Article

Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem

Authors:

Gábor Ivanyos,

Frédéric Magniez,

Miklos SanthaAuthors Info & Claims

SPAA '01: Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures

Pages 263 - 270

https://doi.org/10.1145/378580.378679

Published: 03 July 2001 Publication History

Abstract

In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups, finding hidden subgroups of groups with small commutator subgroup and of groups admitting an elementary Abelian normal 2-subgroup of small index or with cyclic factor group.

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Cited By

Imran MIvanyos G(2024)Efficient quantum algorithms for some instances of the semidirect discrete logarithm problemDesigns, Codes and Cryptography10.1007/s10623-024-01416-892:10(2825-2843)Online publication date: 21-May-2024
https://doi.org/10.1007/s10623-024-01416-8
Battarbee CKahrobaei DPerret LShahandashti S(2024)A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm ProblemPost-Quantum Cryptography10.1007/978-3-031-62743-9_7(202-226)Online publication date: 11-Jun-2024
https://doi.org/10.1007/978-3-031-62743-9_7
Ye ZLi L(2022)Sample complexity of hidden subgroup problemTheoretical Computer Science10.1016/j.tcs.2022.04.014922:C(108-121)Online publication date: 24-Jun-2022
https://dl.acm.org/doi/10.1016/j.tcs.2022.04.014
Show More Cited By

Index Terms

Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation
  1. Models of computation
    1. Concurrency
      1. Parallel computing models
  2. Randomness, geometry and discrete structures

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cover image ACM Conferences

SPAA '01: Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures

July 2001

340 pages

ISBN:1581134096

DOI:10.1145/378580

Chairman:
Arnold Rosenberg
Univ. of Massachusetts

Copyright © 2001 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 03 July 2001

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SPAA '01 Paper Acceptance Rate 34 of 93 submissions, 37%;

Overall Acceptance Rate 447 of 1,461 submissions, 31%

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Cited By

Imran MIvanyos G(2024)Efficient quantum algorithms for some instances of the semidirect discrete logarithm problemDesigns, Codes and Cryptography10.1007/s10623-024-01416-892:10(2825-2843)Online publication date: 21-May-2024
https://doi.org/10.1007/s10623-024-01416-8
Battarbee CKahrobaei DPerret LShahandashti S(2024)A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm ProblemPost-Quantum Cryptography10.1007/978-3-031-62743-9_7(202-226)Online publication date: 11-Jun-2024
https://doi.org/10.1007/978-3-031-62743-9_7
Ye ZLi L(2022)Sample complexity of hidden subgroup problemTheoretical Computer Science10.1016/j.tcs.2022.04.014922:C(108-121)Online publication date: 24-Jun-2022
https://dl.acm.org/doi/10.1016/j.tcs.2022.04.014
Ye ZLi L(2022)Deterministic algorithms for the hidden subgroup problemInformation and Computation10.1016/j.ic.2022.104975289:PAOnline publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1016/j.ic.2022.104975
Hallgren SVollmer U(2009)Quantum computingPost-Quantum Cryptography10.1007/978-3-540-88702-7_2(15-34)Online publication date: 2009
https://doi.org/10.1007/978-3-540-88702-7_2
Dörn SHaase DTorán JWagner F(2009)Isomorphism and Factorization – Classical and Quantum AlgorithmsMathematical Analysis of Evolution, Information, and Complexity10.1002/9783527628025.ch16(433-453)Online publication date: 21-Aug-2009
https://doi.org/10.1002/9783527628025.ch16
Bacon D(2008)How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problemQuantum Information & Computation10.5555/2011772.20117788:5(438-467)Online publication date: 1-May-2008
https://dl.acm.org/doi/10.5555/2011772.2011778
Hallgren SHarrow A(2008)Superpolynomial Speedups Based on Almost Any Quantum CircuitProceedings of the 35th international colloquium on Automata, Languages and Programming - Volume Part I10.1007/978-3-540-70575-8_64(782-795)Online publication date: 7-Jul-2008
https://dl.acm.org/doi/10.1007/978-3-540-70575-8_64
Hallgren S(2007)Polynomial-time quantum algorithms for Pell's equation and the principal ideal problemJournal of the ACM10.1145/1206035.120603954:1(1-19)Online publication date: 1-Mar-2007
https://dl.acm.org/doi/10.1145/1206035.1206039
Arvind VKurur P(2006)Graph Isomorphism is in SPPInformation and Computation10.5555/1149028.1709610204:5(835-852)Online publication date: 1-May-2006
https://dl.acm.org/doi/10.5555/1149028.1709610
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