Add json serialization for PauliSum (quantumlib#5367)

Fixes quantumlib#3071 

One approach to this would have been to serialize frozenset and tuple in Cirq, but this instead takes the approach of not relying on this but appropriately serializing and deserializing these.

Author: dabacon

cirq-core/cirq/json_resolver_cache.py

@@ -146,6 +146,7 @@ def _symmetricalqidpair(qids):
         'PauliString': cirq.PauliString,
         'PauliStringPhasor': cirq.PauliStringPhasor,
         'PauliStringPhasorGate': cirq.PauliStringPhasorGate,
+        'PauliSum': cirq.PauliSum,
         '_PauliX': cirq.ops.pauli_gates._PauliX,
         '_PauliY': cirq.ops.pauli_gates._PauliY,
         '_PauliZ': cirq.ops.pauli_gates._PauliZ,

cirq-core/cirq/ops/linear_combinations.py

@@ -498,6 +498,20 @@ def _unitary_(self) -> np.ndarray:
             return m
         raise ValueError(f'{self} is not unitary')
 
+    def _json_dict_(self):
+        def key_json(k: UnitPauliStringT):
+            return [list(e) for e in sorted(k)]
+
+        return {'items': list((key_json(k), v) for k, v in self._linear_dict.items())}
+
+    @classmethod
+    def _from_json_dict_(cls, items, **kwargs):
+        mapping = {
+            frozenset(tuple(qid_pauli) for qid_pauli in unit_pauli_string): val
+            for unit_pauli_string, val in items
+        }
+        return cls(linear_dict=value.LinearDict(mapping))
+
     def expectation_from_state_vector(
         self,
         state_vector: np.ndarray,

cirq-core/cirq/protocols/json_test_data/PauliSum.json

@@ -0,0 +1,67 @@
+{
+  "cirq_type": "PauliSum",
+  "items": [
+    [
+      [
+        [
+          {
+            "cirq_type": "LineQubit",
+            "x": 0
+          },
+          {
+            "cirq_type": "_PauliX",
+            "exponent": 1.0,
+            "global_shift": 0.0
+          }
+        ],
+        [
+          {
+            "cirq_type": "LineQubit",
+            "x": 1
+          },
+          {
+            "cirq_type": "_PauliX",
+            "exponent": 1.0,
+            "global_shift": 0.0
+          }
+        ]
+      ],
+      {
+        "cirq_type": "complex",
+        "real": 1.0,
+        "imag": 0.0
+      }
+    ],
+    [
+      [
+        [
+          {
+            "cirq_type": "LineQubit",
+            "x": 0
+          },
+          {
+            "cirq_type": "_PauliY",
+            "exponent": 1.0,
+            "global_shift": 0.0
+          }
+        ],
+        [
+          {
+            "cirq_type": "LineQubit",
+            "x": 1
+          },
+          {
+            "cirq_type": "_PauliY",
+            "exponent": 1.0,
+            "global_shift": 0.0
+          }
+        ]
+      ],
+      {
+        "cirq_type": "complex",
+        "real": 0.0,
+        "imag": 1.0
+      }
+    ]
+  ]
+}

cirq-core/cirq/protocols/json_test_data/PauliSum.repr

@@ -0,0 +1 @@
+cirq.PauliSum(cirq.LinearDict({frozenset({(cirq.LineQubit(1), cirq.X), (cirq.LineQubit(0), cirq.X)}): (1+0j), frozenset({(cirq.LineQubit(1), cirq.Y), (cirq.LineQubit(0), cirq.Y)}): (1j)}))

cirq-core/cirq/protocols/json_test_data/spec.py

@@ -47,7 +47,6 @@
         'DiagonalGate',
         'NeutralAtomDevice',
         'PauliInteractionGate',
-        'PauliSum',
         'PauliSumCollector',
         'PauliSumExponential',
         'PauliTransform',