On Quantum Algorithms for Noncommutative Hidden Subgroups

Details On Quantum Algorithms for Noncommutative Hidden Subgroups On Quantum Algorithms for Noncommutative Hidden Subgroups

1998-07-10

arxiv.org/abs/quant-ph/9807029v1

Physics

Quantum Physics

13 pages, no figures, LaTeX2e

Scientific paper

Quantum algorithms for factoring and discrete logarithm 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 difficulties 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.

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