arXiv:2209.10398cs.CC
BQP is not in NP
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Abstract
Quantum computers are widely believed have an advantage over classical computers, and some have even published some empirical evidence that this is the case. However, these publications do not include a rigorous proof of this advantage, which would have to minimally state that the class of problems decidable by a quantum computer in polynomial time, BQP, contains problems that are not in the class of problems decidable by a classical computer with similar time bounds, P. Here, I provide the proof of a stronger result that implies this result: BQP contains problems that lie beyond the much larger classical computing class NP. This proves that quantum computation is able to efficiently solve problems which are far beyond the capabilities of classical computers.
No. As far as we know, no realization of a quantum algorithm can solve NP-complete problems in polynomial many steps. Some people that worked on this topic told me that there seems to be some improvements on the quasi-optimal solution found, but that due to the scale of current…
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