{
  "id": "1403.6910",
  "version": "v1",
  "published": "2014-03-27T03:54:24.000Z",
  "updated": "2014-03-27T03:54:24.000Z",
  "title": "Quantum Circuit for Calculating Mobius-like Transforms Via Grover-like Algorithm",
  "authors": [
    "Robert R. Tucci"
  ],
  "comment": "12 pages(4 files: 1 .tex, 1 .sty, 2 .eps)",
  "categories": [
    "quant-ph"
  ],
  "abstract": "In this paper, we give quantum circuits for calculating two closely related linear transforms that we refer to jointly as Mobius-like transforms. The first is the Mobius transform of a function $f^{-}(S^-)\\in \\mathbb{C}$, where $S^-\\subset \\{0,1,\\ldots,n-1\\}$. The second is a marginal of a probability distribution $P(y^n)$, where $y^n\\in Bool^n$. Known classical algorithms for calculating these Mobius-like transforms take ${\\cal O}(2^n)$ steps. Our quantum algorithm is based on a Grover-like algorithm and it takes ${\\cal O}(\\sqrt{2^n})$ steps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-27T03:54:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum circuit",
      "calculating mobius-like transforms",
      "grover-like algorithm",
      "probability distribution",
      "closely related linear transforms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.6910T"
    }
  }
}