{
  "annotation_id": "7eecc38e-463c-4ef6-8c94-5087720248f6",
  "date_created": "2026-03-02T18:01:51.835000Z",
  "date_modified": "2026-03-02T18:01:51.835000Z",
  "file_hash": "bd24ccdbd4ac5571fa6489d408f45b9d48cf1b2921321494e270859d5621b457",
  "private": false,
  "record": {
    "abstract": "When a logical qubit is protected using a quantum error-correcting code, the\nnet effect of coding, decoherence (a physical channel acting on qubits in the\ncodeword) and recovery can be represented exactly by an effective channel\nacting directly on the logical qubit. In this paper we describe a procedure for\nderiving the map between physical and effective channels that results from a\ngiven coding and recovery procedure. We show that the map for a concatenation\nof codes is given by the composition of the maps for the constituent codes.\nThis perspective leads to an efficient means for calculating the exact\nperformance of quantum codes with arbitrary levels of concatenation. We present\nexplicit results for single-bit Pauli channels. For certain codes under the\nsymmetric depolarizing channel, we use the coding maps to compute exact\nthreshold error probabilities for achievability of perfect fidelity in the\ninfinite concatenation limit.",
    "arxiv_id": "quant-ph/0206061",
    "authors": [
      "Benjamin Rahn",
      "Andrew C. Doherty",
      "Hideo Mabuchi"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.66.032304",
    "title": "Exact Performance of Concatenated Quantum Codes",
    "url": "https://arxiv.org/abs/quant-ph/0206061"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fc13a981-0abd-4b99-a334-72fc5c9c0b0c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}