We factor the number 157573 using an NMR implementation of Gauss sums. Although the current implementation is classical and scales exponentially, we believe that an extension to the quantum regime using entangled states is possible.

arXiv:quant-ph/0609174Physical Review LettersMar 22, 200785 citations

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Contemporary Physics

NMR implementation of exponential sums for integer factorization

M. Štefaňák, W. Merkel, M. Mehring, W. P. Schleich

Published May 1, 2008• 2 citations

Publisher

DOI: 10.1142/9789812818942_0006

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Comment on "NMR Experiment Factors Numbers with Gauss Sums"

Julia A. Wei Xiaohua Jones

Mehring et al. have recently described an elegant nuclear magnetic resonance (NMR) experiment implementing an algorithm to factor numbers based on the properties of Gauss sums. Similar experiments have also been described by Mahesh et al. In fact these algorithms do not factor numbers directly, but rather check whether a trial integer $\ell$ is a factor of a given integer $N$ . Here I show that these NMR schemes cannot be used for factor checking without first implicitly determining whether or not $\ell$ is a factor of $N$ .Mehring et al. have recently described an elegant nuclear magnetic resonance (NMR) experiment implementing an algorithm to factor numbers based on the properties of Gauss sums. Similar experiments have also been described by Mahesh et al. In fact these algorithms do not factor numbers directly, but rather check whether a trial integer $\ell$ is a factor of a given integer $N$. Here I show that these NMR schemes cannot be used for factor checking without first implicitly determining whether or not $\ell$ is a factor of $N$.

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NMR Experiment Factors Numbers with Gauss Sums

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\ell

is a factor of a given integer

N

. Here I show that these NMR schemes cannot be used for factor checking without first implicitly determining whether or not

\ell

is a factor of

N