Deterministic algorithms for the hidden subgroup problem

We present deterministic algorithms for the Hidden Subgroup Problem. The first algorithm, abelian groups, achieves same asymptotic worst-case query complexity as optimal randomized namely~$ \Order(\sqrt{ n}\, )$, where~$n$ is order of group. analogous algorithm non-abelian groups comes within a~$\sqrt{ \log n}$ factor complexity. best known Problem has \emph{expected\/} that sensitive to input, n/m}\, where~$m$ hidden subgroup. In version this article~\cite[Sec.~5]{Nayak21-hsp-classical}, we asked if there a whose similar dependence on Prompted by question, Ye and Li~\cite{YL21-hsp-classical} \emph{abelian\/} which solve problem with~$ n/m }\, )$ queries, find subgroup \Order( \sqrt{ n (\log m) / m} + m ) $ queries. Moreover, they exhibit instances show in general, may be~$\order(\sqrt{ } \,)$, \emph{finding\/} entire also \,)$ or even~$\upomega(\sqrt{ \,) $.}We different complexity~$ groups. arguably simpler. it works (n/m) }\,) large class instances, such those over supersolvable build design all some at cost a~$\log m$ multiplicative increase