We have specifically in mind a logic-gate instantiation of BQP, that is, a polynomial-time uniform family of quantum circuits (that is, a standard gate-based quantum computer), and for P we …

Background The complexity classes BPP, BQP, and QMA are defined semantically. Let me try to explain a little bit what is the difference between a semantic definition and a syntactic one. The …

2014年8月9日 · The argument makes no sense to me. Grover’s algorithm does not solve any NP-complete problem, in fact it solves a P-problem, hence assuming P=BQP does not tell us …

EQP is the class of problems solvable deterministically using a quantum computer in polynomial time - that seems to me to be a good analogue to P, whereas BQP is the quantum analogue of …

But the question of what impact P ≠ NP P ≠ N P would have on BQP B Q P is a perfectly good one, which I bet Scott Aaronson and Greg Kuperberg have lots to say about.

Similarly, quantum walks are BQP-complete, but not all quantum algorithms have a natural quantum walk formulation. Calling any BQP-complete problem a computational primitive is a …

Problems in BQP, such as factoring, are strongly suspected not to be NP-complete either, but it is an open problem to show that that would imply that the polynomial hierarchy collapses.

There is a theorem of Thurston and Garside that a trivial braid can be recognized in polynomial time; maybe the same is true of the unknot. One question that interests me, maybe for no …

Exercise 3.2 of Computational Complexity, a Modern Approach states: Prove: NP != SPACE(n) [Hint: we don't know if either is a subset of the other.] I don't know how to solve this problem. …

What do you by "is known where n is prime". Does there exist a polynomial time algorithm. To be honest, I would be surprised if thats the case. The reason for that is that I believe that it would …