diff --git a/cirq-core/cirq/_compat.py b/cirq-core/cirq/_compat.py
index 566ec1c2a34..7b0923701d5 100644
--- a/cirq-core/cirq/_compat.py
+++ b/cirq-core/cirq/_compat.py
@@ -191,6 +191,9 @@ def _print(self, expr, **kwargs):
     if isinstance(value, Dict):
         return '{' + ','.join(f"{proper_repr(k)}: {proper_repr(v)}" for k, v in value.items()) + '}'
 
+    if hasattr(value, "__qualname__"):
+        return f"{value.__module__}.{value.__qualname__}"
+
     return repr(value)
 
 
diff --git a/cirq-core/cirq/devices/noise_utils.py b/cirq-core/cirq/devices/noise_utils.py
index 4086ba5c741..7fb30a040ba 100644
--- a/cirq-core/cirq/devices/noise_utils.py
+++ b/cirq-core/cirq/devices/noise_utils.py
@@ -16,6 +16,7 @@
 import numpy as np
 
 from cirq import ops, protocols, value
+from cirq._compat import proper_repr
 
 if TYPE_CHECKING:
     import cirq
@@ -78,20 +79,21 @@ def __str__(self):
         return f'{self.gate_type}{self.qubits}'
 
     def __repr__(self) -> str:
-        fullname = f'{self.gate_type.__module__}.{self.gate_type.__qualname__}'
         qubits = ', '.join(map(repr, self.qubits))
-        return f'cirq.devices.noise_utils.OpIdentifier({fullname}, {qubits})'
+        return f'cirq.devices.noise_utils.OpIdentifier({proper_repr(self.gate_type)}, {qubits})'
 
     def _value_equality_values_(self) -> Any:
         return (self.gate_type, self.qubits)
 
     def _json_dict_(self) -> Dict[str, Any]:
-        gate_json = protocols.json_cirq_type(self._gate_type)
-        return {'gate_type': gate_json, 'qubits': self._qubits}
+        if hasattr(self.gate_type, '__name__'):
+            return {'gate_type': protocols.json_cirq_type(self._gate_type), 'qubits': self._qubits}
+        return {'gate_type': self._gate_type, 'qubits': self._qubits}
 
     @classmethod
     def _from_json_dict_(cls, gate_type, qubits, **kwargs) -> 'OpIdentifier':
-        gate_type = protocols.cirq_type_from_json(gate_type)
+        if isinstance(gate_type, str):
+            gate_type = protocols.cirq_type_from_json(gate_type)
         return cls(gate_type, *qubits)
 
 
diff --git a/cirq-core/cirq/devices/noise_utils_test.py b/cirq-core/cirq/devices/noise_utils_test.py
index 412ff1fa192..df9833424ec 100644
--- a/cirq-core/cirq/devices/noise_utils_test.py
+++ b/cirq-core/cirq/devices/noise_utils_test.py
@@ -62,6 +62,13 @@ def test_op_id_swap():
     assert cirq.CZ(q1, q0) in swap_id
 
 
+def test_op_id_instance():
+    q0 = cirq.LineQubit.range(1)[0]
+    gate = cirq.SingleQubitCliffordGate.from_xz_map((cirq.X, False), (cirq.Z, False))
+    op_id = OpIdentifier(gate, q0)
+    cirq.testing.assert_equivalent_repr(op_id)
+
+
 @pytest.mark.parametrize(
     'decay_constant,num_qubits,expected_output',
     [(0.01, 1, 1 - (0.99 * 1 / 2)), (0.05, 2, 1 - (0.95 * 3 / 4))],
diff --git a/cirq-core/cirq/protocols/json_test_data/OpIdentifier.json b/cirq-core/cirq/protocols/json_test_data/OpIdentifier.json
index d33b909367d..e9e3f35d109 100644
--- a/cirq-core/cirq/protocols/json_test_data/OpIdentifier.json
+++ b/cirq-core/cirq/protocols/json_test_data/OpIdentifier.json
@@ -1,10 +1,45 @@
-{
-  "cirq_type": "OpIdentifier",
-  "gate_type": "XPowGate",
-  "qubits": [
-    {
-      "cirq_type": "LineQubit",
-      "x": 1
-    }
-  ]
-}
\ No newline at end of file
+[
+  {
+    "cirq_type": "OpIdentifier",
+    "gate_type": "XPowGate",
+    "qubits": [
+      {
+        "cirq_type": "LineQubit",
+        "x": 1
+      }
+    ]
+  },
+  {
+    "cirq_type": "OpIdentifier",
+    "gate_type": {
+      "cirq_type": "CliffordGate",
+      "n": 1,
+      "rs": [
+        false,
+        false
+      ],
+      "xs": [
+        [
+          true
+        ],
+        [
+          false
+        ]
+      ],
+      "zs": [
+        [
+          false
+        ],
+        [
+          true
+        ]
+      ]
+    },
+    "qubits": [
+      {
+        "cirq_type": "LineQubit",
+        "x": 0
+      }
+    ]
+  }
+]
\ No newline at end of file
diff --git a/cirq-core/cirq/protocols/json_test_data/OpIdentifier.repr b/cirq-core/cirq/protocols/json_test_data/OpIdentifier.repr
index 6b991bb0b2c..010a806a9e2 100644
--- a/cirq-core/cirq/protocols/json_test_data/OpIdentifier.repr
+++ b/cirq-core/cirq/protocols/json_test_data/OpIdentifier.repr
@@ -1,4 +1,10 @@
+[
 cirq.devices.noise_utils.OpIdentifier(
     cirq.ops.common_gates.XPowGate,
     cirq.LineQubit(1)
-)
\ No newline at end of file
+),
+cirq.devices.noise_utils.OpIdentifier(
+    cirq.CliffordGate.from_clifford_tableau(cirq.CliffordTableau(1,rs=np.array([False, False],dtype=np.dtype('bool')), xs=np.array([[True], [False]], dtype=np.dtype('bool')),zs=np.array([[False], [True]], dtype=np.dtype('bool')), initial_state=0)),
+    cirq.LineQubit(0)
+)
+]
\ No newline at end of file