Migrate ApproximateTokenSwapper to only use retworkx and make networkx optional

[mtreinish]

Summary

This commit removes the networkx usage in the ApproximateTokenSwapper to
use retworkx instead. Besides being speeding up the execution of the
pass what's more important here is that this was the last networkx usage
in qiskit-terra (with the exeception of a couple compatibility
converters in qiskit.dagcircuit). So this commit also makes networkx an
optional dependency and updates the 3 methods (which are outside the
common usage scenarios) to use runtime imports and emit a more detailed
import error if networkx isn't installed.

Details and comments

Fixes: #5470
Related to: #5100

[eddieschoute]

Cool, I see you narrowed the allowed types on the graph to integers. I assume that is because only integers are supported by retworkx?

[mtreinish]

Cool, I see you narrowed the allowed types on the graph to integers. I assume that is because only integers are supported by retworkx?

Sort of, retworkx graphs allow any python object as a node's data payload/weight, but all nodes are integer indexed, and unlike networkx, retworkx functions that take a node don't use an associative lookup based on the data payload and must be passed an index. I changed it to just be int because I have it work with only index when calling retworkx. We could change it to use anything but then we'd have to maintain a mapping of node data to node index somewhere (for dagcircuit we store the index in the dagnode, so it doesn't have to be a dict).

[lcapelluto]

Cool! 🎉

[mtreinish]

I ran some quick benchmarks of the token swapper just now:

The big improvement in creation time for retworkx is at 300 nodes, it's the default threshold for using the multiple threads: https://retworkx.readthedocs.io/en/stable/stubs/retworkx.graph_distance_matrix.html It might be worth tuning that a bit and setting it to a lower number.

(both graphs are log-log)

I generated the data with:

import time

import retworkx as rx
import numpy as np
from qiskit.transpiler.passes.routing.algorithms import ApproximateTokenSwapper

np.random.seed(42)
create_time = {}
map_time = {}

for size in np.logspace(2, 3, dtype=int):
    print(size)
    graph = rx.undirected_gnm_random_graph(size, size ** 2 // 10, seed=42)
    for i in graph.node_indexes():
        try:
            graph.remove_edge(i, i)  # Remove self-loops.
        except rx.NoEdgeBetweenNodes:
            continue
    # Make sure the graph is connected by adding C_n
    graph.add_edges_from_no_data(
        [(i, i + 1) for i in range(len(graph) - 1)])
    start = time.time()
    swapper = ApproximateTokenSwapper(graph)
    stop = time.time()
    create_time[size] = stop - start

    # Generate a randomized permutation.
    rand_perm = np.random.permutation(graph.nodes())
    permutation = dict(zip(graph.nodes(), rand_perm))
    mapping = dict(itertools.islice(permutation.items(), 0, size, 2))
    start = time.time()
    out = list(swapper.map(mapping, trials=40))
    stop = time.time()
    map_time[size] = stop - start