Quantum algorithms for solvable groups

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  • 7 November 2000
Abstract
This paper presents polynomial-time quantum algorithms for problems regarding finite solvable groups. In particular, we give polynomial-time (Monte Carlo) quantum algorithms for three basic problems: computing the order of a solvable group, testing membership in a solvable group, and testing isomorphism of two solvable groups. In these problems, groups are assumed to be given by generating sets. The algorithms work in the setting of black-box groups, wherein it has been proved that none of the above problems can be solved classically in polynomial time.

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