{
  "annotation_id": "5974c24b-5ddb-46fb-9b7a-e07a70708dec",
  "date_created": "2026-03-02T18:02:17.039000Z",
  "date_modified": "2026-03-02T18:02:17.039000Z",
  "file_hash": "881ed78006360fe01158ee9aeb8d463c357ce574ec15e01f9b181f2aee6af8a7",
  "private": false,
  "record": {
    "abstract": "We approach the hidden subgroup problem by performing the so-called pretty\ngood measurement on hidden subgroup states. For various groups that can be\nexpressed as the semidirect product of an abelian group and a cyclic group, we\nshow that the pretty good measurement is optimal and that its probability of\nsuccess and unitary implementation are closely related to an average-case\nalgebraic problem. By solving this problem, we find efficient quantum\nalgorithms for a number of nonabelian hidden subgroup problems, including some\nfor which no efficient algorithm was previously known: certain metacyclic\ngroups as well as all groups of the form (Z_p)^r X| Z_p for fixed r (including\nthe Heisenberg group, r=2). In particular, our results show that entangled\nmeasurements across multiple copies of hidden subgroup states can be useful for\nefficiently solving the nonabelian HSP.",
    "arxiv_id": "quant-ph/0504083",
    "authors": [
      "Dave Bacon",
      "Andrew M. Childs",
      "Wim van Dam"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1109/SFCS.2005.38",
    "journal_ref": "Proc. 46th IEEE Symposium on Foundations of Computer Science (FOCS\n  2005), pp. 469-478",
    "title": "From optimal measurement to efficient quantum algorithms for the hidden   subgroup problem over semidirect product groups",
    "url": "https://arxiv.org/abs/quant-ph/0504083"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6852cc90-10fe-48d7-937d-cd9071e0d147",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}