[Needs to be scoped] General single qubit parameterized gate compiler

[tanujkhattar]

Is your feature request related to a use case or problem? Please describe.
A general single qubit parameterized gate compiler was proposed as a compilation building block in #3239. This issue is to scope out what would such a compiler look like and discuss whether it'd a useful addition to Cirq.

P3 - I'm not really blocked by it, it is an idea I'd like to discuss / suggestion based on principle

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[tanujkhattar]

One use case of this compiler would be to support merging parameterized single qubit rotations into a parameterized PhXZ gate, as suggested by @Wuggins

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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

[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

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Issue closed due to inactivity.

[tanujkhattar]

Reopening the issue since we have another request from internal team members for this compiler.

[larchen]

After a quick discussion with Tanuj, the initial thought was to try and implement the following two conversions:

1. Parameterized X / Y / Z pow gates to parameterized PhasedXZGate gate.
2. Merging two parameterized PhasedXZGate gates into a single parameterized PhasedXZGate gate

(1) is fairly trivial, but I couldn't find a simple closed form solution for (2), in which case it may not make much sense to try to compile the parameterized gates into a single PhXZ before the parameters are resolved.

(2) boils down to finding a representation of a', b', c', in terms of a, b, c such that X^a Z^b X^c == Z^a' X^b' X^c', which in general is not so nice.

[tanujkhattar]

From cirq sync:

If it's possible to do analytically, let's do it. The result might end up looking very complicated but that's upto users using the analytical compiler.

[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

[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

[github-actions]

Issue closed due to inactivity.