Implement the inverse of IonQ native gates (#5889)

Implement the inverse of IonQ's native gates, GPIGate, GPI2Gate and MSGate, by implementing `__pow__` method for `power==-1`.

cirq-ionq/cirq_ionq/ionq_native_gates.py

@@ -70,6 +70,15 @@ def _circuit_diagram_info_(
     ) -> Union[str, 'protocols.CircuitDiagramInfo']:
         return protocols.CircuitDiagramInfo(wire_symbols=(f'GPI({self.phase!r})',))
 
+    def __pow__(self, power):
+        if power == 1:
+            return self
+
+        if power == -1:
+            return self
+
+        return NotImplemented
+
 
 GPI = GPIGate(phi=0)
 document(
@@ -137,6 +146,15 @@ def _json_dict_(self) -> Dict[str, Any]:
     def _value_equality_values_(self) -> Any:
         return self.phi
 
+    def __pow__(self, power):
+        if power == 1:
+            return self
+
+        if power == -1:
+            return GPI2Gate(phi=self.phi + 0.5)
+
+        return NotImplemented
+
 
 GPI2 = GPI2Gate(phi=0)
 document(
@@ -219,6 +237,15 @@ def _json_dict_(self) -> Dict[str, Any]:
     def _value_equality_values_(self) -> Any:
         return (self.phi0, self.phi1)
 
+    def __pow__(self, power):
+        if power == 1:
+            return self
+
+        if power == -1:
+            return MSGate(phi0=self.phi0 + 0.5, phi1=self.phi1)
+
+        return NotImplemented
+
 
 MS = MSGate(phi0=0, phi1=0)
 document(

cirq-ionq/cirq_ionq/ionq_native_gates_test.py

@@ -21,6 +21,18 @@
 import cirq_ionq as ionq
 
 
+PARAMS_FOR_ONE_ANGLE_GATE = [0, 0.1, 0.4, math.pi / 2, math.pi, 2 * math.pi]
+PARAMS_FOR_TWO_ANGLE_GATE = [
+    (0, 1),
+    (0.1, 1),
+    (0.4, 1),
+    (math.pi / 2, 0),
+    (0, math.pi),
+    (0.1, 2 * math.pi),
+]
+INVALID_GATE_POWER = [-2, -0.5, 0, 0.5, 2]
+
+
 @pytest.mark.parametrize(
     "gate,nqubits,diagram",
     [
@@ -74,3 +86,50 @@ def test_ms_unitary(phases):
 
     mat = cirq.protocols.unitary(gate)
     numpy.testing.assert_array_almost_equal(mat.dot(mat.conj().T), numpy.identity(4))
+
+
+@pytest.mark.parametrize(
+    "gate",
+    [
+        *[ionq.GPIGate(phi=angle) for angle in PARAMS_FOR_ONE_ANGLE_GATE],
+        *[ionq.GPI2Gate(phi=angle) for angle in PARAMS_FOR_ONE_ANGLE_GATE],
+        *[ionq.MSGate(phi0=angles[0], phi1=angles[1]) for angles in PARAMS_FOR_TWO_ANGLE_GATE],
+    ],
+)
+def test_gate_inverse(gate):
+    """Tests that the inverse of natives gate are correct."""
+    mat = cirq.protocols.unitary(gate)
+    mat_inverse = cirq.protocols.unitary(gate**-1)
+    dim = mat.shape[0]
+
+    numpy.testing.assert_array_almost_equal(mat.dot(mat_inverse), numpy.identity(dim))
+
+
+@pytest.mark.parametrize(
+    "gate",
+    [
+        *[ionq.GPIGate(phi=angle) for angle in PARAMS_FOR_ONE_ANGLE_GATE],
+        *[ionq.GPI2Gate(phi=angle) for angle in PARAMS_FOR_ONE_ANGLE_GATE],
+        *[ionq.MSGate(phi0=angles[0], phi1=angles[1]) for angles in PARAMS_FOR_TWO_ANGLE_GATE],
+    ],
+)
+def test_gate_power1(gate):
+    """Tests that power=1 for native gates are correct."""
+    mat = cirq.protocols.unitary(gate)
+    mat_power1 = cirq.protocols.unitary(gate**1)
+
+    numpy.testing.assert_array_almost_equal(mat, mat_power1)
+
+
+@pytest.mark.parametrize(
+    "gate,power",
+    [
+        *[(ionq.GPIGate(phi=0.1), power) for power in INVALID_GATE_POWER],
+        *[(ionq.GPI2Gate(phi=0.1), power) for power in INVALID_GATE_POWER],
+        *[(ionq.MSGate(phi0=0.1, phi1=0.2), power) for power in INVALID_GATE_POWER],
+    ],
+)
+def test_gate_power_not_implemented(gate, power):
+    """Tests that any power other than 1 and -1 is not implemented."""
+    with pytest.raises(TypeError):
+        _ = gate**power