00% <100.00%> (ø)
pennylane/transforms/control.py	100.00% <100.00%> (ø)
pennylane/_device.py	97.98% <0.00%> (+0.33%)	⬆️
pennylane/ops/qubit/non_parametric_ops.py	100.00% <0.00%> (+0.44%)	⬆️
pennylane/_qubit_device.py	98.72% <0.00%> (+1.91%)	⬆️

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[antalszava]

[sc-15667]