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

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

Corresponding author: dieter.suter@uni-dortmund.de

Received: 13 July 2008
Accepted: 6 October 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.