Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 2003 | public
Journal Article Open

The hidden subgroup problem and quantum computation using group representations

Abstract

The hidden subgroup problem is the foundation of many quantum algorithms. An efficient solution is known for the problem over abelian groups, employed by both Simon's algorithm and Shor's factoring and discrete log algorithms. The nonabelian case, however, remains open; an efficient solution would give rise to an efficient quantum algorithm for graph isomorphism. We fully analyze a natural generalization of the algorithm for the abelian case to the nonabelian case and show that the algorithm determines the normal core of a hidden subgroup: in particular, normal subgroups can be determined. We show, however, that this immediate generalization of the abelian algorithm does not efficiently solve graph isomorphism.

Additional Information

© 2003 Society for Industrial and Applied Mathematics. Received by the editors August 28, 2001; accepted for publication (in revised form) December 16, 2002; published electronically June 10, 2003. A preliminary version of this article appeared in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, Portland, OR, 2000, pp. 627–635. The bulk of this research was completed while the authors were at the University of California, Berkeley. The authors thank Umesh Vazirani for many helpful discussions and the simplification of several of the proofs.

Files

HALsiamjc03.pdf
Files (219.2 kB)
Name Size Download all
md5:48a62998da7d176b6253e0b119306b51
219.2 kB Preview Download

Additional details

Created:
August 21, 2023
Modified:
October 13, 2023