Finding conjugate stabilizer subgroups in PSL(2; q) and related groups

Authors:
Aaron Denney;Cristopher Moore;Alexander Russell
Affiliations:
Center for Quantum Information and Control & Department of Physics and Astronomy, University of New Mexico;Santa Fe Institute, Center for Quantum Information and Control & Department of Computer Science, University of New Mexico;Department of Computer Science and Engineering, University of Connecticut
Venue:
Quantum Information & Computation
Year:
2010

Citing 11
Cited 1

Quantum complexity theory

STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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 power of basis selection in fourier sampling: hidden subgroup problems in affine groups

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem

SIAM Journal on Computing
From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups

FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The Symmetric Group Defies Strong Fourier Sampling

FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Limitations of quantum coset states for graph isomorphism

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the impossibility of a quantum sieve algorithm for graph isomorphism

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups

STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
An efficient quantum algorithm for the hidden subgroup problem in nil-2 groups

LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics

Finding hidden Borel subgroups of the general linear group

Quantum Information & Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We reduce a case of the hidden subgroup problem (HSP) in SL(2; q), PSL(2; q), andPGL(2; q), three related families of finite groups of Lie type, to efficiently solvable HSPsin the affine group AGL(1; q). These groups act on projective space in an "almost"3-transitive way, and we use this fact in each group to distinguish conjugates of itsBorel (upper triangular) subgroup, which is also the stabilizer subgroup of an elementof projective space. Our observation is mainly group-theoretic, and as such breaks littlenew ground in quantum algorithms. Nonetheless, these appear to be the first positiveresults on the HSP in finite simple groups such as PSL(2; q).