{
  "annotation_id": "6aeb6fa2-61cf-4213-950b-703487fe6c9e",
  "date_created": "2026-03-02T18:02:10.103000Z",
  "date_modified": "2026-03-02T18:02:10.103000Z",
  "file_hash": "9e117e177cc8becfaba242f4c393b15efc8b2f92c723cc57f22d33c00ddd32d4",
  "private": false,
  "record": {
    "abstract": "We analyze and study the effects of locality on the fault-tolerance threshold\nfor quantum computation. We analytically estimate how the threshold will depend\non a scale parameter r which estimates the scale-up in the size of the circuit\ndue to encoding. We carry out a detailed semi-numerical threshold analysis for\nconcatenated coding using the 7-qubit CSS code in the local and `nonlocal\u0027\nsetting. First, we find that the threshold in the local model for the [[7,1,3]]\ncode has a 1/r dependence, which is in correspondence with our analytical\nestimate. Second, the threshold, beyond the 1/r dependence, does not depend too\nstrongly on the noise levels for transporting qubits. Beyond these results, we\nfind that it is important to look at more than one level of concatenation in\norder to estimate the threshold and that it may be beneficial in certain\nplaces, like in the transportation of qubits, to do error correction only\ninfrequently.",
    "arxiv_id": "quant-ph/0410047",
    "authors": [
      "Krysta M. Svore",
      "Barbara M. Terhal",
      "David P. DiVincenzo"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.72.022317",
    "journal_ref": "Phys. Rev. A 72, 022317 (2005) (17 pages)",
    "title": "Local Fault-tolerant Quantum Computation",
    "url": "https://arxiv.org/abs/quant-ph/0410047"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b1ba61c6-548e-46bf-a34b-cada6762d6e7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}