{
  "id": "2011.09495",
  "version": "v1",
  "published": "2020-11-18T19:04:51.000Z",
  "updated": "2020-11-18T19:04:51.000Z",
  "title": "(Sub)Exponential advantage of adiabatic quantum computation with no sign problem",
  "authors": [
    "András Gilyén",
    "Umesh Vazirani"
  ],
  "comment": "18 pages, 3 figures",
  "categories": [
    "quant-ph",
    "cs.CC"
  ],
  "abstract": "We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. This strengthens the superpolynomial separation recently proved by Hastings. The Hamiltonian that exhibits this speed-up comes from the adjacency matrix of an undirected graph, and we can view the adiabatic evolution as an efficient $\\mathcal{O}(\\mathrm{poly}(n))$-time quantum algorithm for finding a specific \"EXIT\" vertex in the graph given the \"ENTRANCE\" vertex. On the other hand we show that if the graph is given via an adjacency-list oracle, there is no classical algorithm that finds the \"EXIT\" with probability greater than $\\exp(-n^\\delta)$ using at most $\\exp(n^\\delta)$ queries for $\\delta= \\frac15 - o(1)$. Our construction of the graph is somewhat similar to the \"welded-trees\" construction of Childs et al., but uses additional ideas of Hastings for achieving a spectral gap and a short adiabatic path.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-18T19:04:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adiabatic quantum computation",
      "sign problem",
      "exponential advantage",
      "exponential quantum speedup",
      "short adiabatic path"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}