{
  "annotation_id": "080eb391-b7dd-4709-9830-7a7d816ecbee",
  "date_created": "2026-03-02T18:01:45.851000Z",
  "date_modified": "2026-03-02T18:01:45.851000Z",
  "file_hash": "d61ffe1944ca27ba91606b34d77d958f7d06cd3183e8ff32fadbf102226e0268",
  "private": false,
  "record": {
    "abstract": "We derive the effective channel for a logical qubit protected by an arbitrary\nquantum error-correcting code, and derive the map between channels induced by\nconcatenation. For certain codes in the presence of single-bit Pauli errors, we\ncalculate the exact threshold error probability for perfect fidelity in the\ninfinite concatenation limit. We then use the control theory technique of\nbalanced truncation to find low-order non-asymptotic approximations for the\neffective channel dynamics.",
    "arxiv_id": "quant-ph/0111003",
    "authors": [
      "Benjamin Rahn",
      "Andrew C. Doherty",
      "Hideo Mabuchi"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Exact and Approximate Performance of Concatenated Quantum Codes",
    "url": "https://arxiv.org/abs/quant-ph/0111003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2adc22ee-6a64-48f1-9e22-55076f81be33",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}