Fix measurement keys in subcircuits with parent_path (#4616)

Applies any parent path in subcircuit to measurement key before returning.

Fixes #4620

cirq-core/cirq/circuits/circuit_operation.py

@@ -184,6 +184,9 @@ def _measurement_key_objs_(self) -> AbstractSet[value.MeasurementKey]:
                     for repetition_id in self.repetition_ids
                     for key in circuit_keys
                 }
+            circuit_keys = {
+                protocols.with_key_path_prefix(key, self.parent_path) for key in circuit_keys
+            }
             object.__setattr__(
                 self,
                 '_cached_measurement_key_objs',

cirq-core/cirq/circuits/circuit_operation_test.py

@@ -756,6 +756,16 @@ def test_decompose_repeated_nested_measurements():
     assert op3.mapped_circuit(deep=True) == expected_circuit
 
 
+def test_keys_under_parent_path():
+    a = cirq.LineQubit(0)
+    op1 = cirq.CircuitOperation(cirq.FrozenCircuit(cirq.measure(a, key='A')))
+    assert cirq.measurement_key_names(op1) == {'A'}
+    op2 = op1.with_key_path(('B',))
+    assert cirq.measurement_key_names(op2) == {'B:A'}
+    op3 = op2.repeat(2)
+    assert cirq.measurement_key_names(op3) == {'B:0:A', 'B:1:A'}
+
+
 def test_mapped_circuit_preserves_moments():
     q0, q1 = cirq.LineQubit.range(2)
     fc = cirq.FrozenCircuit(cirq.Moment(cirq.X(q0)), cirq.Moment(cirq.X(q1)))
@@ -802,7 +812,7 @@ def test_tag_propagation():
         assert test_tag not in op.tags
 
 
-def test_keys_under_parent_path():
+def test_mapped_circuit_keeps_keys_under_parent_path():
     q = cirq.LineQubit(0)
     op1 = cirq.CircuitOperation(
         cirq.FrozenCircuit(