{
  "id": "quant-ph/0412072",
  "version": "v2",
  "published": "2004-12-09T15:54:28.000Z",
  "updated": "2005-02-09T16:53:05.000Z",
  "title": "Quantum Compiling with Approximation of Multiplexors",
  "authors": [
    "Robert R. Tucci"
  ],
  "comment": "Ver1:18 pages (files: 1 .tex, 1 .sty, 7 .eps); Ver2:26 pages (files: 1 .tex, 1 .sty, 7 .eps, 7 .m) Ver2 = Ver1 + new material, including 7 Octave/Matlab m-files",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A quantum compiling algorithm is an algorithm for decomposing (\"compiling\") an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose $U_{in}$ is an $\\nb$-bit unstructured unitary matrix (a unitary matrix with no special symmetries) that we wish to compile. For $\\nb>10$, expressing $U_{in}$ as a SEO requires more than a million CNOTs. This calls for a method for finding a unitary matrix that: (1)approximates $U_{in}$ well, and (2) is expressible with fewer CNOTs than $U_{in}$. The purpose of this paper is to propose one such approximation method. Various quantum compiling algorithms have been proposed in the literature that decompose an arbitrary unitary matrix into a sequence of U(2)-multiplexors, each of which is then decomposed into a SEO. Our strategy for approximating $U_{in}$ is to approximate these intermediate U(2)-multiplexors. In this paper, we will show how one can approximate a U(2)-multiplexor by another U(2)-multiplexor that is expressible with fewer CNOTs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-02-09T16:53:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary unitary matrix",
      "quantum compiling algorithm",
      "multiplexors",
      "fewer cnots",
      "approximate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004quant.ph.12072T"
    }
  }
}