{
  "abstract": "A majority of measurable dynamic quantities of a physical system is described as an equilibrium correlation function of the form $G_{AB}(t-t') = \\left<A(t)B(t')\\right>$, where $t'$ represents the impact time and $t$ represents the response time. Conventional quantum algorithms to compute such quantities via Hamiltonian simulation such as the Hadamard test, variational methods, or linear-response-based algorithms share one feature in common: each time point $t-t'$ is calculated by a different quantum circuit, leading to at least $O(N_t)$ total shots, and at least $O(N_t^2)$ total quantum gates. Here, we provide a different approach: utilizing $O(\\log N_t)$ ancilla qubits to store time as a quantum variable, and effectively parallelize the computation of an equilibrium correlation function by requiring only a single quantum circuit for all time points. We show that this circuit needs to be run only $O(\\log N_t)$ times, which in total requires $O(N_t \\log N_t)$ quantum resources in the large system size limits. We prove that this scaling is optimal, and demonstrate our algorithm calculating the Green's function of a one-dimensional spinless Hubbard model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40349",
  "author_total": 4,
  "authors": [
    {
      "name": "Yizhi Shen"
    },
    {
      "name": "Roel Van Beeumen"
    },
    {
      "name": "Wibe A. de Jong"
    },
    {
      "name": "Efekan Kökcü"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31aw3b37gn4rd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40349",
  "fulltext_url": null,
  "id": "31aw3b37gn4rd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40349",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215044183",
  "pdf_url": "https://arxiv.org/pdf/2609.40349",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31aw3b37gn4rd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40349",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40349"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Efficient Calculation of Equilibrium Correlation Functions",
  "title_text": "Efficient Calculation of Equilibrium Correlation Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/31aw3b37gn4rd",
  "venue": "arXiv",
  "versions": []
}