Correlated Decoding for Elongated Compass Codes and Clifford Deformed Compass Codes

For biased noise models, selecting a proper quantum error correcting code and decoder tailored to the dominant noise type will enable quantum computing with lower overhead. Compass codes lower logical error rates in biased noise models compared to the rotated surface code [1]. Correlated decoders have been shown to perform well on standard depolarizing noise channels [2]. We implement and test a correlated decoder for compass codes, finding that correlated decoding outperforms non-correlated decoders for low noise biases. We implement a correlated decoder for a non-CSS equivalent of compass codes: clifford deformed compass codes.

[1] Muyuan Li, Daniel Miller, Michael Newman, Yukai Wu, and Kenneth R. Brown. Phys. Rev. X 9, 021041 – Published 29 May 2019

[2] Madelyn Cain, et. al, arXiv:2403.03272