TY - GEN
T1 - Normal subgroup reconstruction and quantum computation using group representations
AU - Hallgren, Sean
AU - Russell, Alexander
AU - Ta-Shma, Amnon
PY - 2000
Y1 - 2000
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
U2 - 10.1145/335305.335392
DO - 10.1145/335305.335392
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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 -