Compensate for global phase in MatrixGate decomposition

[daxfohl]

Following up on #7112 (which is the first commit in this PR), this PR fixes the issue at its root: it adds a compensating GlobalPhaseOperation when decomposing a MatrixGate. This allows the controlled decomposition tests to use np.testing.assert_allclose as desired, and also allows controlled MatrixGates to be used in decompositions, so that restriction has been removed.

I think this closes #6523, as the core of that issue is being able to decompose controlled MatrixGates, and the specific analytical decomposition methods do not state that they might return any global phase ops, and doing so could be a breaking change. So, this PR fixes the core issue, but with lower likelihood of introducing a breaking change.

cc @pavoljuhas

[daxfohl]

Looks like this creates a global phase in one of the ionq tests, which is not a supported gate in their gateset. I added it to their gateset just to see if it would allow the test to pass (pending). @tanujkhattar what's the best thing to do here? Add it to their gateset? Create a drop_global_phase_ops transformer and add it to their postprocessor? Add a DecomposeArgs field to ignore global phase? Skip this change entirely?

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.65%. Comparing base (5a81b3d) to head (056beff).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #7118      +/-   ##
==========================================
- Coverage   98.65%   98.65%   -0.01%     
==========================================
  Files        1106     1106              
  Lines       95870    95885      +15     
==========================================
+ Hits        94583    94592       +9     
- Misses       1287     1293       +6     

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[pavoljuhas]

I can confirm the test failure in #7071 (comment) does not happen after this change.

[pavoljuhas]

This fixes the test failure on my desktop that happened due to phase difference.
I'd defer to @tanujkhattar if this is an OK change for ionq.

[daxfohl]

@tanujkhattar do you have a recommendation here? This PR compensates for global phase in MatrixGate decomposition, fixing the associated issues regarding the broken decomposition of certain controlled gates that neglect the controlled phase. The change adds global phase ops to compensate, which is straightforward enough, but the remaining concern is that global phase op is not part of the ionq gateset, so the addition of this op during decomposition causes some of their unit tests to break.

For now, to allow their tests to pass, I added global phase ops to their gateset. Is this okay or is there something else we should do? One alternative is we could add a postprocessor to their gateset rules that drops global phase ops from the final circuit (seems straightforward). Alternately we could add a flag to decompose that ignores global phase (not ideal: likely very invasive / backwards-incompatible). Or we could leave things like this with global phase as part of their gateset (preferred). cc @dabacon if there's a direct ionq contact I should be pinging.

[tanujkhattar]

This PR compensates for global phase in MatrixGate decomposition, fixing the associated issues regarding the broken decomposition of certain controlled gates that neglect the controlled phase.

I think this is a much needed fix and I'm very happy to see this finally happening. Thanks for doing this!

For now, to allow their tests to pass, I added global phase ops to their gateset. Is this okay or is there something else we should do?

I think this is fine and we can merge the PR as is. Thanks!