Local Decoders for the 2D and 4D Toric Code

Fault-Tolerant Quantum Technologies Workshop

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 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 samenoise model as in the 2D case. We compare the performance of this decoder with a decoder based ona 4D version of Toom’s cellular automaton rule as well as the decoding method suggested by Dennis et al.