Commute z gates for qscout_compile

[vtomole]

import qiskit
import qiskit_superstaq as qss
qc = qiskit.QuantumCircuit(2, 2)

qc.cz(0, 1)

qc.measure_all()

print(qc)
# prints
#             ░ ┌─┐   
#    q_0: ─■──░─┤M├───
#          │  ░ └╥┘┌─┐
#    q_1: ─■──░──╫─┤M├
#             ░  ║ └╥┘
#    c: 2/═══════╬══╬═
#                ║  ║ 
# meas: 2/═══════╩══╩═
#                0  1  
#



provider = qss.superstaq_provider.SuperstaqProvider(token)



compiler_output = provider.qscout_compile(qc)

print(compiler_output.circuit)
# prints
#      ┌─────────────┐┌───┐┌───────────┐┌─────────────┐┌───┐ ░ ┌─┐   
# q_0: ┤ R(π/2,-π/2) ├┤ Z ├┤0          ├┤ R(π/2,-π/2) ├┤ S ├─░─┤M├───
#      ├─────────────┤├───┤│  Rxx(π/2) │├─────────────┤├───┤ ░ └╥┘┌─┐
# q_1: ┤ R(π/2,-π/2) ├┤ Z ├┤1          ├┤ R(π/2,-π/2) ├┤ S ├─░──╫─┤M├
#      └─────────────┘└───┘└───────────┘└─────────────┘└───┘ ░  ║ └╥┘
# c: 2/═════════════════════════════════════════════════════════╩══╩═
#                                                               0  1 

The z gates came be moved to the right of Rxx because and combined into the s gates.

[cdbf1]

This is an interesting issue because the cirq.commutes() function doesn't recognize the Rxx gate commuting with the pair of Z gates