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Belzebutt13 karma

There seems to be some computing problems for which quantum computers hold a future promise if the current trend holds, for example breaking RSA encryption, to the point where governments are storing data/conversations today hoping that they will break them in a few years.

There are computing problems for which quantum computers seem to provide roughly the same performance as classic computers, i.e. they don't provide a tangible benefit (I don't recall an example of that though).

What are some computing problems TODAY for which quantum computers are already used to considerably speed up the solution, or which a classical computer cannot solve?