Local decoders for the 2D and 4D toric code

Breuckmann, N. P.; Duivenvoorden, K.; Michels, Dominik; Terhal, B.M.

Local decoders for the 2D and 4D toric code

Journal article (2017)

Authors

N. P. Breuckmann Rheinisch-Westfälische Technische Hochschule

K. Duivenvoorden Rheinisch-Westfälische Technische Hochschule

Dominik Michels Rheinisch-Westfälische Technische Hochschule

B.M. Terhal Rheinisch-Westfälische Technische Hochschule

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Published Date

2017

Language

English

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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 [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. [3].