Issue
EPL
Volume 84, Number 4, November 2008
Article Number 40006
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/84/40006
Published online 10 November 2008
EPL, 84 (2008) 40006
DOI: 10.1209/0295-5075/84/40006

NMR implementation of factoring large numbers with Gauß sums: Suppression of ghost factors

X. Peng and D. Suter

Fakultät Physik, Technische Universität Dortmund - 44221 Dortmund, Germany, EU

dieter.suter@uni-dortmund.de

received 13 July 2008; accepted in final form 6 October 2008; published November 2008
published online 10 November 2008

Abstract
Finding the factors of an integer can be achieved by various experimental techniques, based on an algorithm developed by Schleich et al. (Fortschr. Phys.54 (2006) 856), which uses specific properties of Gauß sums. Experimental limitations usually require truncation of these series, but if the truncation parameter is too small, it is no longer possible to distinguish between factors and so-called “ghost" factors. Here, we discuss two techniques for distinguishing between true factors and ghost factors while keeping the number of terms in the sum constant or only slowly increasing. We experimentally test these modified algorithms in a nuclear spin system, using NMR.

PACS
03.67.Lx - Quantum computation architectures and implementations.
02.10.De - Algebraic structures and number theory.
82.56.-b - Nuclear magnetic resonance.

© EPLA 2008