Add default decomposition for cirq.QubitPermutationGate in terms of a…

…djacent swaps (#5093)

- Adds decomposition to `cirq.QubitPermutationGate` in terms of minimum number of adjacent swap operations on qubits. 
- Part of #4858

Closes #5090

cirq-core/cirq/ops/permutation_gate.py

@@ -12,11 +12,11 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-from typing import Any, Dict, Sequence, Tuple, TYPE_CHECKING
+from typing import Any, Dict, Iterable, Sequence, Tuple, TYPE_CHECKING
 
 from cirq import protocols, value
 from cirq._compat import deprecated
-from cirq.ops import raw_types
+from cirq.ops import raw_types, swap_gates
 
 if TYPE_CHECKING:
     import cirq
@@ -74,6 +74,25 @@ def num_qubits(self):
     def _has_unitary_(self):
         return True
 
+    def _decompose_(self, qubits: Sequence['cirq.Qid']) -> 'cirq.OP_TREE':
+        n = len(qubits)
+        qubit_ids = [*range(n)]
+        is_sorted = False
+
+        def _swap_if_out_of_order(idx: int) -> Iterable['cirq.Operation']:
+            nonlocal is_sorted
+            if self._permutation[qubit_ids[idx]] > self._permutation[qubit_ids[idx + 1]]:
+                yield swap_gates.SWAP(qubits[idx], qubits[idx + 1])
+                qubit_ids[idx + 1], qubit_ids[idx] = qubit_ids[idx], qubit_ids[idx + 1]
+                is_sorted = False
+
+        while not is_sorted:
+            is_sorted = True
+            for i in range(0, n - 1, 2):
+                yield from _swap_if_out_of_order(i)
+            for i in range(1, n - 1, 2):
+                yield from _swap_if_out_of_order(i)
+
     def _apply_unitary_(self, args: 'cirq.ApplyUnitaryArgs'):
         # Compute the permutation index list.
         permuted_axes = list(range(len(args.target_tensor.shape)))

cirq-core/cirq/ops/permutation_gate_test.py

@@ -15,6 +15,7 @@
 import pytest
 
 import cirq
+import numpy as np
 from cirq.ops import QubitPermutationGate
 
 
@@ -30,8 +31,12 @@ def test_permutation_gate_repr():
     cirq.testing.assert_equivalent_repr(QubitPermutationGate([0, 1]))
 
 
-def test_permutation_gate_consistent_protocols():
-    gate = QubitPermutationGate([1, 0, 2, 3])
+rs = np.random.RandomState(seed=1234)
+
+
+@pytest.mark.parametrize('permutation', [rs.permutation(i) for i in range(3, 7)])
+def test_permutation_gate_consistent_protocols(permutation):
+    gate = QubitPermutationGate(list(permutation))
     cirq.testing.assert_implements_consistent_protocols(gate)
 
 
@@ -98,6 +103,8 @@ def test_permutation_gate_maps(maps, permutation):
     permutationOp = cirq.QubitPermutationGate(permutation).on(*qs)
     circuit = cirq.Circuit(permutationOp)
     cirq.testing.assert_equivalent_computational_basis_map(maps, circuit)
+    circuit = cirq.Circuit(cirq.I.on_each(*qs), cirq.decompose(permutationOp))
+    cirq.testing.assert_equivalent_computational_basis_map(maps, circuit)
 
 
 def test_setters_deprecated():