{
  "annotation_id": "86173fb6-f1cb-4733-8f67-8d5001a29907",
  "date_created": "2026-03-02T18:02:45.177000Z",
  "date_modified": "2026-03-02T18:02:45.177000Z",
  "file_hash": "f6d8bf774d6f59f0f0c11bf2923d019a434888723e45b9ceb46a641705e1498d",
  "private": false,
  "record": {
    "abstract": "I discuss how to perform fault-tolerant quantum computation with concatenated\ncodes using local gates in small numbers of dimensions. I show that a threshold\nresult still exists in three, two, or one dimensions when\nnext-to-nearest-neighbor gates are available, and present explicit\nconstructions. In two or three dimensions, I also show how nearest-neighbor\ngates can give a threshold result. In all cases, I simply demonstrate that a\nthreshold exists, and do not attempt to optimize the error correction circuit\nor determine the exact value of the threshold. The additional overhead due to\nthe fault-tolerance in both space and time is polylogarithmic in the error rate\nper logical gate.",
    "arxiv_id": "quant-ph/9903099",
    "authors": [
      "Daniel Gottesman"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1080/09500340008244046",
    "journal_ref": "J.Mod.Opt. 47 (2000) 333-345",
    "title": "Fault-Tolerant Quantum Computation with Local Gates",
    "url": "https://arxiv.org/abs/quant-ph/9903099"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6b158d59-5ed4-4f35-88a5-47c1e9ef7267",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}