{
  "id": "2103.08381",
  "version": "v1",
  "published": "2021-03-15T13:34:24.000Z",
  "updated": "2021-03-15T13:34:24.000Z",
  "title": "Non-Abelian statistics with mixed-boundary punctures on the toric code",
  "authors": [
    "Asmae Benhemou",
    "Jiannis K. Pachos",
    "Dan E. Browne"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibit non-Abelian anyonic behaviour [1]. Motivated by this result, we investigated the potential of having non-Abelian statistics from puncture defects on the toric code. We demonstrate that an encoding with mixed-boundary punctures reproduces Ising fusion, and a logical Pauli-$X$ upon their braiding. Our construction paves the way for local lattice defects to exhibit non-Abelian properties that can be employed for quantum information tasks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-15T13:34:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "toric code",
      "non-abelian statistics",
      "order realising abelian anyons",
      "mixed-boundary punctures reproduces ising fusion",
      "support non-local lattice defects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}