{
  "annotation_id": "37b68462-5160-4127-8665-6e22f35e878e",
  "date_created": "2026-03-02T18:02:27.732000Z",
  "date_modified": "2026-03-02T18:02:27.732000Z",
  "file_hash": "b38ecefcb4b230394c9e5a5a9270d226873d6202e34d3f2930e5469170f413d8",
  "private": false,
  "record": {
    "abstract": "We consider the problem of optimally decoding a quantum error correction code\n-- that is to find the optimal recovery procedure given the outcomes of partial\n\"check\" measurements on the system. In general, this problem is NP-hard.\nHowever, we demonstrate that for concatenated block codes, the optimal decoding\ncan be efficiently computed using a message passing algorithm. We compare the\nperformance of the message passing algorithm to that of the widespread\nblockwise hard decoding technique. Our Monte Carlo results using the 5 qubit\nand Steane\u0027s code on a depolarizing channel demonstrate significant advantages\nof the message passing algorithms in two respects. 1) Optimal decoding\nincreases by as much as 94% the error threshold below which the error\ncorrection procedure can be used to reliably send information over a noisy\nchannel. 2) For noise levels below these thresholds, the probability of error\nafter optimal decoding is suppressed at a significantly higher rate, leading to\na substantial reduction of the error correction overhead.",
    "arxiv_id": "quant-ph/0606126",
    "authors": [
      "David Poulin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.74.052333",
    "journal_ref": "Phys. Rev. A 74 052333 (2006)",
    "title": "Optimal and Efficient Decoding of Concatenated Quantum Block Codes",
    "url": "https://arxiv.org/abs/quant-ph/0606126"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b470e538-6205-458e-8b8e-17be7bf34e8f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}