One-Shot Structured Pruning of Quantum Neural Networks via $q$-Group Engineering and Quantum Geometric Metrics
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Quantum Physics arXiv:2512.24019 (quant-ph) [Submitted on 30 Dec 2025] Title:One-Shot Structured Pruning of Quantum Neural Networks via $q$-Group Engineering and Quantum Geometric Metrics Authors:Haijian Shao, Wei Liu, Xing Deng, Yingtao Jiang View a PDF of the paper titled One-Shot Structured Pruning of Quantum Neural Networks via $q$-Group Engineering and Quantum Geometric Metrics, by Haijian Shao and 2 other authors View PDF HTML (experimental) Abstract:Quantum neural networks (QNNs) suffer from severe gate-level redundancy, which hinders their deployment on noisy intermediate-scale quantum (NISQ) devices. In this work, we propose q-iPrune, a one-shot structured pruning framework grounded in the algebraic structure of $q$-deformed groups and task-conditioned quantum geometry. Unlike prior heuristic or gradient-based pruning methods, q-iPrune formulates redundancy directly at the gate level. Each gate is compared within an algebraically consistent subgroup using a task-conditioned $q$-overlap distance, which measures functional similarity through state overlaps on a task-relevant ensemble. A gate is removed only when its replacement by a subgroup representative provably induces a bounded deviation on all task observables. We establish three rigorous theoretical guarantees. First, we prove completeness of redundancy pruning: no gate that violates the prescribed similarity threshold is removed. Second, we show that the pruned circuit is functionally equivalent up to an explicit, task-conditioned error bound, with a closed-form dependence on the redundancy tolerance and the number of replaced gates. Third, we prove that the pruning procedure is computationally feasible, requiring only polynomial-time comparisons and avoiding exponential enumeration over the Hilbert space. To adapt pruning decisions to hardware imperfections, we introduce a noise-calibrated deformation parameter $\lambda$ that modulates the $q$-geometry and redundancy tolerance. Experiments on standard quantum machine learning benchmarks demonstrate that q-iPrune achieves substantial gate reduction while maintaining bounded task performance degradation, consistent with our theoretical guarantees. Comments: Subjects: Quantum Physics (quant-ph); Computer Vision and Pattern Recognition (cs.CV) Cite as: arXiv:2512.24019 [quant-ph] (or arXiv:2512.24019v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.24019 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Haijian Shao [view email] [v1] Tue, 30 Dec 2025 06:37:28 UTC (41 KB) Full-text links: Access Paper: View a PDF of the paper titled One-Shot Structured Pruning of Quantum Neural Networks via $q$-Group Engineering and Quantum Geometric Metrics, by Haijian Shao and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cs cs.CV 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?)