2018/09/26 by Aleksander Kubica, John Preskill · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.123.020501
published as Phys. Rev. Lett. 123, 020501 (2019) · 4+8 pages, 5 figures
arxiv created 2018/09/26 · arxiv updated 2019/07/17
We propose a new cellular automaton (CA), the Sweep Rule, which generalizes Toom's rule to any locally Euclidean lattice. We use the Sweep Rule to design a local decoder for the toric code in d≥ 3 dimensions, the Sweep Decoder, and rigorously establish a lower bound on its performance. We also numerically estimate the Sweep Decoder threshold for the three-dimensional toric code on the cubic and body-centered cubic lattices for phenomenological phase-flip noise. Our results lead to new CA decoders with provable error-correction thresholds for other topological quantum codes including the color code.