Support inverse gate JSON seralization

[justinpan0]

Response to issue #6769

Fix validation

Running the code snippet provided in #6769 now yields correct result:

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",
            "val": {
              "cirq_type": "QubitPermutationGate",
              "permutation": [
                0,
                1,
                2
              ]
            }
          },
          "qubits": [
            {
              "cirq_type": "LineQubit",
              "x": 0
            },
            {
              "cirq_type": "LineQubit",
              "x": 1
            },
            {
              "cirq_type": "LineQubit",
              "x": 2
            }
          ]
        }
      ]
    }
  ]
}
0: ───[0>0]──────
      │
1: ───[1>1]──────
      │
2: ───[2>2]^-1───

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.86%. Comparing base (83a8e0e) to head (1ce0c5d).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #6912   +/-   ##
=======================================
  Coverage   97.86%   97.86%           
=======================================
  Files        1084     1084           
  Lines       94290    94293    +3     
=======================================
+ Hits        92280    92283    +3     
  Misses       2010     2010           

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[dstrain115]

Is there a reason this is calling cirq.inverse vs instantiating the _InverseCompositeGate class? I am not sure which is better.

I guess if we created an inverse for a gate in a newer version of cirq, it could instantiate that instead, which would not be consistent object-wise, but might be a better result? For instance, we could fix this so QubitPermutationGate(0,1,2) ^ -1 returns QubitPermutationGate(2,1,0) or whatever.

In any case, maybe add a comment to explain the behaviour.

[dstrain115]

LGTM pending one comment.