A local automaton for the 2D toric code

• URL: http://arxiv.org/abs/2412.19803v2
• Date: Tue, 03 Jun 2025 00:21:30 GMT
• Title: A local automaton for the 2D toric code
• Abstract summary: We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and G'acs.<n>Our decoder is a circuit of strictly local quantum operations preserving a logical state for exponential time in the presence of circuit-level noise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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