We know that $\text{BPP} \subseteq \text{BQP}$ but we have no proof that $\text{BPP} \subset \text{BQP}$ (though we have proof that $\text{BQP} \neq \text{BPP}$ with an oracle).

Since Simon's problem (as factoring) is easily solvable by a quantum computer, and in exponential time complexity solvable by a classical computer, that's a hint of the separation between BQP and BPP and therefore this can be a pure NP problem. Am I right?

  • $\begingroup$ What research and self-study have you done? There are lots of sources that talk about this topic. $\endgroup$
    – D.W.
    Commented Apr 21, 2014 at 14:49

1 Answer 1


Simon's problem is not a pure NP problem, for two reasons:

  • It is an oracle problem. We are given an oracle for some function $f$. That's not something that you can do within the definition of a NP problem.

  • It is a promise problem. We are given the promise that $f$ will satisfy a particular property (it is two-to-one, and has a particular structure). That too is not something you can do within the definition of a NP problem.

So Simon's problem is not a problem in the formal complexity class NP; it's just something different. For the same reasons, it's not NP-intermediate, either.


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