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From what I gathered, it's similar to how a CPU and GPU compare: different complexity classes, different problems it's efficient on.



The CPU-GPU analogy is very good for all sorts of reasons. For some things there's no speedup, for some important things there's a huge speedup, for other things there's some significant speedup, but not game-changing.

I tend to think of applications where you might want to brute-force search or simulate over some large set as being where quantum computing will be most significant, but I say that very vaguely and timidly.

This gives a number of applications and algorithms; I found some of the references in it really interesting to read:

http://math.nist.gov/quantum/zoo/




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