{
  "id": "2105.04478",
  "version": "v1",
  "published": "2021-05-10T16:16:19.000Z",
  "updated": "2021-05-10T16:16:19.000Z",
  "title": "A sampling-based quasi-probability simulation for fault-tolerant quantum error correction on the surface codes under coherent noise",
  "authors": [
    "Shigeo Hakkaku",
    "Kosuke Mitarai",
    "Keisuke Fujii"
  ],
  "comment": "6 pages, 5 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasi-probability distribution. Then, an unbiased estimator of the logical error probability is constructed by sampling Clifford channels with an appropriate post-processing. We characterize the sampling cost via the channel robustness and find that the proposed sampling-based method is feasible even for planar surface codes with relatively large code distances intractable for full state-vector simulations. As a demonstration, we simulate repetitive faulty syndrome measurements on the planar surface code of distance 5 with 81 qubits. We find that the coherent error increases the logical error rate. This is a practical application of the quasi-probability simulation for a meaningful task and would be useful to explore experimental quantum error correction on the near-term quantum devices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-10T16:16:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fault-tolerant quantum error correction",
      "coherent noise",
      "sampling-based quasi-probability simulation",
      "repetitive faulty syndrome measurements",
      "planar surface code"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}