Extend CommutativeInverseCancellation to cancel pairs of gates up-to-phase

[alexanderivrii]

Summary

Extending CommutativeInverseCancellation transpiler pass to cancel pairs of gates that are inverse up to a phase. Updates the global phase of the circuit accordingly.

Here is a small example:

import numpy as np
from qiskit.circuit import QuantumCircuit
from qiskit.transpiler import PassManager
from qiskit.transpiler.passes import CommutativeInverseCancellation

circuit = QuantumCircuit(1)
circuit.rz(np.pi / 4, 0)
circuit.p(-np.pi / 4, 0)

passmanager = PassManager(CommutativeInverseCancellation(upto_phase_optimization=True))
new_circuit = passmanager.run(circuit)

The pass is able to cancel the RZ and P gates, adjusting the global phase of the circuit to 15 \pi / 8.

Details:

The pass has two new arguments max_qubits and upto_phase_optimization. The new optimization is enabled by setting upto_phase_optimization = True. Generally this leads to more reductions at the expense of increased runtime. Internally, the check is based on constructing and comparing unitary matrices corresponding to various gates in the circuit. The argument max_qubits limits the number of qubits in matrix-based commutativity and inverse checks.

[qiskit-bot]

One or more of the the following people are requested to review this:

• @Qiskit/terra-core
• @ikkoham

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Covered Lines:	59559
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[Cryoris]

It seems like this is a much stronger comparison than just up to global phase: any two adjacent gates that implement the same operation can now be cancelled, whereas before we only cancelled them if they were the same type. It might be worth for the input argument to reflect that.

[Cryoris]

LGTM except I still think this does more than just ignoring global phase. If I define two custom adjacent gates who will cancel each other, this new PR will be able to cancel them -- no matter how these gates are called. This wasn't possible before, was it? If this is correct, how about renaming upto_phase_optimization to something like matrix_based?

[alexanderivrii]

Thanks @Cryoris, I did the renaming as per review comments and offline conversation.

[Cryoris]

Small comments, pretty much looks good to go!

[Cryoris]

LGTM thanks for the adjustments!