Quantum Algorithm for Estimating Gibbs Free Energy and Entropy via Energy Derivatives

Quantum Physics arXiv:2511.17821 (quant-ph) [Submitted on 21 Nov 2025] Title:Quantum Algorithm for Estimating Gibbs Free Energy and Entropy via Energy Derivatives Authors:Shangjie Guo, Corneliu Buda, Nathan Wiebe View a PDF of the paper titled Quantum Algorithm for Estimating Gibbs Free Energy and Entropy via Energy Derivatives, by Shangjie Guo and 2 other authors View PDF Abstract:Estimating vibrational entropy is a significant challenge in thermodynamics and statistical mechanics due to its reliance on quantum mechanical properties. This paper introduces a quantum algorithm designed to estimate vibrational entropy via energy derivatives. Our approach block encodes the exact expression for the second derivative of the energy and uses quantum linear systems algorithms to deal with the reciprocal powers of the gaps that appear in the expression. We further show that if prior knowledge about the values of the second derivative is used then our algorithm can $\epsilon$-approximate the entropy using a number of queries that scales with the condition number $\kappa$, the temperature $T$, error tolerance $\epsilon$ and an analogue of the partition function $\mathcal{Z}$, as $\widetilde{O}\left(\frac{\mathcal{Z}\kappa^2 }{\epsilon T}\right)$. We show that if sufficient prior knowledge is given about the second derivative then the query scales quadratically better than these results. This shows that, under reasonable assumptions of the temperature and a quantum computer can be used to compute the vibrational contributions to the entropy faster than analogous classical algorithms would be capable of. Our findings highlight the potential of quantum algorithms to enhance the prediction of thermodynamic properties, paving the way for advancements in fields such as material science, molecular biology, and chemical engineering. Comments: Subjects: Quantum Physics (quant-ph); Computational Complexity (cs.CC) MSC classes: 68Q12 Cite as: arXiv:2511.17821 [quant-ph] (or arXiv:2511.17821v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.17821 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shangjie Guo [view email] [v1] Fri, 21 Nov 2025 22:27:21 UTC (20 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Algorithm for Estimating Gibbs Free Energy and Entropy via Energy Derivatives, by Shangjie Guo and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: cs cs.CC 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?)