Regression in PyQuil `CPHASE00` conversions

[natestemen]

Description of the issue

When converting a PyQuil program to a Cirq circuit using the cirq_rigetti.circuit_from_quil function the output differs between cirq versions 1.4.1 and 1.3.0. Specifically, in cirq==1.4.1, the CPHASE00 gate is converted into a custom USERGATE gate with complex matrix elements, while in cirq==1.3.0, the gate is correctly recognized and output as CPHASE00.

How to reproduce the issue

1. Create a file pyquil_conv.py with the following script.

   from cirq_rigetti import circuit_from_quil
   from cirq_rigetti.quil_output import QuilOutput
   from pyquil import Program
   
   QUIL_PROGRAM = """
   RZ(pi/2) 0
   CPHASE00(pi/2) 0 1
   """
   
   p = Program(QUIL_PROGRAM)
   circ = circuit_from_quil(p.out())
   print(QuilOutput(circ.all_operations(), circ.all_qubits()))

2. Run the script with cirq==1.4.1

   $ pip list | grep -E "cirq-core|cirq-rigetti"
   cirq-core                       1.4.1
   cirq-rigetti                    1.4.1
   $ python pyquil_conv.py
   # Created using Cirq.
   
   RZ(1.5707963267948966) 0
   DEFGATE USERGATE1:
       6.123233995736766e-17+1.0i, 0.0+0.0i, 0.0+0.0i, 0.0+0.0i
       0.0+0.0i, 1.0+0.0i, 0.0+0.0i, 0.0+0.0i
       0.0+0.0i, 0.0+0.0i, 1.0+0.0i, 0.0+0.0i
       0.0+0.0i, 0.0+0.0i, 0.0+0.0i, 1.0+0.0i
   USERGATE1 0 1

3. Run the script with cirq==1.3.0

   $ pip list | grep -E "cirq-core|cirq-rigetti"
   cirq-core                1.3.0
   cirq-rigetti             1.3.0
   $ python pyquil_conv.py
   # Created using Cirq.
   
   RZ(1.5707963267948966) 0
   CPHASE00(1.5707963267948966) 0 1

Related

When adding support for pyquil v4 a similar example was found in https://github.com/quantumlib/Cirq/pull/6281#issuecomment-2075385259.