Fix C3SXGate to_matrix method (#12742)

* Fix c3sx matrix

* Apply Jake's suggestion

qiskit/circuit/library/standard_gates/x.py

@@ -22,6 +22,7 @@
 from qiskit._accelerate.circuit import StandardGate
 
 _X_ARRAY = [[0, 1], [1, 0]]
+_SX_ARRAY = [[0.5 + 0.5j, 0.5 - 0.5j], [0.5 - 0.5j, 0.5 + 0.5j]]
 
 
 @with_gate_array(_X_ARRAY)
@@ -571,6 +572,7 @@ def __eq__(self, other):
         return isinstance(other, RCCXGate)
 
 
+@with_controlled_gate_array(_SX_ARRAY, num_ctrl_qubits=3, cached_states=(7,))
 class C3SXGate(SingletonControlledGate):
     """The 3-qubit controlled sqrt-X gate.
 

releasenotes/notes/fix-c3sx-gate-matrix-050cf9f9ac3b2b82.yaml

@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    Fixed a missing decorator in :class:`.C3SXGate` that made it fail if :meth:`.Gate.to_matrix` was called.
+    The gate matrix is now return as expected.

test/python/circuit/test_controlled_gate.py

@@ -230,6 +230,12 @@ def test_special_cases_equivalent_to_controlled_base_gate(self):
                 # Ensure that both the array form (if the gate overrides `__array__`) and the
                 # circuit-definition form are tested.
                 self.assertTrue(Operator(special_case_gate).equiv(naive_operator))
+                if not isinstance(special_case_gate, (MCXGate, MCPhaseGate, MCU1Gate)):
+                    # Ensure that the to_matrix method yields the same result
+                    np.testing.assert_allclose(
+                        special_case_gate.to_matrix(), naive_operator.to_matrix(), atol=1e-8
+                    )
+
                 if not isinstance(special_case_gate, CXGate):
                     # CX is treated like a primitive within Terra, and doesn't have a definition.
                     self.assertTrue(Operator(special_case_gate.definition).equiv(naive_operator))

test/python/circuit/test_rust_equivalence.py

@@ -26,7 +26,6 @@
 
 SKIP_LIST = {"rx", "ry", "ecr"}
 CUSTOM_NAME_MAPPING = {"mcx": C3XGate()}
-MATRIX_SKIP_LIST = {"c3sx"}
 
 
 class TestRustGateEquivalence(QiskitTestCase):
@@ -141,9 +140,6 @@ def test_matrix(self):
         """Test matrices are the same in rust space."""
         for name, gate_class in self.standard_gates.items():
             standard_gate = getattr(gate_class, "_standard_gate", None)
-            if name in MATRIX_SKIP_LIST:
-                # to_matrix not defined for type
-                continue
             if standard_gate is None:
                 # gate is not in rust yet
                 continue