fix global phase in initializer

[ewinston]

Summary

Fixes global phase in initializer.

fixes #5230

Details and comments

[jlapeyre]

• Possibly clarifying comment: In the issue Initialize instruction does not preserve global phase #5230, I was worried about the global phase somehow making the circuit less efficient on hardware. But, it looks like, at least in some cases, the global_phase is carried along after applying decompose to a fixed point, in which case it shouldn't matter. That is, the gates are the same.
• I notice that, for 1j * np.array([1.0, 0]), decompose replaces the RZ gate by a U1 gate with a different global phase. Does it make sense to avoid this decompose step by using a U1 gate from the outset?

[ewinston]

@jlapeyre This was switched back to RZ as part of the migration away from u1, u2, u3 gates in qiskit as mentioned in issues #4106 #6165.

[jlapeyre]

This was switched back to RZ

Ok. For the record: Before this PR the decomposition went U1 -> U.
With this PR, the decomposition goes RZ -> U1 -> U.
But, RZ will be changed to decompose directly to U, so that we'll have RZ -> U, in other words, no increased complexity.

LGTM

[Cryoris]

@ewinston Could you add a short bugfix releasenote on this? It would be nice to highlight that this now works with the correct global phase 🙂

[Cryoris]

Also: why is the global phase the sum of the remaining parameters? 🤔

[ewinston]

@Cryoris The "remaining parameters" seemed to capture the phase factors which occur during each iteration of the decomposition.

[Cryoris]

LGTM! 🙂