Gauge compiling as a sweep: merge single qubit gates

[babacry]

Problem Statement

as_sweep() might transform a circuit with consecutive parameterized phxz operations.

Usually, after gauge_compiling, users would optimize the circuit by merging single qubit gates. While merging parameterized circuit isn't supported.

Potential Solutions

Support this in as_sweep() or merging the qubits in cirq.merge_single_qubit_gates_to_phxz.

[babacry]

@NoureldinYosri @eliottrosenberg created this issue to track things, please feel free to update some context or suggestions here.

[NoureldinYosri]

@babacry I suggest creating a new method for this that will take both the circuit and the sweep and return new circuit and new sweep

That is given any two consecutive phasedXZ gates

1. both are parameterized -> drop one set of parameters and update the sweep values for the other
2. only one is parameterized -> update the sweep values for these parameters
3. neither are parameterized -> merge the two gates by falling back to merge_single_qubit_gates_to_phxz