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    "headline": "Ground-State Preparation Reached Its Query Bound",
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    "dek": "Two algorithms and a matching lower bound fixed the expected complexity when a gap threshold is known.",
    "summary": "Two algorithms and a matching lower bound fixed the expected complexity when a gap threshold is known.",
    "body_text": "For a block-encoded Hamiltonian with a unique ground state and a known threshold inside the spectral gap, the authors give expected- and worst-case preparation algorithms. The expected version uses a constant-accuracy spectral filter, amplitude amplification and repeated high-accuracy checks; its Hamiltonian-query count is matched by a lower bound. The result settles the oracle-query scaling under the paper's access and overlap assumptions. It does not translate directly into wall-clock advantage on current quantum hardware.",
    "why_it_matters": "Two algorithms and a matching lower bound fixed the expected complexity when a gap threshold is known.",
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      "It does not translate directly into wall-clock advantage on current quantum hardware."
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        "qualification": "It does not translate directly into wall-clock advantage on current quantum hardware."
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    "tags": [
      "quantum algorithms",
      "ground states",
      "query complexity"
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      "source_id": "source-2026-09-29-014",
      "title": "arXiv preprint 2609.35668",
      "publisher": "arXiv",
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      "published_at": "2026-09-28T13:26:19.000-04:00",
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