{
  "abstract": "The static second hyperpolarizability governs third-order nonlinear-optical responses but is difficult to compute by first-principles methods because finite-field extraction requires a fourth-order energy derivative. The resulting error amplification demands sub-µHa ground-state energies, far beyond conventional chemical accuracy. Standard multi-qubit QPE can in principle meet this precision but requires a wide ancilla register, while single-ancilla iterative QPE (IQPE) is limited by a binary-grid quantization floor. We develop an adaptive Bayesian QPE (BQPE) workflow that uses a single ancilla, terminal measurements, and real-time classical feedback to estimate the eigenphase through a continuous posterior rather than a fixed binary grid. For a linear H4 chain in the STO-3G basis, represented by a six-qubit parity Hamiltonian with one ancilla, BQPE reaches a ground-state energy error of ≈ 10−7 Ha at controlled-U depth mmax ≈ 215, about two orders of magnitude below the IQPE floor. Propagated through the finite-field stencil and Richardson extrapolation, these energies recover the second hyperpolarizability within ±10% of the FCI reference over the stable field-strength plateau, whereas IQPE at the same depth fails to do so. These results indicate that grid-free Bayesian phase estimation can make nonlinear-optical properties accessible on early fault-tolerant quantum computers.",
  "abstract_shown": true,
  "affiliations": [
    "Research Center for Computational Science and Informatics, Resonac Corporation, 8, Ebisu-cho, Yokohama, Kanagawa, Japan, 221-8517"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Katsuki Okuno",
      "orcid": "0009-0002-0423-3349"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8f7wgyqpz37y6.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15008602/v1",
  "fulltext_url": null,
  "id": "8f7wgyqpz37y6",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008602/v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212153859",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15008602/v1",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/8f7wgyqpz37y6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:19Z",
      "native_id": "10.26434/chemrxiv.15008602",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008602/v2"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "source:chemrxiv",
      "subfield": "general"
    }
  ],
  "title": "Finite-Field Second Hyperpolarizability via Adaptive Bayesian Quantum Phase Estimation for Early Fault-Tolerant Quantum Computers: Ground-State Energies Beyond Chemical Accuracy",
  "title_text": "Finite-Field Second Hyperpolarizability via Adaptive Bayesian Quantum Phase Estimation for Early Fault-Tolerant Quantum Computers: Ground-State Energies Beyond Chemical Accuracy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:19Z",
  "url": "https://research.draconitic.com/paper/8f7wgyqpz37y6",
  "venue": "ChemRxiv",
  "versions": []
}