An Efficient Quantum Algorithm for the Hidden Subgroup Problem over some Non-Abelian Groups ^†

The hidden subgroup problem (HSP) plays an important role in quantum computing because many quantum algorithms that are exponentially faster than classical algorithms are special cases of the HSP. In this paper we show that there exists a new efficient quantum algorithm for the HSP on groups ${\mathbb{Z}}_N⋊{\mathbb{Z}}_{q^s}$ where N is an integer with a special prime factorization, q prime number and s any positive integer.

Keywords:
Quantum Algorithms; Hidden Subgroup Problem; Quantum Computational Group Theory