Simulating high-accuracy nuclear motion Hamiltonians in discrete variable representation using Walsh-Hadamard QROM with fault-tolerant quantum computers

Quantum Physics arXiv:2510.19062 (quant-ph) [Submitted on 21 Oct 2025] Title:Simulating high-accuracy nuclear motion Hamiltonians in discrete variable representation using Walsh-Hadamard QROM with fault-tolerant quantum computers Authors:Michał Szczepanik, Ákos Nagy, Emil Żak View a PDF of the paper titled Simulating high-accuracy nuclear motion Hamiltonians in discrete variable representation using Walsh-Hadamard QROM with fault-tolerant quantum computers, by Micha{\l} Szczepanik and 1 other authors View PDF HTML (experimental) Abstract:We present a quantum algorithm for simulating rovibrational Hamiltonians on fault-tolerant quantum computers. The method integrates exact curvilinear kinetic energy operators and general-form potential energy surfaces expressed in a hybrid finite-basis/discrete-variable representation. The Hamiltonian is encoded as a unitary quantum circuit using a quantum read-only memory construction based on the Walsh--Hadamard transform, enabling high-accuracy quantum phase estimation of rovibrational energy levels. Our technique provides asymptotic reductions in both logical-qubit count and T-gate complexity that are exponential in the number of atoms and at least polynomial in the total Hilbert-space size, relative to existing block-encoding techniques based on linear combinations of unitaries. Compared with classical variational methods, it offers exponential memory savings and polynomial reductions in time complexity. The quantum volume required for computing the rovibrational spectrum of water can be reduced by up to $10^{5}$ times compared with other quantum methods, increasing to at least $10^{6}$ for a 30-dimensional (12-atom) model system. For this case with a six-body coupled potential, estimating spectroscopic-accuracy energy levels would require about three months on a $1~\mathrm{MHz}$ fault-tolerant quantum processor with fewer than 300 logical qubits, versus over 30,000 years on the fastest current classical supercomputer. These estimates are approximate and subject to technological uncertainties, and realizing the asymptotic advantage will require substantial quantum resources and continued algorithmic progress. Subjects: Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph); Computational Physics (physics.comp-ph) MSC classes: 81V55, 68Q12, 81P68 ACM classes: F.2.1 Cite as: arXiv:2510.19062 [quant-ph] (or arXiv:2510.19062v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.19062 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Emil Zak [view email] [v1] Tue, 21 Oct 2025 20:31:12 UTC (1,742 KB) Full-text links: Access Paper: View a PDF of the paper titled Simulating high-accuracy nuclear motion Hamiltonians in discrete variable representation using Walsh-Hadamard QROM with fault-tolerant quantum computers, by Micha{\l} Szczepanik and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: physics physics.chem-ph physics.comp-ph References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)