{
  "$type": "site.standard.document",
  "bskyPostRef": {
    "cid": "bafyreifeddgldqqekpsemmaoizazl5lk22nreiwuy22r4aooxbiufj6m6q",
    "uri": "at://did:plc:cx57fsir6oyzywdd4jafsdsw/app.bsky.feed.post/3mncdzlisjgm2"
  },
  "path": "/papers/q-2026-06-02-2125/",
  "publishedAt": "2026-06-02T08:16:58.000Z",
  "site": "https://quantum-journal.org",
  "tags": [
    "Paper",
    "https://doi.org/10.22331/q-2026-06-02-2125"
  ],
  "textContent": "Quantum 10, 2125 (2026).\n\nhttps://doi.org/10.22331/q-2026-06-02-2125\n\nWe 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"
}