{
  "id": "1101.1053",
  "version": "v3",
  "published": "2011-01-05T19:28:13.000Z",
  "updated": "2012-03-21T16:06:27.000Z",
  "title": "An Improved Query for the Hidden Subgroup Problem",
  "authors": [
    "Asif Shakeel"
  ],
  "comment": "26 pages. Expanded the introduction",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP",
    "math.RT"
  ],
  "abstract": "An equal superposition query with |0> in the response register is used in the \"standard method\" of single-query algorithms for the hidden subgroup problem (HSP). Here we introduce a different query, the character query, generalizing the well-known phase kickback trick. This query maximizes the success probability of subgroup identification under a uniform prior, for the HSP in which the oracle functions take values in a finite abelian group. We then apply our results to the case when the subgroups are drawn from a set of conjugate subgroups and obtain a success probability greater than that found by Moore and Russell.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-03-21T16:06:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C35",
      "81R05"
    ],
    "keywords": [
      "hidden subgroup problem",
      "well-known phase kickback trick",
      "equal superposition query",
      "finite abelian group",
      "success probability greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1053S"
    }
  }
}