Inverting gates does not allow to save circuit in json

[nikita-astronaut]

Description of the issue

How to reproduce the issue

U = cirq.Circuit()
K = cirq.Circuit()
K.append(cirq.PhasedFSimGate(0, 0, 0, 0,0).on(cirq.GridQubit(0, 0), cirq.GridQubit(0, 1)))

U.append(K)
U.append(cirq.X.on(cirq.GridQubit(0, 0)))
U.append(cirq.inverse(K))


with open('test.json', 'wb') as f:
    f.write(cirq.to_json(U).encode('utf-8'))
    f.close()

U = cirq.read_json(open('test.json', 'rb'))

---> the following code will fail with:

ValueError: Could not resolve type '_InverseCompositeGate' during deserialization

Cirq version

1.2.0

[tanujkhattar]

I'm surprised this is the case!

@pavoljuhas Can you please take a look?

[pavoljuhas]

@tanujkhattar - this can be reduced to the serialization of an inverted cirq.PhasedFSimGate, which ends up as follows -

>>> print(cirq.to_json(cirq.inverse(cirq.PhasedFSimGate(0))).replace("\\n", "\n"))
{
  "cirq_type": "_InverseCompositeGate"
}

_InverseCompositeGate does not have its own _json_dict_ method so there is no information on what is inverted.

After a quick search through the git history I could not find any tests of _InverseCompositeGate serialization, and its underscored name suggests it is a non-public class.

I wonder why was the serialization omitted for _ICG.
Would you know of more of a context there?

cc: @Strilanc

[tanujkhattar]

There may not be any specific reason;

I think we should go ahead and add _json_dict_ to the gate. We should also consider making _InverseCompositeGate a public gate (and rename it to Adjoint)