Quantum Topological Analysis on Digraphs

[2509.13862] Quantum Topological Analysis on Digraphs Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2509.13862 (quant-ph) [Submitted on 17 Sep 2025 ( v1 ), last revised 21 Aug 2026 (this version, v3)] Title: Quantum Topological Analysis on Digraphs Authors: Yunpeng Zi , Muchun Yang , D. L. Zhou View PDF HTML (experimental) Abstract: Quantum algorithms for topological data analysis provide significant advantages over the best known classical algorithms. Unlike previous work on simplicial complexes built from point clouds, path homology on digraphs is defined for directed graphs and provides a natural topological framework for analyzing data with intrinsic directional structures. Path homology has become an emerging area in Topological Data Analysis (TDA), attracting increasing attention in recent years. We propose a quantum algorithm for path homology on digraphs that offers a significant advantage over the best known classical algorithms. We design a universal encoding protocol for the paths and boundary operators of digraphs on quantum systems. We prove a property of path homology that provides the theoretical guarantee for the algorithm. The speedup of the quantum algorithm for path homology depends on input-access assumptions. The exponential speedup arises when the path space can be efficiently accessed, while for standard digraph input the algorithm provides polynomial speedup. Comments: 26 pages, 2 figures, To be appeared on Quantum Science and Technology Subjects: Quantum Physics (quant-ph) ; Algebraic Topology (math.AT) Cite as: arXiv:2509.13862 [quant-ph] (or arXiv:2509.13862v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2509.13862 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yunpeng Zi [ view email ] [v1] Wed, 17 Sep 2025 09:53:25 UTC (92 KB) [v2] Sun, 28 Sep 2025 03:34:00 UTC (92 KB) [v3] Fri, 21 Aug 2026 02:57:50 UTC (102 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-09 Change to browse by: math math.AT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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