{
  "id": "2003.10511",
  "version": "v1",
  "published": "2020-03-23T19:40:56.000Z",
  "updated": "2020-03-23T19:40:56.000Z",
  "title": "Efficiently computing logical noise in quantum error correcting codes",
  "authors": [
    "Stefanie J. Beale",
    "Joel J. Wallman"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Quantum error correction protocols have been developed to offset the high sensitivity to noise inherent in quantum systems. However, much is still unknown about the behaviour of a quantum error-correcting code under general noise, making it difficult to correct errors effectively; this is largely due to the computational cost of simulating quantum systems large enough to perform nontrivial encodings. In this paper, we develop general methods for reducing the computational complexity of calculating the exact effective logical noise by many orders of magnitude by determining when different recovery operations produce equivalent logical noise. These methods could also be used to better approximate soft decoding schemes for concatenated codes or to reduce the size of a lookup table to speed up the error correction step in implementations of quantum error correcting codes. We give examples of such reductions for the 3-qubit, 5-qubit, Steane, concatenated, and toric codes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-23T19:40:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum error correcting codes",
      "efficiently computing logical noise",
      "produce equivalent logical noise",
      "approximate soft decoding schemes",
      "operations produce equivalent logical"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}