A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations
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Quantum Physics arXiv:2604.02874 (quant-ph) [Submitted on 3 Apr 2026] Title:A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations Authors:Chao Wang, Xi-Ning Zhuang, Menghan Dou, Zhao-Yun Chen, Guo-Ping Guo View a PDF of the paper titled A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations, by Chao Wang and 3 other authors View PDF HTML (experimental) Abstract:We present a unified algorithmic framework for quantum simulation of non-unitary dynamics and matrix functions, governed by the principle of spectral aliasing derived from the Poisson Summation Formula (PSF). By reinterpreting discretization errors as spectral folding in dual domains, we synthesize two distinct algorithmic paths: (i) the Fourier-PSF path, generalizing transmutation methods for time-domain filtering, which is optimal for singular and fractional dynamics $e^{-tH^\alpha}$, here $H\succeq 0$; and (ii) the contour-PSF path, a novel discrete contour transform based on the resolvent formalism, which achieves exponential convergence for holomorphic matrix functions via radius optimization. This dual framework resolves the smoothness-sparsity trade-off: it utilizes the Fourier basis to handle branch-point singularities where analyticity fails, and the Resolvent basis to exploit complex-plane regularity where it exists. We demonstrate the versatility of this framework by efficiently simulating diverse phenomena, from fractional anomalous diffusion to high-precision solutions of stiff differential equations, outperforming existing methods in their respective optimal regimes. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.02874 [quant-ph] (or arXiv:2604.02874v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.02874 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zhao-Yun Chen [view email] [v1] Fri, 3 Apr 2026 08:42:08 UTC (37 KB) Full-text links: Access Paper: View a PDF of the paper titled A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations, by Chao Wang and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)