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- W1567111803 abstract "This work introduces two decision problems, Stabilizer D and Orbit Coset D , and gives quantum reductions from them to the problem Orbit Superposition (Friedl et al., 2003), as well as quantum reductions to them from two group theoretic problems Group Intersection and Double Coset Membership. Based on these reductions, efficient quantum algorithms are obtained for Group Intersection and Double Coset Membership in the setting of black-box groups. Specifically, for solvable groups, this gives efficient quantum algorithms for Group Intersection if one of the underlying solvable groups has a smoothly solvable commutator subgroup, and for Double Coset Membership if one of the underlying solvable groups is smoothly solvable. Finally, it is shown that Group Intersection and Double Coset Membership are in the complexity class SZK.KeywordsProof SystemQuantum AlgorithmSolvable GroupDouble CosetStabilizer SubgroupThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W1567111803 created "2016-06-24" @default.
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- W1567111803 date "2005-01-01" @default.
- W1567111803 modified "2023-10-13" @default.
- W1567111803 title "Quantum Algorithms for a Set of Group Theoretic Problems" @default.
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- W1567111803 doi "https://doi.org/10.1007/11560586_18" @default.
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