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- W1967088292 abstract "In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing normality of a subgroup in a given solvable group, reduce to computing orders of solvable groups and therefore admit polynomial-time quantum algorithms as well. Our algorithm works in the setting of black-box groups, wherein none of these problems have polynomial-time classical algorithms. As an important byproduct, our algorithm is able to produce a pure quantum state that is uniform over the elements in any chosen subgroup of a solvable group, which yields a natural way to apply existing quantum algorithms to factor groups of solvable groups." @default.
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- W1967088292 date "2001-07-06" @default.
- W1967088292 modified "2023-10-14" @default.
- W1967088292 title "Quantum algorithms for solvable groups" @default.
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- W1967088292 doi "https://doi.org/10.1145/380752.380759" @default.
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