Support even powers of SWAP gate in CliffordSimulator

cirq/ops/swap_gates.py

@@ -85,16 +85,28 @@ def _trace_distance_bound_(self) -> Optional[float]:
             return None
         return abs(np.sin(self._exponent * 0.5 * np.pi))
 
+    def _has_stabilizer_effect_(self) -> Optional[bool]:
+        if self._is_parameterized_():
+            return None
+        return self.exponent % 1 == 0
+
     def _act_on_(self, args):
         from cirq import ops, sim, protocols
 
-        if isinstance(args, sim.ActOnStabilizerCHFormArgs) and self._exponent % 2 == 1:
-            args.state.omega *= 1j ** (2 * self.global_shift * self._exponent)
-            protocols.act_on(ops.CNOT, args)
-            args.axes = args.axes[::-1]
-            protocols.act_on(ops.CNOT, args)
-            args.axes = args.axes[::-1]
-            protocols.act_on(ops.CNOT, args)
+        if isinstance(args, (sim.ActOnStabilizerCHFormArgs, sim.ActOnCliffordTableauArgs)):
+            if not self._has_stabilizer_effect_():
+                return NotImplemented
+            if isinstance(args, sim.ActOnStabilizerCHFormArgs):
+                args.state.omega *= 1j ** (2 * self.global_shift * self._exponent)
+
+            if self._exponent % 2 == 1:
+                protocols.act_on(ops.CNOT, args)
+                args.axes = args.axes[::-1]
+                protocols.act_on(ops.CNOT, args)
+                args.axes = args.axes[::-1]
+                protocols.act_on(ops.CNOT, args)
+
+            # An even exponent does not change anything except the global phase above.
             return True
 
         return NotImplemented

cirq/ops/swap_gates_test.py

@@ -75,6 +75,13 @@ def test_text_diagrams():
     )
 
 
+def test_swap_has_stabilizer_effect():
+    assert cirq.has_stabilizer_effect(cirq.SWAP)
+    assert cirq.has_stabilizer_effect(cirq.SWAP ** 2)
+    assert not cirq.has_stabilizer_effect(cirq.SWAP ** 0.5)
+    assert not cirq.has_stabilizer_effect(cirq.SWAP ** sympy.Symbol('foo'))
+
+
 def test_swap_unitary():
     # yapf: disable
     np.testing.assert_almost_equal(

cirq/sim/clifford/clifford_simulator_test.py

@@ -397,13 +397,17 @@ def test_swap():
     circuit = cirq.Circuit(
         cirq.X(a),
         cirq.SWAP(a, b),
+        cirq.SWAP(a, b) ** 4,
         cirq.measure(a, key="a"),
         cirq.measure(b, key="b"),
     )
     r = cirq.CliffordSimulator().sample(circuit)
     assert not r["a"][0]
     assert r["b"][0]
 
+    with pytest.raises(NotImplementedError, match="CliffordSimulator doesn't support"):
+        cirq.CliffordSimulator().simulate((cirq.Circuit(cirq.SWAP(a, b) ** 3.5)))
+
 
 def test_sample_seed():
     q = cirq.NamedQubit('q')