{
  "id": "1808.02781",
  "version": "v1",
  "published": "2018-08-08T13:54:42.000Z",
  "updated": "2018-08-08T13:54:42.000Z",
  "title": "A Factorisation Algorithm in Adiabatic Quantum Computation",
  "authors": [
    "Tien D. Kieu"
  ],
  "comment": "10 pages, 3 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The problem of factorising an positive integer $N$ into two integer factors $x$ and $y$ is first reformulated as an optimisation problem over the positive integer domain of the corresponding Diophantine polynomial $Q_N(x,y)=N^2(N-xy)^2 + x(x-y)^2$, of which the solution is unique with $x\\le \\sqrt{N} \\le y$, and $x=1$ if and only if $N$ is prime. An algorithm in the context of Adiabatic Quantum Computation is then proposed for the general factorisation problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-08T13:54:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adiabatic quantum computation",
      "factorisation algorithm",
      "general factorisation problem",
      "integer factors",
      "positive integer domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}