Deprecates `PauliOp.commutes`

What is the expected enhancement?

Only PauliOp has commutes method among all OperatorBase. I notice that there are some problems with PauliOp.commutes thanks to Qiskit/qiskit-aqua#1415.

1. PauliOp.commutes checks qubit-wise commutation because it was originally introduced for AbelianGrouper. The method name looks misleading. Note that AbelianGrouper does not use it anymore and no other Aqua module use it.
2. PauliOp.commutes takes OperatorBase as argument, but, it always returns False if OperatorBase is not PauliOp. It does not check commutation with other operators. It causes the following behavior.

from qiskit.aqua.operators import X
print(X.commutes(X))
print(X.commutes(X.to_matrix_op()))

output

True
False

The second output False is not expected because X.to_matrix_op() is essentially equal to X.

It would be good to deprecate PauliOp.commutes because of the following reasons.

• No other Aqua module uses it.
• The method name and the behavior do not match now (qubit-wise commutation).
• It checks commutation with only PauliOp and it always returns False with other operators without checking commutation. Overall, I think PauliOp.commutes is misleading.

If users want to check commutation of Pauli operators, they can do it by using the primitives as follows.

from qiskit.aqua.operators import X, Z
a = X^X
b = Z^Z
print(a.primitive * b.primitive == b.primitive * a.primitive)

output

True

~~or using https://github.com/Qiskit/qiskit-terra/pull/5299.~~ (see https://github.com/Qiskit/qiskit-aqua/issues/1416#issuecomment-723728545)

[t-imamichi]

Yes, it makes sense to delete it. Because I used PauliOp.commutes for unit tests of test_abelian_grouper.py (this is the only use case of PauliOp.commutes in Qiskit), I need to replace it. I ask Hamamura-san to delete PauliOp.commutes and update test_abelian_grouper.py as part of #5537 because it introduces commutator function and related to this issue. https://github.com/Qiskit/qiskit-terra/blob/f53a4b0bd1c951b6b1ccc3c8c33eec6e9cf3288e/test/python/opflow/test_abelian_grouper.py#L50 https://github.com/Qiskit/qiskit-terra/blob/f53a4b0bd1c951b6b1ccc3c8c33eec6e9cf3288e/test/python/opflow/test_abelian_grouper.py#L92

[ikkoham]

+1

Sorry, my is_commutative is not for this purpose. (I made a mistake in the previous issue) To check the commutativity of Pauli, PauliTable.commutes is useful.

PauliTable(a.primitive).commutes(b.primitive)

(note that PauliTable will be deprecated.)