{
  "id": "quant-ph/0409035",
  "version": "v2",
  "published": "2004-09-06T13:37:37.000Z",
  "updated": "2005-07-06T17:10:27.000Z",
  "title": "Quantum Verification of Matrix Products",
  "authors": [
    "Harry Buhrman",
    "Robert Spalek"
  ],
  "comment": "15 pages, submitted; v2: rewritten, clarified, and fixed some proofs",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We present a quantum algorithm that verifies a product of two n*n matrices over any field with bounded error in worst-case time n^{5/3} and expected time n^{5/3} / min(w,sqrt(n))^{1/3}, where w is the number of wrong entries. This improves the previous best algorithm that runs in time n^{7/4}. We also present a quantum matrix multiplication algorithm that is efficient when the result has few nonzero entries.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-07-06T17:10:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum verification",
      "matrix products",
      "quantum matrix multiplication algorithm",
      "quantum algorithm",
      "worst-case time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004quant.ph..9035B"
    }
  }
}