Papers › Local Decoders for the 2D and 4D Toric Code
Local Decoders for the 2D and 4D Toric Code
Nikolas P. Breuckmann, Kasper Duivenvoorden, Dominik Michels, Barbara M. Terhal
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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 .
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