One-Shot Structured Pruning of Quantum Neural Networks via $q$-Group Engineering and Quantum Geometric Metrics
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| Format: | Preprint |
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2025
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| _version_ | 1866909978587037696 |
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| author | Shao, Haijian Liu, Wei Deng, Xing Jiang, Yingtao |
| author_facet | Shao, Haijian Liu, Wei Deng, Xing Jiang, Yingtao |
| contents | 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 $λ$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_24019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-Shot Structured Pruning of Quantum Neural Networks via $q$-Group Engineering and Quantum Geometric Metrics Shao, Haijian Liu, Wei Deng, Xing Jiang, Yingtao Quantum Physics Computer Vision and Pattern Recognition 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 $λ$ 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. |
| title | One-Shot Structured Pruning of Quantum Neural Networks via $q$-Group Engineering and Quantum Geometric Metrics |
| topic | Quantum Physics Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2512.24019 |