Fix annotated operation is modified during parameter assignment (#12869)

(cherry picked from commit f508ac7)

qiskit/circuit/annotated_operation.py

@@ -133,7 +133,7 @@ def __eq__(self, other) -> bool:
 
     def copy(self) -> "AnnotatedOperation":
         """Return a copy of the :class:`~.AnnotatedOperation`."""
-        return AnnotatedOperation(base_op=self.base_op, modifiers=self.modifiers.copy())
+        return AnnotatedOperation(base_op=self.base_op.copy(), modifiers=self.modifiers.copy())
 
     def to_matrix(self):
         """Return a matrix representation (allowing to construct Operator)."""

test/python/circuit/test_annotated_operation.py

@@ -204,6 +204,17 @@ def test_invalid_params_access(self):
             with self.assertRaises(AttributeError):
                 _ = annotated.validate_parameter(1.2)
 
+    def test_invariant_under_assign(self):
+        """Test the annotated operation is not changed by assigning."""
+        p = Parameter("p")
+        annotated = RXGate(p).control(2, annotated=True)
+        circuit = QuantumCircuit(annotated.num_qubits)
+        circuit.append(annotated, circuit.qubits)
+        bound = circuit.assign_parameters([1.23])
+
+        self.assertEqual(list(circuit.parameters), [p])
+        self.assertEqual(len(bound.parameters), 0)
+
 
 if __name__ == "__main__":
     unittest.main()