![]() You can already quickly run an algorithm which will get you a journey plan that's maybe 99% as good as the optimum.Īctually, I think there is a theorem that finding an algorithm that efficiently produces highly-accurate approximate solutions to arbitrary problems in NP-hard is about as hard solving NP-complete problems exactly.Īll this aside, it's worth noting that D-Wave is only claiming to provide a square-root speed-up for NP-complete problems, and there is some doubt as to whether they can even deliver that, as they scale up to larger numbers of quantum computers. Nobody is going to use Travelling Salesman in the real world to plan journeys. The one place quantum computers are potentially useful is crypto-nearly all of which revolves around the hardness of factoring and discrete logs (which I think is a very strange coincidence, if it is one).ĭisclaimer: I am a physicist who works on quantum computing and also has a computer science background But with our knowledge now, even if you fit a traveling salesman instance, the quantum computer wouldn't know what to do with it.Īs GP pointed out, we do have excellent approximations for TSP and most practical problems-the issue is mathematical-that we don't have algorithms that can guarantee the absolute best solution. The evidence is that the only two problems quantum computers can solve in polytime right now that a turing machine can't are integer factorization and discrete log, neither of which is believed to be NP-hard.īTW, of course a problem instance must fit in memory-but the idea is that we should be able to build a 1000 qubit computer, while going through 2^1000 possibilities to brute-force a problem of size 1000 is intractable. ![]() This is, of course, not shown-for all we know, it could even be strictly bigger than NP. You are pretty much correct-traveling salesman is NP-hard and most theorists believe that BQP, the class of problems efficiently solvable by a quantum computer in polynomial time, is strictly smaller than NP (and therefore contains no NP-complete problems).
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