Make order of traversal deterministic in merge_operations primitive (…

…#4764)

This PR fixes the iteration order of operations in a single moment in the `merge_operations` transformer primitive by iterating over operations in sorted order, sorted based on `op.qubits`.

cirq-core/cirq/transformers/transformer_primitives.py

@@ -188,7 +188,7 @@ def apply_merge_func(op1: ops.Operation, op2: ops.Operation) -> Optional[ops.Ope
     ret_circuit = circuits.Circuit()
     for current_moment in circuit:
         new_moment = ops.Moment()
-        for op in current_moment:
+        for op in sorted(current_moment.operations, key=lambda op: op.qubits):
             op_qs = set(op.qubits)
             idx = ret_circuit.prev_moment_operating_on(tuple(op_qs))
             if idx is not None and op_qs.issubset(ret_circuit[idx][op_qs].operations[0].qubits):

cirq-core/cirq/transformers/transformer_primitives_test.py

@@ -325,6 +325,29 @@ def merge_func(op1, op2):
     )
 
 
+@pytest.mark.parametrize('qubit_order', ([0, 1], [1, 0]))
+def test_merge_operations_deterministic_order(qubit_order):
+    q = cirq.LineQubit.range(2)
+    c_orig = cirq.Circuit(cirq.identity_each(*q), cirq.H.on_each(q[i] for i in qubit_order))
+    cirq.testing.assert_has_diagram(
+        c_orig,
+        '''
+0: ───I───H───
+      │
+1: ───I───H───''',
+    )
+    c_new = cirq.merge_operations(
+        c_orig, lambda op1, op2: op2 if isinstance(op1.gate, cirq.IdentityGate) else None
+    )
+    cirq.testing.assert_has_diagram(
+        c_new,
+        '''
+0: ───H───────
+
+1: ───────H───''',
+    )
+
+
 @pytest.mark.parametrize("op_density", [0.1, 0.5, 0.9])
 def test_merge_operations_complexity(op_density):
     prng = cirq.value.parse_random_state(11011)