{
  "id": "quant-ph/0610130",
  "version": "v1",
  "published": "2006-10-16T13:59:33.000Z",
  "updated": "2006-10-16T13:59:33.000Z",
  "title": "Grover's algorithm on a Feynman computer",
  "authors": [
    "Diego de Falco",
    "Dario Tamascelli"
  ],
  "journal": "J. Phys. A: Math. Gen. 37 (2004) 909-930",
  "doi": "10.1088/0305-4470/37/3/025",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We present an implementation of Grover's algorithm in the framework of Feynman's cursor model of a quantum computer. The cursor degrees of freedom act as a quantum clocking mechanism, and allow Grover's algorithm to be performed using a single, time-independent Hamiltonian. We examine issues of locality and resource usage in implementing such a Hamiltonian. In the familiar language of Heisenberg spin-spin coupling, the clocking mechanism appears as an excitation of a basically linear chain of spins, with occasional controlled jumps that allow for motion on a planar graph: in this sense our model implements the idea of \"timing\" a quantum algorithm using a continuous-time random walk. In this context we examine some consequences of the entanglement between the states of the input/output register and the states of the quantum clock.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-16T13:59:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grovers algorithm",
      "feynman computer",
      "feynmans cursor model",
      "continuous-time random walk",
      "basically linear chain"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}