Ghost factors in Gauss-sum factorization with transmon qubits

TL;DR

This paper investigates ghost factors in Gauss-sum factorization using transmon qubits, focusing on Type II ghost factors that are resistant to existing suppression techniques, and proposes preprocessing to improve factor discernability.

Contribution

It introduces preprocessing as a novel strategy to enhance ghost factor suppression and extends the maximum factorizable number in transmon-based Gauss sum factorization.

Findings

Preprocessing increases discernability of factors.

The method approaches the decoherence limit of the qubit.

Enhanced maximum factorizable number achieved.

Abstract

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.