Generalized Belief Propagation Algorithms for Decoding of Surface Codes

• URL: http://arxiv.org/abs/2212.03214v2
• Date: Tue, 6 Jun 2023 13:41:54 GMT
• Title: Generalized Belief Propagation Algorithms for Decoding of Surface Codes
• Authors: Josias Old and Manuel Rispler
• Abstract summary: We present a generalized belief propagation method with an outer re-initialization loop that successfully decodes surface codes. We report a threshold of 17% under independent bit-and phase-flip data noise (to be compared to the ideal threshold of 20.6%) and a threshold value of 14%$under depolarizing data noise (compared to the ideal threshold of 18.9%), which are on par with thresholds achieved by non-BP post-processing methods.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g. notably for the quantum low-density parity check (LDPC) code class of random expander codes. However, it is also well-known that the performance of BP breaks down when facing topological codes such as the surface code, where naive BP fails entirely to reach a below-threshold regime, i.e. the regime where error correction becomes useful. Previous works have shown, that this can be remedied by resorting to post-processing decoders outside the framework of BP. In this work, we present a generalized belief propagation method with an outer re-initialization loop that successfully decodes surface codes, i.e. opposed to naive BP it recovers the sub-threshold regime known from decoders tailored to the surface code and from statistical-mechanical mappings. We report a threshold of 17% under independent bit-and phase-flip data noise (to be compared to the ideal threshold of 20.6%) and a threshold value of 14%$under depolarizing data noise (compared to the ideal threshold of 18.9%), which are on par with thresholds achieved by non-BP post-processing methods.

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