TY - GEN

T1 - Normal subgroup reconstruction and quantum computation using group representations

AU - Hallgren, Sean

AU - Russell, Alexander

AU - Ta-Shma, Amnon

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033692053&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033692053&partnerID=8YFLogxK

U2 - 10.1145/335305.335392

DO - 10.1145/335305.335392

M3 - Conference contribution

AN - SCOPUS:0033692053

SN - 1581131844

SN - 9781581131840

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 627

EP - 635

BT - Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000

T2 - 32nd Annual ACM Symposium on Theory of Computing, STOC 2000

Y2 - 21 May 2000 through 23 May 2000

ER -