Treat classically controlled ops as non-Clifford in dynamical_decoupling

cirq-core/cirq/transformers/dynamical_decoupling.py

@@ -27,6 +27,7 @@
 from cirq import ops, protocols
 from cirq.circuits import Circuit, FrozenCircuit, Moment
 from cirq.protocols import unitary_protocol
+from cirq.protocols.control_key_protocol import control_keys
 from cirq.protocols.has_stabilizer_effect_protocol import has_stabilizer_effect
 from cirq.protocols.has_unitary_protocol import has_unitary
 from cirq.transformers import transformer_api
@@ -121,7 +122,7 @@ 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)
+    return has_unitary(op) and has_stabilizer_effect(op) and not control_keys(op)
 
 
 def _calc_busy_moment_range_of_each_qubit(circuit: FrozenCircuit) -> dict[ops.Qid, list[int]]:

cirq-core/cirq/transformers/dynamical_decoupling_test.py

@@ -21,7 +21,7 @@
 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
 from cirq.transformers.dynamical_decoupling import _CellType, _Grid
 
 
@@ -55,6 +55,22 @@ def assert_dd(
     assert_sim_eq(input_circuit, transformed_circuit)
 
 
+def test_classically_controlled_no_update_succeeds():
+    """Test case diagrams.
+    Input:
+    a: ───M───I───
+          ║   ║
+    a: ═══@═══^═══
+    """
+    a = cirq.NamedQubit('a')
+
+    input_circuit = cirq.Circuit(
+        cirq.Moment(measure(a, key="a")), cirq.Moment(I(a).with_classical_controls("a"))
+    )
+    output_circuit = add_dynamical_decoupling(input_circuit)
+    cirq.testing.assert_same_circuits(input_circuit, output_circuit)
+
+
 def test_no_insertion() -> None:
     """Test case diagrams.
     Input: