Ghost factors in Gauss-sum factorization with transmon qubits
Lin Htoo Zaw, Yuanzheng Paul Tan, Long Hoang Nguyen, Rangga P. Budoyo, Kun Hee Park, Zhi Yang Koh, Alessandro Landra, Christoph Hufnagel, Yung Szen Yap, Teck Seng Koh, Rainer Dumke
DOI 10.1103/PhysRevA.104.062606 · Physical Review A
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Abstract
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.
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