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arXiv · 1809.10145

Cellular-automaton decoders with provable thresholds for topological codes

Aleksander Kubica·John Preskill
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Abstract

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 $d\geq 3$ 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.

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Aleksander Kubica, John Preskill. 2018-09-26. Cellular-automaton decoders with provable thresholds for topological codes. https://doi.org/10.1103/physrevlett.123.020501

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