Normal subgroup reconstruction and quantum computation using group representations

Sean Hallgren, Alexander Russell, Amnon Ta-Shma

Research output: Chapter in Book/Report/Conference proceedingConference contribution

54 Scopus citations

Abstract

The Hidden Subgroup Problem is the foundation of many quantum algorithms. An efficient solution is known for the problem over Abelian groups and this was used in Simon's algorithm and Shor's Factoring and Discrete Log algorithms. The non-Abelian case is open; an efficient solution would give rise to an efficient quantum algorithm for Graph Isomorphism. We fully analyze a natural generalization of the Abelian case solution to the non-Abelian case, and give an efficient solution to the problem for normal subgroups. We show, however, that this immediate generalization of the Abelian algorithm does not efficiently solve Graph Isomorphism.

Original languageEnglish (US)
Title of host publicationProceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000
Pages627-635
Number of pages9
DOIs
StatePublished - Dec 1 2000
Event32nd Annual ACM Symposium on Theory of Computing, STOC 2000 - Portland, OR, United States
Duration: May 21 2000May 23 2000

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference32nd Annual ACM Symposium on Theory of Computing, STOC 2000
CountryUnited States
CityPortland, OR
Period5/21/005/23/00

All Science Journal Classification (ASJC) codes

  • Software

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