{
  "annotation_id": "128a8d44-41be-4378-9998-9d1a573c97a4",
  "date_created": "2026-03-02T18:02:20.023000Z",
  "date_modified": "2026-03-02T18:02:20.023000Z",
  "file_hash": "eda5336d9e9fcfe4f94b44fb32309df3072461ac0a393c2bd2be72a7fe47ec94",
  "private": false,
  "record": {
    "abstract": "We consider an approach to deciding isomorphism of rigid n-vertex graphs (and\nrelated isomorphism problems) by solving a nonabelian hidden shift problem on a\nquantum computer using the standard method. Such an approach is arguably more\nnatural than viewing the problem as a hidden subgroup problem. We prove that\nthe hidden shift approach to rigid graph isomorphism is hard in two senses.\nFirst, we prove that Omega(n) copies of the hidden shift states are necessary\nto solve the problem (whereas O(n log n) copies are sufficient). Second, we\nprove that if one is restricted to single-register measurements, an exponential\nnumber of hidden shift states are required.",
    "arxiv_id": "quant-ph/0510185",
    "authors": [
      "Andrew M. Childs",
      "Pawel Wocjan"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.26421/QIC7.5-6",
    "journal_ref": "Quantum Information and Computation, Vol. 7, No. 5-6 (2007)\n  504-521",
    "title": "On the quantum hardness of solving isomorphism problems as nonabelian   hidden shift problems",
    "url": "https://arxiv.org/abs/quant-ph/0510185"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3d20c8ff-0cd9-44eb-9de9-5c025b897990",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}