{
  "id": "0902.3496",
  "version": "v1",
  "published": "2009-02-20T01:24:05.000Z",
  "updated": "2009-02-20T01:24:05.000Z",
  "title": "Connection Between Continuous and Discrete Time Quantum Walks on d-Dimensional Lattices; Extensions to General Graphs",
  "authors": [
    "Domenico D'Alessandro"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "I obtain the dynamics of the continuous time quantum walk on a $d$-dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on the same lattice. This extends the main result of arXiv:quant-ph/0606050 which proved this limit for the infinite line. By highlighting the main features of the limiting procedure, I then extend it to general graphs. For a given discrete time quantum walk on a general graph, I single out the type of continuous dynamics (Hamiltonians) that can be obtained as a limit of the discrete time dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-20T01:24:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete time quantum walk",
      "general graph",
      "d-dimensional lattices",
      "connection",
      "extensions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/S0034-4877(10)80025-4",
      "journal": "Reports on Mathematical Physics",
      "year": 2010,
      "month": "Aug",
      "volume": 66,
      "number": 1,
      "pages": 85
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010RpMP...66...85D"
    }
  }
}