A Sublinear-Time Quantum Algorithm for High-Dimensional Reaction Rates
Summarize this article with:
Quantum Physics arXiv:2601.15523 (quant-ph) [Submitted on 21 Jan 2026] Title:A Sublinear-Time Quantum Algorithm for High-Dimensional Reaction Rates Authors:Tyler Kharazi, Ahmad M. Alkadri, Kranthi K. Mandadapu, K.
Birgitta Whaley View a PDF of the paper titled A Sublinear-Time Quantum Algorithm for High-Dimensional Reaction Rates, by Tyler Kharazi and 3 other authors View PDF Abstract:The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We introduce a quantum algorithm that overcomes this for computing reaction rates. Using a sum-of-squares representation, we develop a Gaussian linear combination of Hamiltonian simulations (Gaussian-LCHS) to represent the non-unitary propagator with $O\left(\sqrt{t\|H\|\log(1/\epsilon)}\right)$ queries to its block encoding. Crucially, we pair this with {a} novel technique to directly estimate matrix elements without exponential decay. For $\eta$ pairwise interacting particles discretized with $N$ plane waves per degree of freedom, we estimate reactive flux to error $\epsilon$ using $\widetilde{O}\left((\eta^{5/2}\sqrt{t\beta}\alpha_V + \eta^{3/2}\sqrt{t/\beta}N)/\epsilon\right)$ quantum gates, where $\alpha_V = \max_{r}|V'(r)/r|$. For non-convex potentials, the {sharpest classical} worst-case analytical bounds to simulate the related overdamped Langevin {equation} scale as $O(te^{\Omega(\eta)}/\epsilon^4)$. This {implies} an exponential separation in particle number $\eta$, a quartic speedup in $\epsilon$, and quadratic speedup in $t$. While specialized classical heuristics may outperform these bounds in practice, this demonstrates a rigorous route toward quantum advantage for high-dimensional dissipative dynamics. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.15523 [quant-ph] (or arXiv:2601.15523v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.15523 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tyler Kharazi [view email] [v1] Wed, 21 Jan 2026 23:20:46 UTC (1,608 KB) Full-text links: Access Paper: View a PDF of the paper titled A Sublinear-Time Quantum Algorithm for High-Dimensional Reaction Rates, by Tyler Kharazi and 3 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)