NMR implementation of factoring large numbers with Gauß sums: Suppression of ghost factorsX. Peng and D. Suter
Fakultät Physik, Technische Universität Dortmund - 44221 Dortmund, Germany, EU
received 13 July 2008; accepted in final form 6 October 2008; published November 2008
published online 10 November 2008
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.
03.67.Lx - Quantum computation architectures and implementations.
02.10.De - Algebraic structures and number theory.
82.56.-b - Nuclear magnetic resonance.
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