Preserve global phase in analytical decompositions

[tanujkhattar]

Is your feature request related to a use case or problem? Please describe.
two_qubit_matrix_to_cz_operations and three_qubit_matrix_to_operations are used from within the decompose method of MatrixGate but they currently ignore global phase; because of which we don't support decomposing controlled versions of MatrixGate.

Describe the solution you'd like
In general, it'd be nice to write a method which, given a target unitary a and actual unitary b returns a cirq.GlobalPhaseGate() which can be used to match b to a s.t. a = global_phase_gate.coefficient * b. This would require minor modification to match_global_phasewhich already exists and can be used from within multiple anlaytical decompositions to "preserve" global phase by simply returning a GlobalPhaseGate() with the right phase.

We should also try to update as many anlaytical_decomposition as possible to preserve global phase.

This can be used to solve issues like #6517

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[github-actions]

This issue is stale because it has been open 30 days with no activity. Remove stale label or comment or this will be closed in 30 days