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Abstract: . A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and hidden or unknown subgroups of Abelian groups. It is already known how to phrase the first four problems as the estimation of eigenvalues of certain unitary operators. Here we show how the solution to the more general Abelian hidden subgroup problem can also be described and analysed as such. We then point out how certain... (Update)
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BibTeX entry: (Update)
M. Mosca and A. Ekert. The hidden subgroup problem and eigenvalue estimation on a quantum computer. In Proceedings of NASA QCQC conference, volume 1509 of Lecture Notes in Computer Science. Springer, 1998. http://citeseer.ist.psu.edu/mosca98hidden.html More
@article{ mosca99hidden,
author = "Michele Mosca and Artur Ekert",
title = "The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer",
journal = "Lecture Notes in Computer Science",
volume = "1509",
pages = "174--188",
year = "1999",
url = "citeseer.ist.psu.edu/mosca98hidden.html" }
Citations (may not include all citations):1065 Handbook of Applied Cryptography (context) - Menezes, van Oorschot et al. - 1997 ACM
168 Algorithms for quantum computation: Discrete logarithms and .. - Shor - 1994 DBLP
144 the Power of Quantum Computation - Simon - 1994
118 the Church-Turing principle and the universal quantum comput.. (context) - Deutsch - 1985
50 Quantum Algorithms Revisited - Cleve, Ekert et al. - 1998
35 Quantum cryptanalysis of hidden linear functions (context) - Boneh, Lipton - 1995
24 A Rigorous Time Bound For Factoring Integers (context) - Lenstra, Jr - 1992
15 Semi-classical Fourier Transform for Quantum Computation - Griffiths, Niu - 1996
9 Quantum Algorithms and the Fourier Transform - Jozsa - 1998
6 Testing the shift-equivalence of polynomials by deterministi.. - Grigoriev - 1997
6 Quantum measurements and the Abelian stabiliser problem (context) - Kitaev - 1995
4 Conjugated Operators in Quantum Algorithms (context) - Hyer - 1997 ACM
1 note in preparation (context) - Ekert, Mosca - 1998
The graph only includes citing articles where the year of publication is known.
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