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Abstract:

We discuss the implementation of arbitrary precision composite pulses developed using the methods of Brown et al. [K.R. Brown, A.W. Harrow, I.L. Chuang, Arbitrarily accurate composite pulse sequences, Phys. Rev. A 70 (2004) 052318]. We give explicit results for pulse sequences designed to tackle both the simple case of pulse length errors and the more complex case of off-resonance errors. The results are developed in the context of NMR quantum computation, but could be applied more widely.

Abstract:

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 $N$.