[BUG] cancel_inverses does not cancel adjoint operators with different wire order that are symmetric on wires

[mudit2812]

Expected behavior

If I have an operator and it's adjoint applied next to each other, where they are both applied on the same set of wires, but not in the exact same wire order, I expect them to be cancelled if they are known to be symmetric on all wires.

Actual behavior

Such operators are not cancelled. This is because in qml.transforms.optimization.cancel_inverses._ops_equal, we explicitly check for wire equality. Later in the transform, we also check for wire symmetry, but by that point, operators are already no longer being considered for cancellation.

Additional information

No response

Source code

import pennylane as qml

op = qml.IsingXX(1.5, [0, 1])

tape = qml.tape.QuantumScript(
    [
        qml.IsingXX(1.5, [0, 1]),
        qml.adjoint(qml.IsingXX(1.5, [1, 0])),
    ],
)

[transformed_tape], _ = qml.transforms.cancel_inverses(tape)
print(transformed_tape.circuit)
[IsingXX(1.5, wires=[0, 1]), Adjoint(IsingXX(1.5, wires=[1, 0]))]

If I update qml.transforms.optimization.cancel_inverses._ops_equal to stop checking for equality, running the same code gives the following output:
[]

Tracebacks

No response

System information

pl dev

Existing GitHub issues

• I have searched existing GitHub issues to make sure the issue does not already exist.