Fix inconsistent Pauli gate multiplication

cirq-core/cirq/ops/pauli_string.py

@@ -271,6 +271,8 @@ def __mul__(self, other):
             known = True
         elif isinstance(other, (PauliString, numbers.Number)):
             known = True
+        elif (as_pauli_string := _try_interpret_as_pauli_string(other)) is not None:
+            return self * as_pauli_string
         if known:
             return PauliString(
                 cast(PAULI_STRING_LIKE, other),
@@ -297,6 +299,8 @@ def __rmul__(self, other) -> PauliString:
 
         if isinstance(other, raw_types.Operation) and isinstance(other.gate, identity.IdentityGate):
             return self  # pragma: no cover
+        elif (as_pauli_string := _try_interpret_as_pauli_string(other)) is not None:
+            return as_pauli_string * self
 
         # Note: PauliString case handled by __mul__.
         return NotImplemented
@@ -1103,17 +1107,14 @@ def _validate_qubit_mapping(
 def _try_interpret_as_pauli_string(op: Any):
     """Return a reprepresentation of an operation as a pauli string, if it is possible."""
     if isinstance(op, gate_operation.GateOperation):
-        gates = {
-            common_gates.XPowGate: pauli_gates.X,
-            common_gates.YPowGate: pauli_gates.Y,
-            common_gates.ZPowGate: pauli_gates.Z,
-        }
-        if (pauli := gates.get(type(op.gate), None)) is not None:
-            exponent = op.gate.exponent  # type: ignore
-            if exponent % 2 == 0:
-                return PauliString()
-            if exponent % 2 == 1:
-                return pauli.on(op.qubits[0])
+        try:
+            pauli_expansion_op = protocols.pauli_expansion(op)
+            if pauli_expansion_op is not None and len(pauli_expansion_op) == 1:
+                gate, coef = next(iter(pauli_expansion_op.items()))
+                return coef * PauliString({q: gate for q in op.qubits})
+        except TypeError:
+            # return None if there is no Pauli expansion for this GateOperation.
+            pass
     return None
 
 

cirq-core/cirq/ops/raw_types.py

@@ -483,10 +483,18 @@ def _commutes_(self, other: Any, *, atol: float = 1e-8) -> None | NotImplemented
 
     def _mul_with_qubits(self, qubits: tuple[cirq.Qid, ...], other):
         """cirq.GateOperation.__mul__ delegates to this method."""
+        from cirq.ops.pauli_string import _try_interpret_as_pauli_string
+
+        if (as_pauli_string := _try_interpret_as_pauli_string(self.on(*qubits))) is not None:
+            return as_pauli_string * other
         return NotImplemented
 
     def _rmul_with_qubits(self, qubits: tuple[cirq.Qid, ...], other):
         """cirq.GateOperation.__rmul__ delegates to this method."""
+        from cirq.ops.pauli_string import _try_interpret_as_pauli_string
+
+        if (as_pauli_string := _try_interpret_as_pauli_string(self.on(*qubits))) is not None:
+            return other * as_pauli_string
         return NotImplemented
 
     def _json_dict_(self) -> dict[str, Any]: