Quantum algorithms for the hidden subgroup problem on some semi-direct product groups by reduction to Abelian cases

Abstract

We consider the hidden subgroup problem on the semi-direct product of cyclic groups Z N ⋊ Z p , where p is a prime that does not divide p j − 1 for any of the prime factors p j of N, and show that the hidden subgroup problem can be reduced to other ones for which solutions are already known.