Qasm for pauli X sqrts

[stubbi]

addresses #3728

The issue mentions to check other stabilizer operations like X**-0.5, Y0.5, Y-0.5, Z**0.5 too. According to the qiskit docs, there exist only X**0.5 as xs and X**-0.5 as xsdg. Both of these conversions have been implemented and tests are passing locally.

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[stubbi]

@googlebot I fixed it.

[stubbi]

closing for now, got to fix the coverage check

[tanujkhattar]

It looks stabilizer_simulator supports sx, s, sdg but not sxdg.

1. For ZPowGate; cirq.Z ** 0.5 currently outputs rz(pi*0.5) but should output s. Similarly cirq.Z ** -0.5 should output sdg.

2. For XPowGate; I'm not sure why their simulator does not support sxdg. Maybe @Strilanc can comment what should be expected behaviour here.

[tanujkhattar]

FYI, if we transpile a circuit withsxdg to the stabilizer_simulator backend, it decomposes sxdg to SHS. Maybe we should directly output this decomposition for cirq.X ** -0.5 ?

In [2]: circ = QuantumCircuit(2)
    ...: circ.sx(0)
    ...: circ.sxdg(1)
    ...: print(circ)
    ...: simulator = Aer.get_backend('aer_simulator_stabilizer')
    ...: circ = transpile(circ, simulator)
    ...: print(circ)
      ┌────┐
q_0: ─┤ √X ├─
     ┌┴────┴┐
q_1: ┤ √XDG ├
     └──────┘
global phase: -π/4
     ┌────┐
q_0: ┤ √X ├──────────
     ├───┬┘┌───┐┌───┐
q_1: ┤ S ├─┤ H ├┤ S ├
     └───┘ └───┘└───┘

In the meantime, please make the changes for cirq.ZPowGate.

[stubbi]

@tanujkhattar thanks for your review, good catches!

I added the requested changes for the ZPowGate and opened an issue in qiskit-aer to ask if the sxdg isn't included on purpose or had been overlooked.

I would propose to revert the changes for XPowGate(-0.5) for now and wait for a reply in the qiskit issue to see if we have to change its output to sxdg or s h s. What do you think?

[tanujkhattar]

Sounds good, Please revert the changes to sxdg and update the original issue with the details (let's keep it open so we can track the progress on the qiskit issue).

[stubbi]

@tanujkhattar I reverted the changes for sxdg and left a comment in the issue

[tanujkhattar]

LGTM