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].
| Original language | English |
|---|---|
| Pages (from-to) | 181-208 |
| Number of pages | 28 |
| Journal | Quantum Information and Computation |
| Volume | 17 |
| Issue number | 3-4 |
| Publication status | Published - 1 Mar 2017 |
Bibliographical note
Funding 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.
Publisher Copyright:
© Rinton Press.