Handle all possible 1-qubit Clifford gates in Clifford simulator

[fedimser]

I used the fact that all 1-qubit gates can be generated by H and S gates, and there are only 24 of them (up to phase) - proof.
So, I can explicitly generate all those 24 gates as sequences of H and S gates (see generation code).
Then, I can compare given gate with all of those 24 gates and check if they differ only in phase. If so, I can implement given gate using existing implementation of S and H gates.

So, this PR ensures that Clifford simulator supports all possible 1-qubit Clifford gates.

Also updated function in mux.py which checks if circuit is Clifford circuit.
There was one test of determinism in mux_test.py which started failing, because now it's simulated on Clifford simulator. Currently Clifford simulator doesn't support taking seed parameter, so I changed that test to use another gate, which is not Clifford gate.

[fedimser]

This PR is related to issue #2423.

[fedimser]

@smitsanghavi, please have a look (looks like I can't add reviewers to this PR).

[smitsanghavi]

Added a few high level comments before diving deeper.

[smitsanghavi]

This handling is being replaced with a has_stabilizer_effect protocol in #2760

[fedimser]

That PR have not been merged yet. As soon as it's merged, I'll update this PR to extend _has_stabilizer_effect_ on all matrices and to use it to check if gate can be simulated by Clifford simulator.

By the way, I think there is more elgeant way of implementing this - instead of defining _has_stabilizer_effect_ at every gate, we can do the following:
In has_stabilizer_effect_protocol.py check if gate has 2x2 uniary matrix (name it U).
If so, check that U@X@U.conj().T and U@Z@U.conj.T are in set X, -X, Y, -Y, Z, -Z.

This is also better than trying to match unitary with 24 matrices, as I am doing in this PR.

[Strilanc]

I think this functionality belongs on cirq.SingleQubitCliffordGate. Define a static method on that class called from_unitary which takes a 2x2 unitary matrix or object with a 2x2 unitary matrix and returns an instance of cirq.SingleQubitCliffordGate.

You can also define a cirq.SingleQubitCliffordGate.ALL field which enumerates the 24 possible instances.

[fedimser]

I added a method from_unitary to SingleQubitCliffordGate.
Since SingleQubitCliffordGate already has method decompose_rotation, and we know how to decompose rotations into H and S gates, I don't need precalculated list of all possible Clifford gates anymore.
Please take another look.

[smitsanghavi]

LGTM. Please wait for Craig's approval too.

[cduck]

I suggest also adding tests for the Clifford operations GlobalPhaseOperation and PauliString. I think these may hit corner cases that aren't handled yet.

[fedimser]

I added tests for PauliString and GlobalPhaseOperation.

GlobalPhaseOperation doesn't have any qubits, so it wasn't handled by my current implementation (which works for ops on exactly 1 qubit). So I just handled it separately (without involving single qubit Clifford gate).

Fixed.

[fedimser]

Craig, I can't merge this PR because you requested changes, but I addressed them. I think that some action from you is required to acknowledge that changes were made.
@Strilanc

stale

[Strilanc]

LGTM (after merge conflict is fixed)

[fedimser]

Can we please merge this now?
I understand that I also need to update has_stabilizer_effect (because PR #2760 is now merged) and use that method to determine whether operation is supported by the CLifford simulator, but I'd rather do it in a separate, simple PR.