Quantum computational algorithm for hidden symmetry subgroup problems on semi-direct product of cyclic groups

Abstract

We characterize the algebraic structure of semi-direct product of cyclic groups, ${\mathbb{Z}}_N⋊{\mathbb{Z}}_p$, where $p$ is an odd prime number which does not divide $q-1$ for any prime factor $q$ of $N$, and provide a polynomial-time quantum computational algorithm solving hidden symmetry subgroup problem of the groups.