{
  "abstract": "We determine the optimal query complexity of ground-state preparation to trace-distance error $\\varepsilon$ when an energy threshold in the spectral gap is known. Let $U_H$ be an $α$-block-encoding of a Hamiltonian with unique ground state $|ψ_0\\rangle$, and suppose $|\\langleψ_0|U_I|0\\rangle|\\geγ$ for a state-preparation oracle $U_I$. The threshold lies at least $Δ/2$ above the ground-state energy and at least $Δ/2$ below every excited-state energy. We give two algorithms that prepare a state within trace distance $\\varepsilon$ of the ground state. One uses $O((α/Δ)(γ^{-1}+\\log(1/\\varepsilon)))$ calls to $U_H$ in expectation; the other uses $O((α/(γΔ))\\log(1/\\varepsilon))$ calls to $U_H$ in the worst case. We prove a lower bound matching the expected query count; the corresponding worst-case lower bound follows from Somma and de Wolf [SdW26]. The respective bounds on calls to $U_I$ are $O(1/γ)$ in expectation and $O(γ^{-1}\\log(1/\\varepsilon))$ in the worst case. On $(N+1)$-dimensional systems, these $U_I$ bounds are also optimal when the expected or worst-case count of $U_H$ calls, respectively, is $o((α/Δ)\\sqrt N)$. Both algorithms use a constant-accuracy spectral filter to construct a purifier, which we then sequentially compose during amplitude amplification to prepare a state with constant overlap with the ground state. The expected-query algorithm repeats the preparation followed by one high-accuracy spectral filter until success. The worst-case algorithm uses filters of increasing accuracy and limits the total number of queries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35668",
  "author_total": 4,
  "authors": [
    {
      "name": "Boyang Chen"
    },
    {
      "name": "Minbo Gao"
    },
    {
      "name": "Xinzhao Wang"
    },
    {
      "name": "Shuo Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1k1wdntjcz8yf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35668",
  "fulltext_url": null,
  "id": "1k1wdntjcz8yf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35668",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214799333",
  "pdf_url": "https://arxiv.org/pdf/2609.35668",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1k1wdntjcz8yf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2609.35668",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35668"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal Query Complexity for Ground-State Preparation",
  "title_text": "Optimal Query Complexity for Ground-State Preparation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/1k1wdntjcz8yf",
  "venue": "arXiv",
  "versions": []
}