A local automaton for the 2D toric code
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910248982282240 |
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| author | Balasubramanian, Shankar Davydova, Margarita Lake, Ethan |
| author_facet | Balasubramanian, Shankar Davydova, Margarita Lake, Ethan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19803 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A local automaton for the 2D toric code Balasubramanian, Shankar Davydova, Margarita Lake, Ethan Quantum Physics Statistical Mechanics Strongly Correlated Electrons Probability Cellular Automata and Lattice Gases 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. |
| title | A local automaton for the 2D toric code |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons Probability Cellular Automata and Lattice Gases |
| url | https://arxiv.org/abs/2412.19803 |