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Abstract: We isolate and generalize a technique implicit in many quantum algorithms, including Shor's algorithms for factoring and discrete log. In particular, we show that the distribution sampled after a Fourier transform over Z p can be eciently approximated by transforming over Z q for any q in a large range. Our result places no restrictions on the superposition to be transformed, generalizing previous applications. In addition, our proof easily generalizes to multi-dimensional transforms for any... (Update)
Context of citations to this paper: More
...group is not even known. Boneh and Lipton [3] handle a case when a periodic function is not fixed on a coset. Hales and Hallgren [11, 12] generalize the results for the case when the underlying Abelian group is unknown, but an estimate is known for the cardinality of its...
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8: Polynomial-time algorithms for prime factorization and discrete logarithms on a .. - Shor - 1995
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BibTeX entry: (Update)
L. Hales and S. Hallgren. Quantum Fourier sampling simplified. In Proceedings of the ThirtyFirst Annual ACM Symposium on Theory of Computing, pages 330--338, 1999. http://citeseer.ist.psu.edu/hales99quantum.html More
@inproceedings{ hales99quantum,
author = "Lisa Hales and Sean Hallgren",
title = "Quantum {Fourier} sampling simplified",
pages = "330--338",
year = "1999",
url = "citeseer.ist.psu.edu/hales99quantum.html" }
Citations (may not include all citations):173 Quantum complexity theory - Bernstein, Vazirani - 1997
144 the power of quantum computation - Simon - 1994
45 Polynomial-time algorithms for prime factorization and discr.. (context) - Shor - 1997
35 Quantum cryptanalysis of hidden linear functions (context) - Boneh, Lipton - 1995
25 Quantum measurements and the abelian stabilizer problem - Yu - 1995
23 On quantum algorithms for noncommutative hidden subgroups - Ettinger, yer - 1999
20 Quantum computation of Fourier transforms over symmetric gro.. (context) - Beals - 1997
13 Generalized FFTS - A Survey of Some Recent Results - Maslen, Rockmore - 1996
5 A note on computing fourier transforms by quantum programs (context) - Cleve - 1994
1 Appriximate quantum Fourier transform and decoherence (context) - Barenco, Ekert et al. - 1996
Documents on the same site (http://www.cs.berkeley.edu/~hallgren/):
Normal Subgroup Reconstruction and Quantum Computation.. - Hallgren, Russell, al. (2000) (Correct)
An Improved Quantum Fourier Transform Algorithm and Applications - Hales, Hallgren (2000) (Correct)
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