Treat classically controlled ops as non-Clifford in dynamical_decoupling

cirq-core/cirq/transformers/dynamical_decoupling.py

@@ -119,7 +119,9 @@ def _is_single_qubit_gate_moment(moment: Moment) -> bool:
 
 
 def _is_clifford_op(op: ops.Operation) -> bool:
-    return has_unitary(op) and has_stabilizer_effect(op)
+    if op.gate:
+        return has_unitary(op.gate) and has_stabilizer_effect(op.gate)
+    return False
 
 
 def _calc_busy_moment_range_of_each_qubit(circuit: FrozenCircuit) -> dict[ops.Qid, list[int]]:

cirq-core/cirq/transformers/dynamical_decoupling_test.py

@@ -20,7 +20,7 @@
 import pytest
 
 import cirq
-from cirq import add_dynamical_decoupling, CNOT, CZ, CZPowGate, H, X, Y, Z
+from cirq import add_dynamical_decoupling, CNOT, CZ, CZPowGate, H, I, measure, X, Y, Z
 
 
 def assert_sim_eq(circuit1: cirq.AbstractCircuit, circuit2: cirq.AbstractCircuit):
@@ -53,6 +53,22 @@ def assert_dd(
     assert_sim_eq(input_circuit, transformed_circuit)
 
 
+def test_classically_controlled_no_update_succeeds():
+    """Test case diagrams.
+    Input:
+    0: ───M───I───
+          ║   ║
+    c: ═══@═══^═══
+    """
+    a = cirq.NamedQubit('a')
+
+    add_dynamical_decoupling(
+        cirq.Circuit(
+            cirq.Moment(measure(a, key="a")), cirq.Moment(I(a).with_classical_controls("a"))
+        )
+    )
+
+
 def test_no_insertion():
     """Test case diagrams.
     Input: