Operator equality with (clean) ancillas

[alexanderivrii]

Summary

This PR adds a new method equal_with_ancillas to the Operator class that checks whether the two operators are equal in the subspace where the ancilla qubits are zero.

While this is not immediately required for #12961 and #12911, it allows to check correctness of various synthesis methods and transformations in the presence of clean ancilla qubits. (The dirty ancilla qubits should be interpreted as regular qubits and don't matter).

Details and comments

Many thanks to @ShellyGarion for the idea how to implement this in a simple way.

Here is an example (which also appears in the release notes):

qc1 = QuantumCircuit(4)
qc1.x(0)
qc1.x(2)
qc1.cx(1, 0)
qc1.cx(1, 2)
qc1.cx(1, 3)
op1 = Operator(qc1)

qc2 = QuantumCircuit(4)
qc2.x(0)
qc2.x(2)
op2 = Operator(qc2)

assert op1 != op2
assert op1.equal_with_ancillas(op2, [1])

The first assertion checks that the two circuits are not equal, and they are not -- due to the CX gates from qubit 1 to other qubits. However, the two circuits are equal if qubit 1 is initially zero, then the CX gates do not matter.

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Qiskit/terra-core

[coveralls]

Pull Request Test Coverage Report for Build 10471646092

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

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Details

• 24 of 25 (96.0%) changed or added relevant lines in 1 file are covered.
• 31 unchanged lines in 5 files lost coverage.
• Overall coverage increased (+0.009%) to 89.596%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/quantum_info/operators/operator_utils.py	24	25	96.0%

Files with Coverage Reduction	New Missed Lines	%
qiskit/circuit/library/basis_change/qft.py	1	90.43%
crates/qasm2/src/lex.rs	3	92.73%
qiskit/transpiler/preset_passmanagers/generate_preset_pass_manager.py	4	91.76%
crates/qasm2/src/parse.rs	6	97.61%
qiskit/quantum_info/operators/operator.py	17	94.34%

Totals
Change from base Build 10408599020:	0.009%
Covered Lines:	67633
Relevant Lines:	75487

---

💛 - Coveralls

[alexanderivrii]

As @Cryoris suggested offline, it is better to make this function private for now. So I have prefixed it with the underscore and removed the lovingly-created release notes.

[eliarbel]

Change the order to match the actual args order

[alexanderivrii]

Good point, done in 4de623a.

[eliarbel]

Suggested change

	bool: True if operators are equal up to clean ancilla qubits.
	bool: True iff operators are equal up to clean ancilla qubits.

[alexanderivrii]

Done in 4de623a.

[eliarbel]

Maybe List[int] instead of list?

[alexanderivrii]

Done in 4de623a (well, list[int], which I believe is now a bit more preferred).

[eliarbel]

Add type checking on other similarly to how it's done in equiv()

[alexanderivrii]

The equiv code does more than just type-checking: if converts other to an Operator when it's not already, so for example one can check the equivalence of an Operator and a QuantumCircuit. I don't think this fully makes sense for this (currently private) function.

[eliarbel]

Might be a nitpicking, but I disliked the loop duplication up to the if condition ...
So to alleviate this and hopefully also improve readability, consider something like this:

        pattern = []
        ancillas = []
        for q in range(num_qubits):
            if q in ancilla_qubits:
                ancillas.append(q)
            else:
                pattern.append(q)
        pattern += ancillas

[alexanderivrii]

That's a great suggestion, done in 4de623a.

[alexanderivrii]

Thanks @Cryoris and @eliarbel for the reviews!

I haven't fully understood Julien's comment the first time: as the new function is not yet used anywhere in the main Qiskit code, for now it's better to make it a private function and not have it in operator.py. This is now done in 4de623a. I have created a special file operator_utils.py for this function since no other place seemed suitable: the utils directory contains some high-level utilities (commutator, anti-commutator), the predicates.py is used by the Operator class while the new function uses the Operator class, etc.

Eli, I have addressed your review comments in 4de623a.

[eliarbel]

LGTM

I approve for merge, though I'm not 100% happy with adding a new file ('operator_utils.py') just for this, knowing that there is a chance that '_equiv_with_ancillas' would become public and even part of Operator. Since there are already _ methods in Operator, roughly in the same vein like _multiply and _add I would prefer to keep '_equiv_with_ancillas' in Operator and spare an additional new file in the module.

[Cryoris]

_multiply and _add are used in overloading the __rmult__ and __add__ operations on the public interface, but the ancilla equality wouldn't be connected to a user-facing API 🙂