MCXGate.inverse to return gate of same mode as original gate.

qiskit/circuit/library/standard_gates/x.py

@@ -752,6 +752,10 @@ def __init__(self, num_ctrl_qubits, label=None, ctrl_state=None, _name='mcx'):
                          num_ctrl_qubits=num_ctrl_qubits, label=label, ctrl_state=ctrl_state)
         self.base_gate = XGate()
 
+    def inverse(self):
+        """Invert this gate. The MCX is its own inverse."""
+        return MCXGate(num_ctrl_qubits=self.num_ctrl_qubits, ctrl_state=self.ctrl_state)
+
     @staticmethod
     def get_num_ancilla_qubits(num_ctrl_qubits, mode='noancilla'):
         """Get the number of required ancilla qubits without instantiating the class.
@@ -811,6 +815,10 @@ class MCXGrayCode(MCXGate):
     def __init__(self, num_ctrl_qubits, label=None, ctrl_state=None):
         super().__init__(num_ctrl_qubits, label=label, ctrl_state=ctrl_state, _name='mcx_gray')
 
+    def inverse(self):
+        """Invert this gate. The MCX is its own inverse."""
+        return MCXGrayCode(num_ctrl_qubits=self.num_ctrl_qubits, ctrl_state=self.ctrl_state)
+
     def _define(self):
         """Define the MCX gate using the Gray code."""
         # pylint: disable=cyclic-import
@@ -840,6 +848,10 @@ def get_num_ancilla_qubits(num_ctrl_qubits, mode='recursion'):
         """Get the number of required ancilla qubits."""
         return MCXGate.get_num_ancilla_qubits(num_ctrl_qubits, mode)
 
+    def inverse(self):
+        """Invert this gate. The MCX is its own inverse."""
+        return MCXRecursive(num_ctrl_qubits=self.num_ctrl_qubits, ctrl_state=self.ctrl_state)
+
     def _define(self):
         """Define the MCX gate using recursion."""
         # pylint: disable=cyclic-import
@@ -896,6 +908,12 @@ def __init__(self, num_ctrl_qubits, dirty_ancillas=False, label=None, ctrl_state
         super().__init__(num_ctrl_qubits, label=label, ctrl_state=ctrl_state, _name='mcx_vchain')
         self._dirty_ancillas = dirty_ancillas
 
+    def inverse(self):
+        """Invert this gate. The MCX is its own inverse."""
+        return MCXVChain(num_ctrl_qubits=self.num_ctrl_qubits,
+                         dirty_ancillas=self._dirty_ancillas,
+                         ctrl_state=self.ctrl_state)
+
     @staticmethod
     def get_num_ancilla_qubits(num_ctrl_qubits, mode='v-chain'):
         """Get the number of required ancilla qubits."""

releasenotes/notes/4953-Inverse-of-MCX-gates-generated-without-qubits-for-ancillae-d8858552eb2cd3f9.yaml

@@ -12,3 +12,8 @@ fixes:
     For ``C3XGate`` with a non-zero ``angle``, inverting the gate via
     ``C3XGate.inverse()`` had previously generated an incorrect inverse gate.
     This has been corrected.
+  - |
+    The ``MCXGate`` modes have been updated to return a gate of the same mode
+    when calling ``.inverse()``. This resolves an issue where in some cases,
+    transpiling a circuit containing the inverse of an ``MCXVChain`` gate would
+    raise an error.

test/python/circuit/test_gate_definitions.py

@@ -120,7 +120,6 @@ def test_cx_definition(self):
 @ddt
 class TestStandardGates(QiskitTestCase):
     """Standard Extension Test."""
-
     @unpack
     @data(
         *inspect.getmembers(
@@ -152,6 +151,42 @@ def test_definition_parameters(self, class_name, gate_class):
         if gate.definition is not None:
             self.assertEqual(gate.definition.parameters, set(param_vector))
 
+    @unpack
+    @data(
+        *inspect.getmembers(
+            standard_gates,
+            predicate=lambda value: (inspect.isclass(value)
+                                     and issubclass(value, Gate)))
+    )
+    def test_inverse(self, class_name, gate_class):
+        """Verify self-inverse pair yield identity for all standard gates."""
+
+        free_params = _get_free_params(gate_class)
+        n_params = len(free_params)
+        float_vector = [0.1 + 0.1*i for i in range(n_params)]
+
+        if class_name in ('MCPhaseGate', 'MCU1Gate'):
+            float_vector = float_vector[:-1]
+            gate = gate_class(*float_vector, num_ctrl_qubits=2)
+        elif class_name in ('MCXGate', 'MCXGrayCode', 'MCXRecursive', 'MCXVChain'):
+            num_ctrl_qubits = 3
+            float_vector = float_vector[:-1]
+            gate = gate_class(num_ctrl_qubits, *float_vector)
+        elif class_name == 'MSGate':
+            num_qubits = 3
+            float_vector = float_vector[:-1]
+            gate = gate_class(num_qubits, *float_vector)
+        else:
+            gate = gate_class(*float_vector)
+
+        from qiskit.quantum_info.operators.predicates import is_identity_matrix
+
+        self.assertTrue(is_identity_matrix(Operator(gate).dot(gate.inverse()).data))
+
+        if gate.definition is not None:
+            self.assertTrue(is_identity_matrix(Operator(gate).dot(gate.definition.inverse()).data))
+            self.assertTrue(is_identity_matrix(Operator(gate).dot(gate.inverse().definition).data))
+
 
 class TestGateEquivalenceEqual(QiskitTestCase):
     """Test the decomposition of a gate in terms of other gates