Quantum algorithm for the hidden subgroup problem on a class of semidirect product groups

Details Quantum algorithm for the hidden subgroup problem on a class of semidirect product groups Quantum algorithm for the hidden subgroup problem on a class of semidirect product groups

2007-03-23

arxiv.org/abs/quant-ph/0703223v2

Physics

Quantum Physics

5 pages, no figures

Scientific paper

We present efficient quantum algorithms for the hidden subgroup problem (HSP) on the semidirect product of cyclic groups $\Z_{p^r}\rtimes_{\phi}\Z_{p^2}$, where $p$ is any odd prime number and $r$ is any integer such that $r>4$. We also address the HSP in the group $\Z_{N}\rtimes_{\phi}\Z_{p^2}$, where $N$ is an integer with a special prime factorization. These quantum algorithms are exponentially faster than any classical algorithm for the same purpose.

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