  A challenge in the Gauss sums factorization scheme is the presence of ghost
factors - non-factors that behave similarly to actual factors of an integer -
which might lead to the misidentification of non-factors 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.
Discernability is a figure of merit introduced to characterize this behavior.
We introduce preprocessing as a strategy to increase the discernability 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.
