The traveling salesman problem isn't hard. It's one of those things that's NP-hard only for pathological cases, as is linear programming. Solutions to the TSP which produce a near-optimum result, and the optimal result most of the time, are easy. (Connect nodes arbitrarily. Then randomly cut two links to split path into three sections, try all ways to reconnect the three sections, pick the best. Repeat until no improvement for a while. Bell Labs, 1960s.)
Now, if quantum computing could help with factoring, we'd have a problem.
[1] https://books.google.com/books?id=tTkEAAAAMBAJ&pg=PA40&lpg=P...