Fix FABLE template to return the correct result in JIT mode

doc/releases/changelog-dev.md

@@ -102,6 +102,9 @@
 * The ``qml.Qubitization`` template now orders the ``control`` wires first and the ``hamiltonian`` wires second, which is the expected according to other templates.
   [(#6229)](https://github.com/PennyLaneAI/pennylane/pull/6229)
 
+* The ``qml.FABLE`` template now returns the correct value when JIT is enabled.
+  [(#6263)](https://github.com/PennyLaneAI/pennylane/pull/6263)
+
 * <h3>Contributors ✍️</h3>
 
 This release contains contributions from (in alphabetical order):

pennylane/templates/subroutines/fable.py

@@ -129,7 +129,7 @@
         super().__init__(input_matrix, wires=wires, id=id)
 
     @staticmethod
     def compute_decomposition(input_matrix, wires, tol=0):  # pylint:disable=arguments-differ
         r"""Sequence of gates that represents the efficient circuit produced by the FABLE technique
 
         Args:
@@ -166,7 +166,11 @@
                 for c_wire in nots:
                     op_list.append(qml.CNOT(wires=[c_wire] + ancilla))
                 op_list.append(qml.RY(2 * theta, wires=ancilla))
-                nots[wire_map[control_index]] = 1
+                nots = {}
+                if wire_map[control_index] in nots:
+                    del nots[wire_map[control_index]]
+                else:
+                    nots[wire_map[control_index]] = 1
             else:
                 if abs(2 * theta) > tol:
                     for c_wire in nots:

tests/templates/test_subroutines/test_fable.py

@@ -285,6 +285,29 @@ def circuit_jax(input_matrix):
         gradient_jax = grad_fn(input_matrix_jax)
         assert np.allclose(gradient_numeric, gradient_jax[0, 0], rtol=0.001)
 
+    @pytest.mark.jax
+    def test_jit_result(self):
+        """Test that the value returned in JIT mode equals the value returned without JIT."""
+        import jax
+
+        def fable(input_matrix):
+            qml.FABLE(input_matrix, wires=range(5), tol=0)
+            return qml.expval(qml.PauliZ(wires=0))
+
+        input_matrix = np.array(
+            [
+                [-0.5, -0.4, 0.6, 0.7],
+                [0.9, 0.9, 0.8, 0.9],
+                [0.8, 0.7, 0.9, 0.8],
+                [0.9, 0.7, 0.8, 0.3],
+            ]
+        )
+
+        device = qml.device("default.qubit", wires=5)
+        interpreted_fn = qml.QNode(fable, device)
+        jitted_fn = jax.jit(interpreted_fn)
+        assert np.allclose(jitted_fn(input_matrix), interpreted_fn(input_matrix))
+
     @pytest.mark.jax
     def test_fable_grad_jax_jit_error(self, input_matrix):
         """Test that FABLE is differentiable when using jax."""