Conversion to JSON failure

[glanzz]

Description of the issue
Any circuit with the inverse QubitPermutation gate added will fail if it is loaded from JSON.
How to reproduce the issue

import cirq as c

qubits = c.LineQubit.range(3)
circuit = c.Circuit()

circuit.append(c.QubitPermutationGate(permutation=[0,1,2])(qubits[0], qubits[1], qubits[2])**-1)

print(circuit)
json_text = c.to_json(circuit)
print(json_text)
circuit = c.read_json(json_text=json_text)
print(circuit)

0: ───[0>0]──────
      │
1: ───[1>1]──────
      │
2: ───[2>2]^-1───
{
  "cirq_type": "Circuit",
  "moments": [
    {
      "cirq_type": "Moment",
      "operations": [
        {
          "cirq_type": "GateOperation",
          "gate": {
            "cirq_type": "_InverseCompositeGate"
          },
          "qubits": [
            {
              "cirq_type": "LineQubit",
              "x": 0
            },
            {
              "cirq_type": "LineQubit",
              "x": 1
            },
            {
              "cirq_type": "LineQubit",
              "x": 2
            }
          ]
        }
      ]
    }
  ]
}
Traceback (most recent call last):
  File "/Users/xxx/json_failure.py", line 11, in <module>
    circuit = c.read_json(json_text=json_text)
              ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/xxx/cirqenv/lib/python3.11/site-packages/cirq/protocols/json_serialization.py", line 561, in read_json
    return json.loads(json_text, object_hook=obj_hook)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/json/__init__.py", line 359, in loads
    return cls(**kw).decode(s)
           ^^^^^^^^^^^^^^^^^^^
  File "/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/json/decoder.py", line 337, in decode
    obj, end = self.raw_decode(s, idx=_w(s, 0).end())
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Library/Frameworks/Python.framework/Versions/3.11/lib/python3.11/json/decoder.py", line 353, in raw_decode
    obj, end = self.scan_once(s, idx)
               ^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/xxx/cirqenv/lib/python3.11/site-packages/cirq/protocols/json_serialization.py", line 352, in __call__
    cls = factory_from_json(cirq_type, resolvers=self.resolvers)
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/xxx/cirqenv/lib/python3.11/site-packages/cirq/protocols/json_serialization.py", line 431, in factory_from_json
    raise ValueError(f"Could not resolve type '{type_str}' during deserialization")
ValueError: Could not resolve type '_InverseCompositeGate' during deserialization

Cirq version
You can get the cirq version by printing cirq.__version__. From the command line:

Cirq: 1.4.1

[mhucka]

Discussed during bit.ly/cirq-cynq today (2024-10-16): the conclusion is Cirq slhould either fully support the serialization or raise an error. Fully supporting it would is the preferred outcome.