Cache lexicographical topological sort key in DAGNode (Qiskit#4040)

This commit caches the string sort key used for lexicographical
topological sort as an attribute in DAGNode objects. Currently when
retworkx's lexicographical topological sort call is called it needs to
call the python callable provided to get a string used for sorting.
Prior to this commit about 70% of the cumulative time spent in the
lexicographical topological sort function is spent in python. This is
because everytime it is sorting a new DAGNode it has to call
str(x.qargs) which spends all that time constructing the string
including a dict.get() and bit and register repr() calls, etc. To avoid
this unecessary overhead at run time this commit adds a sort_key
attribute to the DAGNode class which is set during __init__() and
updates to the qargs property. Then the DAGCircuit lexicographical
topological sort wrapper method changes the callable to use this
attribute. Doing this eliminates all the overhead from calling back to
python because it simply becomes attribute access.

Author: mtreinish

qiskit/dagcircuit/dagnode.py

@@ -30,6 +30,7 @@ def __init__(self, data_dict, nid=-1):
         """Create a node """
         self._node_id = nid
         self.data_dict = data_dict
+        self.sort_key = str(self.qargs)
 
     @property
     def type(self):
@@ -64,6 +65,7 @@ def qargs(self):
     def qargs(self, new_qargs):
         """Sets the qargs to be the given list of qargs."""
         self.data_dict['qargs'] = new_qargs
+        self.sort_key = str(new_qargs)
 
     @property
     def cargs(self):

qiskit/dagcircuit/retworkx_dagcircuit.py

@@ -107,7 +107,7 @@ def topological_nodes(self):
             generator(DAGNode): node in topological order
         """
         def _key(x):
-            return str(x.qargs)
+            return x.sort_key
 
         return iter(rx.lexicographical_topological_sort(
             self._multi_graph,