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May 20, 2013 at 22:50 comment added FrankH @BenCrowell Please reconsider your down vote with my new improved answer. I think I addressed all your objections...
May 20, 2013 at 22:47 history edited FrankH CC BY-SA 3.0
Improved the answer
May 20, 2013 at 22:24 comment added FrankH @BenCrowell I made a mistake in using the factoring problem. I should have used any of the problems where there is a known classical computer complexity class. The current quantum computers are very trivial - factoring 15 for example. A real quantum computer that does a non trivial problem faster than current classical computers will be non controversial and very convincing. I will leave another comment when I have updated the answer and perhaps you will take away the down vote.
May 20, 2013 at 20:39 comment added user4552 I think there are several problems with this answer. (1) It's an open problem whether factorization is outside the P complexity class. Although it's suspected that it is, there is no proof. (2) You can't prove by experiments what complexity class a problem is in, because the complexity class depends on the limiting behavior. (3) Quantum computers have already been built. (4) Inability to build more complex quantum computers could be due to practical problems, not the failure of this interpretation of quantum mechanics.
May 20, 2013 at 19:53 history answered FrankH CC BY-SA 3.0