{
  "abstract": "Suppose a Hamiltonian $H$ has a unique ground state $|ψ_0\\rangle$ with an eigenvalue $E_0$, and we have an estimate $\\tilde{E}_0$ such that $|\\tilde{E}_0-E_0|\\leqδ$, and there is a gap of at least $3δ$ between $E_0$ and all other eigenvalues. Suppose we have a unitary $A$ available that can produce a \"guiding state'\" $A|0\\rangle$ that has overlap at least $γ$ with $|ψ_0\\rangle$. We show how to obtain an $η$-approximation of $|ψ_0\\rangle$ with probability at least $1-\\varepsilon$ using $O(\\log(1/\\varepsilon)/γδ+ \\log(1/η)/δ)$ applications of $U=e^{iH}$ its inverse, and $O(\\log(1/\\varepsilon)/γ)$ applications of $A$ and its inverse. We give two different algorithms, one based on interleaving amplitude amplification and error-reduction in the style of [HMdW03], and one using the composition of transducers. This paper is the state-preparation follow-up to our two recent ground-state-energy estimation papers [JW26,SdW26]. Combined with the optimal energy-estimation of [JW26], our results show the claimed upper bound for ground-state preparation. The bound is optimal up to a constant factor in terms of the number of applications of $U$ and $U^\\dagger$ if $\\varepsilon=η$, as follows from [SdW26]. In one of our approaches to ground state preparation, we construct transducers for amplitude amplification and LCU that might be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38091",
  "author_total": 4,
  "authors": [
    {
      "name": "Stacey Jeffery"
    },
    {
      "name": "Rolando D. Somma"
    },
    {
      "name": "Freek Witteveen"
    },
    {
      "name": "Ronald de Wolf"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/avwzw67z5n10p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38091",
  "fulltext_url": null,
  "id": "avwzw67z5n10p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38091",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214979197",
  "pdf_url": "https://arxiv.org/pdf/2609.38091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/avwzw67z5n10p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.38091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38091"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal Ground-State Preparation with a Guiding State",
  "title_text": "Optimal Ground-State Preparation with a Guiding State",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/avwzw67z5n10p",
  "venue": "arXiv",
  "versions": []
}