{
  "annotation_id": "9f45e787-049a-421c-bea8-6bf39206e82e",
  "date_created": "2026-03-02T18:01:56.115000Z",
  "date_modified": "2026-03-02T18:01:56.115000Z",
  "file_hash": "57b56f16a5f2786d2ff253fbad6b016acba385fad9c75d6ab3f14e206b735712",
  "private": false,
  "record": {
    "abstract": "We give efficient quantum algorithms for the problems of Hidden Translation\nand Hidden Subgroup in a large class of non-abelian solvable groups including\nsolvable groups of constant exponent and of constant length derived series. Our\nalgorithms are recursive. For the base case, we solve efficiently Hidden\nTranslation in $\\Z_{p}^{n}$, whenever $p$ is a fixed prime. For the induction\nstep, we introduce the problem Translating Coset generalizing both Hidden\nTranslation and Hidden Subgroup, and prove a powerful self-reducibility result:\nTranslating Coset in a finite solvable group $G$ is reducible to instances of\nTranslating Coset in $G/N$ and $N$, for appropriate normal subgroups $N$ of\n$G$. Our self-reducibility framework combined with Kuperberg\u0027s subexponential\nquantum algorithm for solving Hidden Translation in any abelian group, leads to\nsubexponential quantum algorithms for Hidden Translation and Hidden Subgroup in\nany solvable group.",
    "arxiv_id": "quant-ph/0211091",
    "authors": [
      "K. Friedl",
      "G. Ivanyos",
      "F. Magniez",
      "M. Santha",
      "P. Sen"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1137/130907203",
    "journal_ref": "SIAM Journal on Computing 43:1 (2014)",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Hidden Translation and Translating Coset in Quantum Computing",
    "url": "https://arxiv.org/abs/quant-ph/0211091"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f62c22b1-92e0-4343-99c7-e1131137cee4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}