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arXiv · 2412.19803

A local automaton for the 2D toric code

Shankar Balasubramanian·Margarita Davydova·Ethan Lake
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Abstract

We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and G\'acs. 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.

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Shankar Balasubramanian, Margarita Davydova, Ethan Lake. 2024-12-27. A local automaton for the 2D toric code. https://doi.org/10.22331/q-2026-06-02-2125

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