{
  "id": "quant-ph/0310052",
  "version": "v2",
  "published": "2003-10-08T08:10:47.000Z",
  "updated": "2003-10-17T03:15:19.000Z",
  "title": "Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm",
  "authors": [
    "Tien D. Kieu"
  ],
  "comment": "Typos fixed, substantial results added in Section III, new reference and footnotes added. Now 22 pages, one figure",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We review the proposal of a quantum algorithm for Hilbert's tenth problem and provide further arguments towards the proof that: (i) the algorithm terminates after a finite time for any input of Diophantine equation; (ii) the final ground state which contains the answer for the Diophantine equation can be identified as the component state having better-than-even probability to be found by measurement at the end time--even though probability for the final ground state in a quantum adiabatic process need not monotonically increase towards one in general. Presented finally are the reasons why our algorithm is outside the jurisdiction of no-go arguments previously employed to show that Hilbert's tenth problem is recursively non-computable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-10-17T03:15:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum adiabatic algorithm",
      "final ground state",
      "diophantine equation",
      "quantum adiabatic process",
      "quantum algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003quant.ph.10052K"
    }
  }
}