Quantum Algorithms for Heterogeneous PDEs: The Neutron Diffusion Eigenvalue Problem
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Quantum Physics arXiv:2604.05098 (quant-ph) [Submitted on 6 Apr 2026] Title:Quantum Algorithms for Heterogeneous PDEs: The Neutron Diffusion Eigenvalue Problem Authors:Andrew M. Childs, Lincoln Johnston, Brian Kiedrowski, Mahathi Vempati, Jeffery Yu View a PDF of the paper titled Quantum Algorithms for Heterogeneous PDEs: The Neutron Diffusion Eigenvalue Problem, by Andrew M. Childs and 4 other authors View PDF HTML (experimental) Abstract:We develop a hybrid classical-quantum algorithm to solve a type of linear reaction-diffusion equation, the neutron diffusion (generalized) k-eigenvalue problem that establishes nuclear criticality. The algorithm handles an equation with piecewise constant coefficients, describing a problem in a heterogeneous medium. We apply uniform finite elements and show that the quantum algorithm provides significant polynomial end-to-end speedup over its classical counterparts. This speedup leverages recent advances in quantum linear systems -- fast inversion and quantum preconditioning -- and uses Hamiltonian simulation as a subroutine. Our results suggest that quantum algorithms may provide speedups for heterogeneous PDEs, though the extent of this advantage over the fastest classical algorithm depends on the effectiveness of other classical approaches such as nonuniform or adaptive meshing for a given problem instance. Subjects: Quantum Physics (quant-ph); Analysis of PDEs (math.AP) Cite as: arXiv:2604.05098 [quant-ph] (or arXiv:2604.05098v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.05098 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mahathi Vempati [view email] [v1] Mon, 6 Apr 2026 18:57:21 UTC (630 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Algorithms for Heterogeneous PDEs: The Neutron Diffusion Eigenvalue Problem, by Andrew M. Childs and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: math math.AP 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?) 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?)