{
  "id": "quant-ph/0104053",
  "version": "v1",
  "published": "2001-04-10T19:20:41.000Z",
  "updated": "2001-04-10T19:20:41.000Z",
  "title": "Quantum Formulas: a Lower Bound and Simulation",
  "authors": [
    "Vwani P. Roychowdhury",
    "Farrokh Vatan"
  ],
  "comment": "22 pages, LaTeX, 6 figures. Final and extended version of quant-ph/9903042. To appear in SIAM Journal on Computing",
  "categories": [
    "quant-ph",
    "cs.CC"
  ],
  "abstract": "We show that Nechiporuk's method for proving lower bounds for Boolean formulas can be extended to the quantum case. This leads to an $\\Omega(n^2 / \\log^2 n)$ lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas states that the majority function does not have a linear-size quantum formula. We also show that quantum formulas can be simulated by Boolean circuits of almost the same size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-10T19:20:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simulation",
      "explicit lower bound",
      "quantum formulas states",
      "proving lower bounds",
      "boolean formulas"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001quant.ph..4053R"
    }
  }
}