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Local Decoders for the 2D and 4D Toric Code

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arxiv 1609.00510 v2 pith:YLIYBXEA submitted 2016-09-02 quant-ph

Nikolas P. Breuckmann , Kasper Duivenvoorden , Dominik Michels , Barbara M. Terhal This is my paper · ORCID
classification quant-ph
keywords decodercodetoricarxivautomatoncellulardecodersfaulty
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abstract

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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Cited by 2 Pith papers

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