2016/09/19 by Nikolas P. Breuckmann, Kasper Duivenvoorden, Dominik Michels +1 · 1 citation
Physics and Astronomy · #quant-ph
published as Quantum Information and Computation Vol. 17 No. 3-4 (2017) 0181 · 22 pages, 21 figures; fixed typos, updated Figures 6,7,8,9
arxiv created 2016/09/19 · arxiv updated 2017/03/09
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 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 arXiv:1312.2546 . 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. arXiv:quant-ph/0110143 .