convert SingleQubitCliffordGate to phasedXZ during serialization (#6419)

Author: NoureldinYosri

cirq-google/cirq_google/serialization/circuit_serializer.py

@@ -175,7 +175,9 @@ def _serialize_gate_op(
                 out=msg.phasedxpowgate.exponent,
                 arg_function_language=arg_function_language,
             )
-        elif isinstance(gate, cirq.PhasedXZGate):
+        elif isinstance(gate, (cirq.PhasedXZGate, cirq.ops.SingleQubitCliffordGate)):
+            if isinstance(gate, cirq.ops.SingleQubitCliffordGate):
+                gate = gate.to_phased_xz_gate()
             arg_func_langs.float_arg_to_proto(
                 gate.x_exponent,
                 out=msg.phasedxzgate.x_exponent,

cirq-google/cirq_google/serialization/circuit_serializer_test.py

@@ -668,3 +668,16 @@ def test_measurement_gate_deserialize() -> None:
     msg = cg.CIRCUIT_SERIALIZER.serialize(circuit)
 
     assert cg.CIRCUIT_SERIALIZER.deserialize(msg) == circuit
+
+
+def test_circuit_with_cliffords():
+    q = cirq.NamedQubit('q')
+    circuit = cirq.Circuit(
+        g(q) for g in cirq.ops.SingleQubitCliffordGate.all_single_qubit_cliffords
+    )
+    want = cirq.Circuit(
+        g.to_phased_xz_gate()(q)
+        for g in cirq.ops.SingleQubitCliffordGate.all_single_qubit_cliffords
+    )
+    msg = cg.CIRCUIT_SERIALIZER.serialize(circuit)
+    assert cg.CIRCUIT_SERIALIZER.deserialize(msg) == want