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

Authors:
Gábor Ivanyos;Frédéric Magniez;Miklos Santha
Affiliations:
Computer and Automation, Research Institute, Hungarian, Academy of Sciences, H-1518 Budapest, P.O. Box 63;CNRS-LRI, UMR 8623, Université Paris-Sud, 91405 Orsay, France;CNRS-LRI, UMR 8623, Université Paris-Sud, 91405 Orsay, France
Venue:
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Year:
2001

Citing 10
Cited 13

Fast Monte Carlo algorithms for permutation groups

Selected papers of the 23rd annual ACM symposium on Theory of computing
On the Power of Quantum Computation

SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

SIAM Journal on Computing
Normal subgroup reconstruction and quantum computation using group representations

STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum algorithms for solvable groups

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum mechanical algorithms for the nonabelian hidden subgroup problem

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum computation and quantum information

Quantum computation and quantum information
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)

CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem

ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
On quantum algorithms for noncommutative hidden subgroups

STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science

Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum algorithms for some hidden shift problems

SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Recent Quantum Algorithms

MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Hidden translation and orbit coset in quantum computing

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Generic quantum Fourier transforms

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The quantum query complexity of the hidden subgroup problem is polynomial

Information Processing Letters - Devoted to the rapid publication of short contributions to information processing
The hidden subgroup problem and permutation group theory

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Graph isomorphism is in SPP

Information and Computation
Generic quantum Fourier transforms

ACM Transactions on Algorithms (TALG)
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem

Journal of the ACM (JACM)
Graph Isomorphism is in SPP

Information and Computation
How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem

Quantum Information & Computation
Quantum algorithms for a set of group theoretic problems

ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

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.