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@ARTICLE{Old:915883,
      author       = {Old, Josias and Rispler, Manuel},
      title        = {{G}eneralized {B}elief {P}ropagation {A}lgorithms for
                      {D}ecoding of {S}urface {C}odes},
      reportid     = {FZJ-2022-05753},
      year         = {2022},
      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.},
      cin          = {PGI-2},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5224 - Quantum Networking (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5224},
      typ          = {PUB:(DE-HGF)25},
      url          = {https://juser.fz-juelich.de/record/915883},
}