{
  "annotation_id": "a2fe2149-3103-4954-8e80-14f4c35fefd4",
  "date_created": "2026-03-02T18:02:27.456000Z",
  "date_modified": "2026-03-02T18:02:27.456000Z",
  "file_hash": "a0952e51fa5626baa5394fb3bfac14f87c5b418a415ba220daf9f625a20c048a",
  "private": false,
  "record": {
    "abstract": "A striking feature of quantum error correcting codes is that they can\nsometimes be used to correct more errors than they can uniquely identify. Such\ndegenerate codes have long been known, but have remained poorly understood. We\nprovide a heuristic for designing degenerate quantum codes for high noise\nrates, which is applied to generate codes that can be used to communicate over\nalmost any Pauli channel at rates that are impossible for a nondegenerate code.\nThe gap between nondegenerate and degenerate code performance is quite large,\nin contrast to the tiny magnitude of the only previous demonstration of this\neffect. We also identify a channel for which none of our codes outperform the\nbest nondegenerate code and show that it is nevertheless quite unlike any\nchannel for which nondegenerate codes are known to be optimal.",
    "arxiv_id": "quant-ph/0604107",
    "authors": [
      "Graeme Smith",
      "John A. Smolin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.98.030501",
    "journal_ref": "Phys. Rev. Lett. 98, 030501 (2007)",
    "title": "Degenerate Quantum Codes for Pauli Channels",
    "url": "https://arxiv.org/abs/quant-ph/0604107"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d91010e6-8f65-4a93-a789-eadebed5e51a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}