ECR Gate Compatibility

[pcwysoc]

Is your feature request related to a problem? Please describe. Current code for interfacing with IBM devices is not compatible with the ECR gate. However, all but one of the available IBM devices uses the ECR gate.

Describe the solution you'd like I believe we should refactor the IBM code to convert directly from pyGSTi circuits to Qiskit circuits, as this would smoothly integrate the ECR gate.

Describe alternatives you've considered I've considered trying to convert ECR gates to OpenQASM 2.0 as we currently do. However, this leads to very fragile QASM code:

OPENQASM 2.0; include "qelib1.inc"; gate rzx(param0) q0,q1 { h q1; cx q0,q1; rz(param0) q1; cx q0,q1; h q1; } gate ecr q0,q1 { rzx(pi/4) q0,q1; x q0; rzx(-pi/4) q0,q1; } qreg q[3]; creg c[1]; ecr q[1],q[2]; ecr q[0],q[2]; measure q[2] -> c[0]; barrier q[0],q[1],q[2];

This works for jobs submitted through Runtime or the Quantum Composer on the IBM website, but seems to fail for jobs submitted through backend.run():

I'm concerned that if we pursue this avenue that the fix would be unstable.