{
  "annotation_id": "8c74b4d7-884e-4eb2-bd63-6697ca29ee63",
  "date_created": "2026-03-02T18:02:37.844000Z",
  "date_modified": "2026-03-02T18:02:37.844000Z",
  "file_hash": "a4ec5e4055d10fc5ae27817c5eb77a8a3e0e1b2c3541734efba4c0065805b8f9",
  "private": false,
  "record": {
    "abstract": "We study the resources needed to construct topological 2D stabilizer codes as\na way to estimate in part their efficiency and this leads us to perform a\ncomparative study of surface codes and color codes. This study clarifies the\nsimilarities and differences between these two types of stabilizer codes. We\ncompute the error correcting rate $C:=n/d^2$ for surface codes $C_s$ and color\ncodes $C_c$ in several instances. On the torus, typical values are $C_s=2$ and\n$C_c=3/2$, but we find that the optimal values are $C_s=1$ and $C_c=9/8$. For\nplanar codes, a typical value is $C_s=2$, while we find that the optimal values\nare $C_s=1$ and $C_c=3/4$. In general, a color code encodes twice as much\nlogical qubits as a surface code does.",
    "arxiv_id": "quant-ph/0703272",
    "authors": [
      "H. Bombin",
      "M. A. Martin-Delgado"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.str-el"
    ],
    "doi": "10.1103/PhysRevA.76.012305",
    "journal_ref": "Phys. Rev. A 76, 012305 (2007)",
    "title": "Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study",
    "url": "https://arxiv.org/abs/quant-ph/0703272"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d0bc5edd-fe66-4f7f-aca5-843d97c5c793",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}