Contour-integral based quantum eigenvalue transformation: analysis and applications
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Quantum Physics arXiv:2601.11959 (quant-ph) [Submitted on 17 Jan 2026] Title:Contour-integral based quantum eigenvalue transformation: analysis and applications Authors:Shan Jiang, Dong An View a PDF of the paper titled Contour-integral based quantum eigenvalue transformation: analysis and applications, by Shan Jiang and Dong An View PDF HTML (experimental) Abstract:Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the efficiency of quantum algorithms based on contour integral representation for eigenvalue transformations from both theoretical and practical aspects. Theoretically, we establish a complete complexity analysis of the contour integral approach proposed in [Takahira, Ohashi, Sogabe, and Usuda. Quant. Inf. Comput., 22, 11\&12, 965--979 (2021)]. Moreover, we combine the contour integral approach and the sampling-based linear combination of unitaries to propose a quantum algorithm for estimating observables of eigenvalue transformations using only $3$ additional qubits. Practically, we design contour integral based quantum algorithms for Hamiltonian simulation, matrix polynomials, and solving linear ordinary differential equations, and show that the contour integral algorithm can outperform all the existing quantum algorithms in the case of solving asymptotically stable differential equations. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.11959 [quant-ph] (or arXiv:2601.11959v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.11959 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shan Jiang [view email] [v1] Sat, 17 Jan 2026 08:29:36 UTC (142 KB) Full-text links: Access Paper: View a PDF of the paper titled Contour-integral based quantum eigenvalue transformation: analysis and applications, by Shan Jiang and Dong AnView PDFHTML (experimental)TeX 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?)