Equality of `SparsePauliOp`s with different orders

What is the expected enhancement?

Two SparsePauliOps with different orders are judges as “not equal” as follows.

from qiskit.quantum_info import SparsePauliOp

a = SparsePauliOp.from_list([('X', 1), ('Y', 2)])
b = SparsePauliOp.from_list([('Y', 2), ('X', 1)])
print(a == b)

output

False

Is it better to return True for this comparison or mention the order dependency in the docsting of __eq__?

@ikkoham also told me another case as follow. A redundant operator (coeff is 0) makes the comparison “not equal”.

from qiskit.quantum_info import SparsePauliOp

a = SparsePauliOp.from_list([('X', 1)])
b = SparsePauliOp.from_list([('X', 1), ('Y', 0)])
print(a == b)

False

If we need to compare two operator with different order and/or redundant operators, I think we need to call as follows. Is there any simple alternatives?

np.allclose((a - b).simplify().coeffs, [0])

Update

I updated SparsePauliOp in #7656 as follows.

• Leave __eq__ as is (elementary-wise comparison)
• Add equiv for equivalence check

[t-imamichi]

I tries a dict-based simplify with rust and it succeeded to improve the performance. So, I want to move it forward. Then, I need to deal with this issue #7657 to pass the unit test. As Julien suggested, there is a method to check the equivalence equiv, e.g., quantum_info.Pauli.equiv So, I’m thinking of the following plan. Do you have any suggestion?

• Leave SparsePauliOp.__eq__ as is (entrywise equality).
• Add SparsePauliOp.equiv as np.allclose((a - b).simplify().coeffs, [0]) (numerical equivalence)

If necessary, I will add rtol and atol of np.allclose to SparsePauliOp.equiv. FYI SparsePauliOp.__eq__ uses the default rtol and atol of np.allclose. https://github.com/Qiskit/qiskit-terra/blob/77219b5c7b7146b1545c5e5190739b36f4064b2f/qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py#L133

[t-imamichi]

I made #7656 so that it won’t break changes The summary is

• Leave SparsePauliOp.__eq__ as is (elementary-wise comparison)
• Add SparsePauliOp.equiv for equivalence check

PauliSumOp.equals used SparsePauliOp.__eq__ for equivalence check. It was a wrong algorithm theoretically, but it happened to work fine because SparsePauliOp.simplify sorted the operators (but, the API doc does not guarantee it). So I replace that part with the new SparsePauliOp.equiv in #7656 because I updated SparsePauliOp.simplify with a faster algorithm without sort. These changes do not break unit tests and they are also consistent with the API docs.