{
  "annotation_id": "ef5e7190-d235-4395-b512-779fd88c4c23",
  "date_created": "2026-03-02T18:02:20.774000Z",
  "date_modified": "2026-03-02T18:02:20.774000Z",
  "file_hash": "7c2a9396b0a65de1515227adccc1c68b20bfb307d236b551b3364b3d4a6d49ed",
  "private": false,
  "record": {
    "abstract": "Operator quantum error correction is a recently developed theory that\nprovides a generalized framework for active error correction and passive error\navoiding schemes. In this paper, we describe these codes in the stabilizer\nformalism of standard quantum error correction theory. This is achieved by\nadding a \"gauge\" group to the standard stabilizer definition of a code that\ndefines an equivalence class between encoded states. Gauge transformations\nleave the encoded information unchanged; their effect is absorbed by virtual\ngauge qubits that do not carry useful information. We illustrate the\nconstruction by identifying a gauge symmetry in Shor\u0027s 9-qubit code that allows\nus to remove 4 of its 8 stabilizer generators, leading to a simpler decoding\nprocedure and a wider class of logical operations without affecting its\nessential properties. This opens the path to possible improvements of the error\nthreshold of fault-tolerant quantum computing.",
    "arxiv_id": "quant-ph/0508131",
    "authors": [
      "David Poulin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.95.230504",
    "journal_ref": "Phys. Rev. Lett. 95 230504 (2005)",
    "title": "Stabilizer Formalism for Operator Quantum Error Correction",
    "url": "https://arxiv.org/abs/quant-ph/0508131"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9252dfdd-b22e-4f2f-b958-2ab1748e3a6c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}