{
  "id": "0803.1911",
  "version": "v2",
  "published": "2008-03-13T07:52:43.000Z",
  "updated": "2008-04-02T15:43:51.000Z",
  "title": "On group theory for quantum gates and quantum coherence",
  "authors": [
    "Michel Planat",
    "Philippe Jorrand"
  ],
  "comment": "10 pages, to appear in J Phys A: Math and Theo (Fast Track Communication)",
  "journal": "Journal of Physics A Mathematical and Theoretical 41 (2008) 182001",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.GR",
    "math.MP"
  ],
  "abstract": "Finite group extensions offer a natural language to quantum computing. In a nutshell, one roughly describes the action of a quantum computer as consisting of two finite groups of gates: error gates from the general Pauli group P and stabilizing gates within an extension group C. In this paper one explores the nice adequacy between group theoretical concepts such as commutators, normal subgroups, group of automorphisms, short exact sequences, wreath products... and the coherent quantum computational primitives. The structure of the single qubit and two-qubit Clifford groups is analyzed in detail. As a byproduct, one discovers that M20, the smallest perfect group for which the commutator subgroup departs from the set of commutators, underlies quantum coherence of the two-qubit system. One recovers similar results by looking at the automorphisms of a complete set of mutually unbiased bases.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-02T15:43:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum gates",
      "group theory",
      "coherent quantum computational primitives",
      "finite group extensions offer",
      "underlies quantum coherence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1911P"
    }
  }
}