Ghost Factors in Gauss Sum Factorization with Transmon Qubits

  1. Lin Htoo Zaw,
  2. Yuanzheng Paul Tan,
  3. Long Hoang Nguyen,
  4. Rangga P. Budoyo,
  5. Kun Hee Park,
  6. Zhi Yang Koh,
  7. Alessandro Landra,
  8. Christoph Hufnagel,
  9. Yung Szen Yap,
  10. Teck Seng Koh,
  11. and Rainer Dumke
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.
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