Avoid overhead for synthesized nodes lookup (#13424) (#13425)

After #12550 a hash implementation was added to the implementation
of DAGOpNode to be able to have identical instances of dag nodes used be
usable in a set or dict. This is because after #12550 changed the
DAGCircuit so the DAGOpNode instances were just a python view of the
data contained in the nodes of a dag. While prior to #12550 the actual
DAGOpNode objects were returned by reference from DAG methods. However,
this hash implementation has additional overhead compared to the object
identity based version used before. This has caused a regression in some
cases for high level synthesis when it's checking for nodes it's already
synthesized. This commit addresses this by changing the dict key to be
the node id instead of the node object. The integer hashing is
significantly faster than the object hashing.

(cherry picked from commit 8c6ad02)

Co-authored-by: Matthew Treinish <[email protected]>

qiskit/transpiler/passes/synthesis/high_level_synthesis.py

@@ -382,7 +382,7 @@ def _run(
 
             # If the synthesis changed the operation (i.e. it is not None), store the result.
             if synthesized is not None:
-                synthesized_nodes[node] = (synthesized, synthesized_context)
+                synthesized_nodes[node._node_id] = (synthesized, synthesized_context)
 
             # If the synthesis did not change anything, just update the qubit tracker.
             elif not processed:
@@ -407,8 +407,9 @@ def _run(
         outer_to_local = context.to_local_mapping()
 
         for node in dag.topological_op_nodes():
-            if node in synthesized_nodes:
-                op, op_context = synthesized_nodes[node]
+
+            if op_tuple := synthesized_nodes.get(node._node_id, None):
+                op, op_context = op_tuple
 
                 if isinstance(op, Operation):
                     out.apply_operation_back(op, node.qargs, node.cargs)