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We reduce a case of the hidden subgroup problem (HSP) in SL(2; q), PSL(2; q), and PGL(2; q), three related families of finite groups of Lie type, to efficiently solvable HSPs in the affine group AGL(1; q).
Fast Fourier analysis for s l 2 sl_{2} over a finite field and related numerical experiments
John D. Lafferty and Daniel Rockmore · 1992
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Quantum complexity theory (preliminary abstract)
Ethan Bernstein and Umesh Vazirani · 1993
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Permutation Groups
John D. Dixon and Brian Mortimer · 1996
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Finite Fields
Rudolf Lidl and Harald Niederreiter · 1997
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Hidden translation and orbit coset in quantum computing
Katalin Friedl, Gábor Ivanyos, Frédéric Magniez, Miklos Santha, and Pranab Sen · 2003
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Representation Theory: a First Course
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Cristopher Moore, Daniel Rockmore, Alexander Russell, and Leonard J. Schulman · 2004
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From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups
Dave Bacon, Andrew M. Childs, and Wim van Dam · 2005
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A subexponential-time quantum algorithm for the dihedral hidden subgroup problem
Greg Kuperberg · 2005
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The symmetric group defies Fourier sampling
Cristopher Moore, Alexander Russell, and Leonard Schulman · 2005
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Limitations of quantum coset states for graph isomorphism
Sean Hallgren, Cristopher Moore, Martin Rötteler, Alexander Russell, and Pranab Sen · 2006
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On the impossibility of a quantum sieve algorithm for graph isomorphism: unconditional results
Cristopher Moore, Alexander Russell, and Piotr Śniady · 2006
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An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups
Gábor Ivanyos, Luc Sanselme, and Miklos Santha · 2007
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An efficient quantum algorithm for the hidden subgroup problem in nil-2 groups
Gábor Ivanyos, Luc Sanselme, and Miklos Santha · 2008
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