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Abstract: We present the view of quantum algorithms as a search-theoretic problem. We show that the Fourier transform, used to solve the Abelian hidden subgroup problem, is an example of an efficient elimination observable which eliminates a constant fraction of the candidate secret states with high probability. Finally, we show that elimination observables do not always exist by considering the geometry of the hidden subgroup states of the dihedral group DN . 1 Introduction In the classic game... (Update)
Context of citations to this paper: More
...samples in the HSP algorithm) is enough to reconstruct the hidden subgroup, with exponential classical post processing time. In [23, 22, 25], they address the question of whether or not any algorithm is possible at all. They show that the tensor products of coset states for di...
...[5] give a solution for the HSP over the dihedral group D n with polynomially many queries and exponential (classical sequential) time. In [6] and [7] they address whether any measurement will distinguish subgroup states. Roetteler and Beth [19] give a solution to the HSP for...
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BibTeX entry: (Update)
Mark Ettinger and Peter H yer. Quantum state detection via elimination. Technical report, quantph /9905099, 1999. http://citeseer.ist.psu.edu/article/ettinger99quantum.html More
@article{ ettinger99quantum,
author = "Mark Ettinger and Peter H{\o}yer",
title = "On Quantum Algorithms for Noncommutative Hidden Subgroups",
journal = "Lecture Notes in Computer Science",
volume = "1563",
pages = "478--487",
year = "1999",
url = "citeseer.ist.psu.edu/article/ettinger99quantum.html" }
Citations (may not include all citations):40 Quantum measurements and the Abelian stabilizer problem (context) - Kitaev
34 Quantum Detection and Estimation Theory (context) - Carl - 1976
29 Group-theoretic algorithms and graph isomorphism (context) - Christoph - 1982
3 Mathematics of multidimensional Fourier transform algorithms (context) - Richard, An et al. - 1997
3 Wiley-Teubner Series in Computer Science (context) - Martin - 1988
1 Available at Los Alamos e-Print achive as (context) - Mark, Hyer et al.
The graph only includes citing articles where the year of publication is known.
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