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 . 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. .
|Original language||English (US)|
|Number of pages||28|
|Journal||Quantum Information and Computation|
|State||Published - Mar 1 2017|
Bibliographical noteFunding Information:
We thank Jim Harrington for initially providing us with his software implementation of the decoder. This work is supported by the European Research Council (EQEC, ERC Consol-idator Grant No: 682726). We would like to thank Michael Kastyorano for valuable feedback on the 4D toric code results and Fernando Pastawski for discussing his results on the Toom's rule decoder.
© Rinton Press.
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Computational Theory and Mathematics