Local decoders for the 2D and 4D toric code (pp0181-0208)
          Nikolas P. Breuckmann, Kasper Duivenvoorden, Dominik Michels, and Barbara M. Terhal
          doi: https://doi.org/10.26421/QIC17.3-4-1
Abstracts: We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington [1] which explicitly has a finite speed of communication and computation. For a model of independent X and Z errors and faulty syndrome measurements with identical probability, we report a threshold of 0.133% for this Harrington decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings [2]. Incorporating a method for handling faulty syndromes we estimate a threshold of 1.59% for the same noise model as in the 2D case. We compare the performance of this decoder with a decoder based on a 4D version of Toom’s cellular automaton rule as well as the decoding method suggested by Dennis et al.
Key words: 2D decoder, 4D toric code, cellular automaton rule