{
  "annotation_id": "9f1d87f0-4b41-44c0-aea8-318aa55b0820",
  "date_created": "2026-03-02T18:02:34.653000Z",
  "date_modified": "2026-03-02T18:02:34.653000Z",
  "file_hash": "f003c9f82a613f7e32f4051fff1e10a650582b1fa543d5f92454a25919672959",
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  "record": {
    "abstract": "We show that any stabilizer code over a finite field is equivalent to a\ngraphical quantum code. Furthermore we prove that a graphical quantum code over\na finite field is a stabilizer code. The technique used in the proof\nestablishes a new connection between quantum codes and quadratic forms. We\nprovide some simple examples to illustrate our results.",
    "arxiv_id": "quant-ph/0703112",
    "authors": [
      "Markus Grassl",
      "Andreas Klappenecker",
      "Martin Roetteler"
    ],
    "categories": [
      "quant-ph",
      "cs.IT",
      "math.IT"
    ],
    "doi": "10.1109/ISIT.2002.1023317",
    "journal_ref": "Proceedings 2002 IEEE International Symposium on Information\n  Theory (ISIT 2002), Lausanne, Switzerland, June/July 2002, p. 45",
    "title": "Graphs, Quadratic Forms, and Quantum Codes",
    "url": "https://arxiv.org/abs/quant-ph/0703112"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "850ceecd-4785-4983-8956-cab6c1b5dfee",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}