Deterministic polynomial-time quantum algorithms for Simon’s problem

Abstract

D. R. Simon stated a problem, so-called Simon’s problem, whose computational complexity is in the class BQP^ψ but not in BPP^ψ, where ψ is the function or oracle given in the problem. This result indicates that BPP may be strictly included in its quantum counterpart, BQP. Later, G. Brassard and P. Høyer showed that Simon’s problem and its extended version can be solved by a deterministic polynomial time quantum algorithm. That is, these problems are in the class EQP^ψ. In this paper, we show that Simon’s problem and its extended version can be deterministically solved in a simpler and more concrete way than that proposed by G. Brassard and P. Høyer.