{
  "annotation_id": "584fb354-9c17-4e29-907a-015f09bcd5b5",
  "date_created": "2026-03-02T18:01:53.121000Z",
  "date_modified": "2026-03-02T18:01:53.121000Z",
  "file_hash": "50d922fdf3e0a378f6d4866ba7e7a9aae369508cb65ac3d61732e8ada32e3974",
  "private": false,
  "record": {
    "abstract": "There are well known necessary and sufficient conditions for a quantum code\nto correct a set of errors. We study weaker conditions under which a quantum\ncode may correct errors with probabilities that may be less than one. We work\nwith stabilizer codes and as an application study how the nine qubit code, the\nseven qubit code, and the five qubit code perform when there are errors on more\nthan one qubit. As a second application, we discuss the concept of syndrome\nquality and use it to suggest a way that quantum error correction can be\npractically improved.",
    "arxiv_id": "quant-ph/0209058",
    "authors": [
      "Jesse Fern",
      "John Terilla"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Probabilistic quantum error correction",
    "url": "https://arxiv.org/abs/quant-ph/0209058"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d989ecf0-c565-4856-91dc-efa40c792fc1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}