Gates in the gate set are not considered solved in the graph (#8526)

**Context:**
A `KeyError` is raised when trying to access the decomposition rule of
an operator that is in the gate set.

**Description of the Change:**
Now the graph correctly returns `False` when `is_solved_for` is called
on an op in the gate set, and the correct error is raised when trying to
access the decomposition rule of such an operator.

**Benefits:**

**Possible Drawbacks:**

**Related GitHub Issues:**
[sc-102050]

Author: astralcai

doc/releases/changelog-dev.md

@@ -196,6 +196,9 @@
   when a device that extends the ``LegacyDevice`` does not declare support for mid-circuit measurements.
   [(#8486)](https://github.com/PennyLaneAI/pennylane/pull/8486)
 
+* Fixes a bug where a `KeyError` is raised when querying the decomposition rule for an operator in the gate set from a :class:`~pennylane.decomposition.DecompGraphSolution`.
+  [(#8526)](https://github.com/PennyLaneAI/pennylane/pull/8526)
+
 <h3>Contributors ✍️</h3>
 
 This release contains contributions from (in alphabetical order):

pennylane/decomposition/decomposition_graph.py

@@ -552,7 +552,7 @@ def _all_solutions(
         def _is_solved(op_node: _OperatorNode):
             return (
                 op_node in self._all_op_indices
-                and self._all_op_indices[op_node] in visitor.distances
+                and self._all_op_indices[op_node] in visitor.predecessors
             )
 
         def _is_feasible(op_node: _OperatorNode):

tests/decomposition/test_decomposition_graph.py

@@ -42,7 +42,6 @@
     side_effect=lambda x: decompositions[_to_name(x)],
 )
 class TestDecompositionGraph:
-
     def test_weighted_graph_solve(self, _):
         """Tests solving a simple graph for the optimal decompositions with weighted gates."""
 
@@ -230,6 +229,15 @@ def custom_decomp(wires):
         # edges from the dummy starting node to the target gate set.
         assert len(graph._graph.edges()) == 11
 
+        solution = graph.solve()
+
+        # verify that is_solved_for returns False for gates in the gate set
+        assert not solution.is_solved_for(qml.RX(0.5, wires=0))
+
+        # verify that the correct error is raised
+        with pytest.raises(DecompositionError, match="is unsolved in this decomposition graph."):
+            solution.decomposition(qml.RX(0.5, wires=0))
+
     def test_graph_solve(self, _):
         """Tests solving a simple graph for the optimal decompositions."""