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    "headline": "Coherent Oracle Access Cut Hidden-Subgroup Error Scaling",
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    "dek": "The query model achieved a quadratic improvement that arbitrary collective sample measurements could not match.",
    "summary": "The query model achieved a quadratic improvement that arbitrary collective sample measurements could not match.",
    "body_text": "For finite abelian groups, the authors prove matching upper and lower bounds for the state hidden-subgroup problem. Coherent access to state preparation and its inverse improves dependence on error from inverse-linear to inverse-square-root, while the sample-only model remains inverse-linear even with collective measurements. The separation depends on the stronger access model.",
    "why_it_matters": "The query model achieved a quadratic improvement that arbitrary collective sample measurements could not match.",
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      "Coherent access to state preparation and its inverse improves dependence on error from inverse-linear to inverse-square-root, while the sample-only model remains inverse-linear even with collective measurements."
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    "tags": [
      "hidden subgroup",
      "oracle access",
      "quantum complexity"
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    {
      "source_id": "source-2026-09-29-017",
      "title": "arXiv preprint 2609.35656",
      "publisher": "arXiv",
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    "title": "Coherent Oracle Access Cut Hidden-Subgroup Error Scaling",
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