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Abstract: Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a "classical" (macroscopic) signal resulting from the measurement of one bit (embodied in a twostate quantum system) is employed to determine the type of measurement carried out on the next bit, and so forth. In this way the two-bit gates in the Fourier transform... (Update)
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.... of Q = 2 m , which is simpler than the general case, since classical techniques for fast Fourier transforms can be adopted[172, 51, 72, 80, 109] I will give here a nice description by Cleve et al. 70] Later I ll describe Kitaev s[123] more general quantum Fourier transform,...
.... the quantum Fourier transform: to the approximate quantum Fourier transform (Coppersmith [Cop94] over various domains (Griffiths, Niu [GN96] Hoyer [Hoy97] over symmetric groups (Beals [Bea98] over certain non abelian groups (Pueschel, Roetteler, Bet [PRB98] Vedral,...
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BibTeX entry: (Update)
R. B. Griffiths, C. Niu, Semiclassical Fourier Transform for Quantum Computation, (Online preprint quant-ph/9511007), Phys.Rev.Lett. 76 (1996) 3228-3231. http://citeseer.ist.psu.edu/griffiths96semiclassical.html More
@misc{ griffiths95semiclassical,
author = "Robert B.~Griffiths and Chi-Sheng Niu",
title = "Semiclassical {F}ourier Transform for Quantum Computation",
howpublished = "Los Alamos Physics Preprint Archive, {\url http://xxx.lanl.gov/abs/quant-ph/9511007}",
year = "1995",
url = "citeseer.ist.psu.edu/griffiths96semiclassical.html" }
Citations (may not include all citations):6 The Interpretation of Quantum Mechanics (context) - Omnes - 1994
5 Ekert and R (context) - Barenco, Deutsch - 1995
3 quant-ph (context) - Chuang, Yamamoto
1 submitted to SIAM J (context) - Shor, quant-ph
1 Barenco and A Ekert (context) - Deutsch - 1995
1 as pointed out to us by D (context) - result, measurement et al. - 1993
1 a reduced density matrix; this makes no difference for the f.. (context) - if
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