{
  "id": "1311.2372",
  "version": "v2",
  "published": "2013-11-11T08:14:21.000Z",
  "updated": "2014-10-03T13:26:14.000Z",
  "title": "Exponential of a Matrix, a Nonlinear Problem and Quantum Gates",
  "authors": [
    "Willi-Hans Steeb",
    "Yorick Hardy"
  ],
  "comment": "one more example added, comments are welcome",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We describe solutions of the matrix equation $\\exp(z(A-I_n))=A$, where $z \\in {\\mathbb C}$. Applications in quantum computing are given. Both normal and nonnormal matrices are studied. For normal matrices, the Lambert W-function plays a central role.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-11T08:14:21.000Z",
      "comment": "comments are welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-03T13:26:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear problem",
      "quantum gates",
      "exponential",
      "lambert w-function plays",
      "matrix equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.4905382",
      "journal": "Journal of Mathematical Physics",
      "year": 2015,
      "month": "Jan",
      "volume": 56,
      "number": 1,
      "pages": "012201"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JMP....56a2201S"
    }
  }
}