{
  "id": "2209.15523",
  "version": "v1",
  "published": "2022-09-30T15:14:15.000Z",
  "updated": "2022-09-30T15:14:15.000Z",
  "title": "Convergence condition of simulated quantum annealing for closed and open systems",
  "authors": [
    "Yusuke Kimura",
    "Hidetoshi Nishimori"
  ],
  "comment": "9 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We derive a generic condition for simulated quantum annealing to converge to thermal equilibrium at a given, typically low, temperature. Both closed and open systems are treated. We rewrite the classical master equation for simulated quantum annealing into an imaginary-time Schr\\\"odinger equation, to which we apply the imaginary-time variant of asymptotic adiabatic condition to deduce the convergence condition. The result agrees qualitatively with a rigorous convergence condition of simulated quantum annealing for closed systems, which was derived from the theory of inhomogeneous Markov process. Also observed is qualitative agreement with a rigorous convergence condition of quantum annealing for closed systems under the real-time Schr\\\"odinger dynamics. This coincidence of convergence conditions for classical stochastic processes for simulated quantum annealing and the real-time quantum dynamics for quantum annealing is highly non-trivial and calls for further scrutiny.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-30T15:14:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simulated quantum annealing",
      "open systems",
      "rigorous convergence condition",
      "real-time quantum dynamics",
      "closed systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}