Implement PauliStringPhasorGate (quantumlib#4696)

BREAKING CHANGE: PauliStringPhasor no longer inherits from PauliStringGateOperation.

Implements PauliStringPhasor in terms of a GateOperation on a new class PauliStringPhasorGate.

Mostly involved moving existing functions from the operation to the gate, and then having the operation call those methods under the hood.

Closes quantumlib#1561, xref quantumlib#4683

@tanujkhattar

Author: daxfohl

cirq-core/cirq/__init__.py

@@ -259,6 +259,7 @@
     PauliString,
     PauliStringGateOperation,
     PauliStringPhasor,
+    PauliStringPhasorGate,
     PauliSum,
     PauliSumExponential,
     PauliSumLike,

cirq-core/cirq/json_resolver_cache.py

@@ -118,6 +118,8 @@ def _parallel_gate_op(gate, qubits):
         'ParallelGateFamily': cirq.ParallelGateFamily,
         'PauliMeasurementGate': cirq.PauliMeasurementGate,
         'PauliString': cirq.PauliString,
+        'PauliStringPhasor': cirq.PauliStringPhasor,
+        'PauliStringPhasorGate': cirq.PauliStringPhasorGate,
         '_PauliX': cirq.ops.pauli_gates._PauliX,
         '_PauliY': cirq.ops.pauli_gates._PauliY,
         '_PauliZ': cirq.ops.pauli_gates._PauliZ,

cirq-core/cirq/ops/__init__.py

@@ -233,6 +233,7 @@
 
 from cirq.ops.pauli_string_phasor import (
     PauliStringPhasor,
+    PauliStringPhasorGate,
 )
 
 from cirq.ops.pauli_string_raw_types import (