Quantum algorithms for factoring and finding discrete loga-ithms have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden subgroups of noncommutative groups. We present a quantum algorithm for the special case of dihedral groups which determines the hidden subgroup in a linear number of calls to the input function. We also explore the dificulties of developing an algorithm to process the data to explicitly calculate a generating set for the subgroup. A general framework for the noncommutative hidden subgroup problem is discussed and we indicate future research directions.
CITATION STYLE
Ettinger, M., & Høyer, P. (1999). On quantum algorithms for noncommutative hidden subgroups. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1563, pp. 478–487). Springer Verlag. https://doi.org/10.1007/3-540-49116-3_45
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