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

Abstract

ABSTRACT. 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 Z N Z q s where N is an integer with a special prime factorization, q prime number and s any positive integer.

Photonic scheme of discrete quantum Fourier transform for quantum algorithms via quantum dots

“…In various quantum algorithms and quantum computations, such as quantum phase estimation algorithm 1–3 , the factoring problem 4–7 , the discrete logarithm problem 2,4,8,9 , and the hidden subgroup problem 10–12 , a discrete quantum Fourier transform (DQFT) 2,13–19 plays a critical role in accomplishing quantum information processing. Thus, for the experimental implementation of DQFT, a variety of physical resources have been used, including those based on linear optical systems 20–22 , nonlinear optical systems 17,23–25 , nuclear magnetic resonance or ion trap systems 26–29 , superconducting circuits 30 , and cavity-QED 15,31–33 .…”