{
  "annotation_id": "fb37175b-28e6-40cd-93d5-f87b63727a34",
  "date_created": "2026-03-02T18:02:27.407000Z",
  "date_modified": "2026-03-02T18:02:27.407000Z",
  "file_hash": "f01e55fabe9885376ce604bec0ba02f4c6883864c190b199fa01ab85c5ecae44",
  "private": false,
  "record": {
    "abstract": "One of the most promising and versatile approaches to creating new quantum\nalgorithms is based on the quantum hidden subgroup (QHS) paradigm, originally\nsuggested by Alexei Kitaev. This class of quantum algorithms encompasses the\nDeutsch-Jozsa, Simon, Shor algorithms, and many more.\n  In this paper, our strategy for finding new quantum algorithms is to\ndecompose Shor\u0027s quantum factoring algorithm into its basic primitives, then to\ngeneralize these primitives, and finally to show how to reassemble them into\nnew QHS algorithms. Taking an \"alphabetic building blocks approach,\" we use\nthese primitives to form an \"algorithmic toolkit\" for the creation of new\nquantum algorithms, such as wandering Shor algorithms, continuous Shor\nalgorithms, the quantum circle algorithm, the dual Shor algorithm, a QHS\nalgorithm for Feynman integrals, free QHS algorithms, and more.\n  Toward the end of this paper, we show how Grover\u0027s algorithm is most\nsurprisingly \"almost\" a QHS algorithm, and how this result suggests the\npossibility of an even more complete \"algorithmic tookit\" beyond the QHS\nalgorithms.",
    "arxiv_id": "quant-ph/0607046",
    "authors": [
      "Samuel J. Lomonaco Jr.",
      "Louis H. Kauffman"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit",
    "url": "https://arxiv.org/abs/quant-ph/0607046"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ffc7e227-1964-40db-afe5-7fb8666195c4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}