1. Is there any NP-Problem that can't be (maybe even proven) solved by quantum computers. I'm not talking about quantum NP-Problems (if that's even a thing), but about normal NP.
  2. If that NP Problem exists could you also use it for cryptography, since I don't want to buy a quantum computer just to be secure.

EDIT: I'm not talking about NP-complete, because that would have no use (I think) in cryptography and also not about symmetric key encryption.

  • $\begingroup$ Closely related question; you have wrong ideas what NP-hardness means. $\endgroup$
    – Raphael
    Jan 31 '17 at 18:11
  • $\begingroup$ Yea I did, but now I think I understood it after some more research. $\endgroup$
    – Zonko
    Jan 31 '17 at 18:18
  • 1
    $\begingroup$ What is NP problem? If it NP-complete then there is no such problem known because relation between BQP and NP is currently unknown. If it is NP-hard, then recall BQP is in PSPACE so just take any problem outside of it. If it is a problem in NP and not necessary complete, then this is even stronger then unsolvability of NP-complete problem. If I remember correctly, even $BQP \in NP$ is unknown. $\endgroup$
    – Eugene
    Jan 31 '17 at 19:50

Nobody really knows whether quantum computers can solve all NP complete problems in polynomial time or not. There is strong evidence that they cannot: Strengths and Weaknesses of Quantum Computing, but no definite proof.


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