A challenge in the Gauss-sum factorization scheme is the presence of ghost factors, nonfactors that behave similarly to actual factors of an integer, which might lead to the misidentification of nonfactors as factors or vice versa, especially in the presence of noise. We investigate type II ghost factors, which are the class of ghost factors that cannot be suppressed with techniques previously laid out in the literature. The presence of type II ghost factors and the coherence time of the qubit set an upper limit for the total experiment time, and hence the largest factorizable number with this scheme. Discernibility is a figure of merit introduced to characterize this behavior. We introduce preprocessing as a strategy to increase the discernibility of a system, and demonstrate the technique with a transmon qubit. This can bring the total experiment time of the system closer to its decoherence limit, and increase the largest factorizable number.
Recent experiments have shown that truncated Gauss sums allow us to find the factors of an integer N . This method relies on the fact that for a factor the absolute value of the Gauss sum is unity. However, for every integer N there exist integers which are not factors, but where the Gauss sum reaches a value which is arbitrarily close to unity. In order to distinguish such ghost factors from real factors we need to amplify this difference. We show that a proper choice of the truncation parameter of the Gauss sum suppresses the ghost factors below a threshold value. We derive the scaling law of the truncation parameter on the number to be factored. Moreover, we show that this scaling law is also necessary for the success of our factorization scheme, even if we relax the threshold or allow limited error tolerance.