A local automaton for the 2D toric code

Quantum 2026 Open access

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Authors: Shankar Balasubramanian, Margarita Davydova, Ethan Lake
DOI: 10.22331/q-2026-06-02-2125
Cited by: 2
References: 52

Abstract

We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and Gács. Our decoder is a circuit of strictly local quantum operations preserving a logical state for exponential time in the presence of circuit-level noise without the need for non-local classical computation or communication. Our construction is not translation invariant in spacetime, but can be made time-translation invariant in 3D with stacks of 2D toric codes. This solves the open problem of constructing a local topological quantum memory below four dimensions.

Fields of Study & Subjects

Cellular Automata and Applications Coding theory and cryptography Advanced Data Storage Technologies

Publication details

Journal / source
Quantum
Publisher
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Volume
10
Pages
2125–2125
Publication date
2 June 2026
Language
EN