{
  "annotation_id": "63187350-4c1a-4d1e-b4ac-c922ec77e9d9",
  "date_created": "2026-03-02T18:02:23.619000Z",
  "date_modified": "2026-03-02T18:02:23.619000Z",
  "file_hash": "8da7905ef866a6fdc06eac2d1382a902dd5865979723c6fe244c31dfde3715db",
  "private": false,
  "record": {
    "abstract": "We prove the existence of topological quantum error correcting codes with\nencoding rates $k/n$ asymptotically approaching the maximum possible value.\nExplicit constructions of these topological codes are presented using surfaces\nof arbitrary genus. We find a class of regular toric codes that are optimal.\nFor physical implementations, we present planar topological codes.",
    "arxiv_id": "quant-ph/0602063",
    "authors": [
      "H. Bombin",
      "M. A. Martin-Delgado"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.str-el",
      "cs.GR",
      "hep-th",
      "math-ph",
      "math.AT",
      "math.CO",
      "math.MP"
    ],
    "doi": "10.1103/PhysRevA.73.062303",
    "journal_ref": "Phys.Rev.A73:062303,2006",
    "title": "Topological Quantum Error Correction with Optimal Encoding Rate",
    "url": "https://arxiv.org/abs/quant-ph/0602063"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1476c30c-4f4e-4baf-ad57-59f76c945099",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}