Set-up a most basic circuit equivalence checker

[yaelbh]

Summary

The first pull request in the list: #5692 (comment)

Details and comments

Still in progress, to be ready requires:

• Testing.
• Documentation.
• Style and lint.

[yaelbh]

What can be done to perform CI testing to the Aer option of the equivalence checker? I see four options:

1. Skip tests that import Aer (as far as I see, this is what the VQE tests do with AerPauliExpectation) - code will remain untested for many platforms.
2. Move the equivalence checker to another repository: qiskit-aer, or its own repository - cumbersome.
3. Copy the very same tests to qiskit-aer - code duplication.
4. Make Terra's CI install Aer and run these tests properly - this is my preferred option. Since the same issue arises also with AerPauliExpectation, we conclude that this is a general problem that requires a general solution.

[yaelbh]

Following the discussion in #5783, I'll modify the tests to skip Aer if not installed.

[yaelbh]

@chriseclectic @ajavadia @1ucian0 @burgholzer Ready for a new cycle of review. Note that some of the previous review comments were not addressed in the code but in answers in #5692.

[1ucian0]

Suggested change

	phase (str): Options are 'global' - ignoring global phase;
	or 'equal' - not ignoring global phase.
	up_to_global_phase (bool): Option ignoring global phase or not.

[yaelbh]

Please see #5700 (comment)

[ecpeterson]

I'm curious: why trap raise at all? Is it saving the user work to have to check a boolean for failure vs letting them do their own trapping?

[yaelbh]

@ecpeterson Which raise are you referring to?

[ecpeterson]

I mean the unknown raise that's trapped here: https://github.com/Qiskit/qiskit-terra/pull/5700/files#diff-0bd9ce629c038afb2f5894b7da1497a43a7121518abd96f859dbd4a309b0e376R136 .

[yaelbh]

@ecpeterson Essentially yes (save the user work etc.). The idea is that the equivalence checker doesn't crash but always return a result. If something went wrong, this will be reflected in the result.

[1ucian0]

does this PR closes #761 ?

[edoaltamura]

Have there been recent updates about this PR or circuit equivalence in general?

[burgholzer]

Have there been recent updates about this PR or circuit equivalence in general?

Please excuse the shameless plug here:

If you are interested in an easy-to-use and scalable equivalence checker that works out of the box with Qiskit, have a look at MQT QCEC (https://github.com/cda-tum/mqt-qcec, pip install mqt.qcec).

Verifying the equivalence of two Qiskit circuits is as easy as

from mqt.qcec import verify 

res = verify(qc1, qc2)

Note that the tool uses dedicated data structures (decision diagrams and ZX calculus) plus dedicated verification schemes to make the verification way more scalable than the simple construction and comparison of the circuits' unitaries. More information can be found in the documentation at https://mqt.rtfd.io/projects/qcec