{
  "id": "1501.04396",
  "version": "v1",
  "published": "2015-01-19T06:10:30.000Z",
  "updated": "2015-01-19T06:10:30.000Z",
  "title": "Perfect state transfer in products and covers of graphs",
  "authors": [
    "Gabriel Coutinho",
    "Chris Godsil"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO",
    "quant-ph"
  ],
  "abstract": "A continuous-time quantum walk on a graph $X$ is represented by the complex matrix $\\exp (-\\mathrm{i} t A)$, where $A$ is the adjacency matrix of $X$ and $t$ is a non-negative time. If the graph models a network of interacting qubits, transfer of state among such qubits throughout time can be formalized as the action of the continuous-time quantum walk operator in the characteristic vectors of the vertices. Here we are concerned with the problem of determining which graphs admit a perfect transfer of state. More specifically, we will study graphs whose adjacency matrix is a sum of tensor products of $01$-matrices, focusing on the case where a graph is the tensor product of two other graphs. As a result, we will construct many new examples of perfect state transfer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-19T06:10:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perfect state transfer",
      "tensor product",
      "continuous-time quantum walk operator",
      "adjacency matrix",
      "qubits throughout time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150104396C"
    }
  }
}