{
  "abstract": "Suppose we can apply the unitary $U=e^{i H}$ for some Hamiltonian $H$, and are given access to a unitary that prepares a guiding state promised to have overlap at least $γ>0$ with the ground space of $H$. Our goal is to estimate the ground-state energy of $H$ within additive error $δ> 0$ and success probability at least $1-\\varepsilon$, $\\varepsilon>0$. How many applications of $U$ and its inverse $U^{-1}$ are necessary and sufficient? This quantity corresponds to the total Hamiltonian-simulation time needed. An upper bound $O(\\log(1/\\varepsilon)\\log(1/γ)/γδ)$ was known, and was improved to $O(\\log(1/\\varepsilon)/γδ)$ very recently [JW26]. A matching lower bound was known whenever one of the three parameters $δ,γ,\\varepsilon$ was held constant [MdW26]. In this paper we prove the joint lower bound $Ω(\\log(1/\\varepsilon)/γδ)$ with the tight $\\varepsilon$-dependence provided the dimension of $H$ is at least $\\log(1/\\varepsilon)/γ^2$. Furthermore, we show that this same lower bound (with slightly larger dimension) holds for both the special case in which the ground state is guaranteed to be unique and $H$ has a gap of $δ$ between its first and second eigenvalue; and for ground-state preparation, where $δ$ denotes the spectral gap and $\\varepsilon$ now is the approximation error. The lower bounds also apply when the Hamiltonian can be accessed via its block-encoding, and when fractional powers of $U$ are allowed, as in continuous-time Hamiltonian simulation. Lastly, improved upper bounds are known when $H$ is nonnegative and presented as a sum of squares; and our results imply the lower bound $Ω(\\log(1/\\varepsilon)/γ\\sqrtδ)$ for this case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.24493",
  "author_total": 2,
  "authors": [
    {
      "name": "Rolando D. Somma"
    },
    {
      "name": "Ronald de Wolf"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aam957z895mx7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.24493",
  "fulltext_url": null,
  "id": "aam957z895mx7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.24493",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7204261529",
  "pdf_url": "https://arxiv.org/pdf/2608.24493",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aam957z895mx7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2608.24493",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.24493"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal Lower Bound for Ground-State Energy Estimation with a Guiding State",
  "title_text": "Optimal Lower Bound for Ground-State Energy Estimation with a Guiding State",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/aam957z895mx7",
  "venue": "arXiv",
  "versions": []
}