Make cirq.FREDKIN gate self-inverse (#6135)

* Make FREDKIN gate self-inverse

* Fix formatting

* Simplify test to check CSWAP matrix is self inverse

cirq-core/cirq/ops/three_qubit_gates.py

@@ -661,6 +661,11 @@ def _qasm_(self, args: 'cirq.QasmArgs', qubits: Tuple['cirq.Qid', ...]) -> Optio
     def _value_equality_values_(self):
         return ()
 
+    def __pow__(self, power):
+        if power == 1 or power == -1:
+            return self
+        return NotImplemented
+
     def __str__(self) -> str:
         return 'FREDKIN'
 

cirq-core/cirq/ops/three_qubit_gates_test.py

@@ -94,8 +94,9 @@ def test_unitary():
     )
 
     assert cirq.has_unitary(cirq.CSWAP)
+    u = cirq.unitary(cirq.CSWAP)
     np.testing.assert_allclose(
-        cirq.unitary(cirq.CSWAP),
+        u,
         np.array(
             [
                 [1, 0, 0, 0, 0, 0, 0, 0],
@@ -110,6 +111,7 @@ def test_unitary():
         ),
         atol=1e-8,
     )
+    np.testing.assert_allclose(u @ u, np.eye(8))
 
     diagonal_angles = [2, 3, 5, 7, 11, 13, 17, 19]
     assert cirq.has_unitary(cirq.ThreeQubitDiagonalGate(diagonal_angles))
@@ -156,7 +158,7 @@ def test_eq():
     eq.add_equality_group(cirq.TOFFOLI(a, b, c), cirq.CCX(a, b, c))
     eq.add_equality_group(cirq.TOFFOLI(a, c, b), cirq.TOFFOLI(c, a, b))
     eq.add_equality_group(cirq.TOFFOLI(a, b, d))
-    eq.add_equality_group(cirq.CSWAP(a, b, c), cirq.FREDKIN(a, b, c))
+    eq.add_equality_group(cirq.CSWAP(a, b, c), cirq.FREDKIN(a, b, c), cirq.FREDKIN(a, b, c) ** -1)
     eq.add_equality_group(cirq.CSWAP(b, a, c), cirq.CSWAP(b, c, a))