用李群与量子几何双重表示，一键剪枝量子神经网络
LiePrune: Lie Group and Quantum Geometric Dual Representation for One-Shot Structured Pruning of Quantum Neural Networks
- 基于李群与量子几何双重空间表示门电路
- 压缩超10倍，性能几乎不变甚至提升
- 适合量子机器学习研究者和硬件受限场景
量子神经网络（QNNs）和参数化量子线路（PQCs）是近期量子机器学习的关键组件。然而，其可扩展性受参数过多、平坦区问题及硬件限制制约。我们提出LiePrune，首个基于数学原理的一次性结构化剪枝框架，利用李群结构与量子几何信息。每个门在李群-李代数对偶空间与量子几何特征空间中联合表示，实现可证明的冗余检测与激进压缩。在量子分类（MNIST、FashionMNIST）、量子生成建模（Bars-and-Stripes）和量子化学（LiH VQE）任务上的实验表明，LiePrune实现超过10倍压缩，任务性能几乎无损甚至提升，且提供冗余检测、函数逼近与计算复杂度的可证明保证。
原文摘要 · Abstract (English)
Quantum neural networks (QNNs) and parameterized quantum circuits (PQCs) are key building blocks for near-term quantum machine learning. However, their scalability is constrained by excessive parameters, barren plateaus, and hardware limitations. We propose LiePrune, the first mathematically grounded one-shot structured pruning framework for QNNs that leverages Lie group structure and quantum geometric information. Each gate is jointly represented in a Lie group--Lie algebra dual space and a quantum geometric feature space, enabling principled redundancy detection and aggressive compression. Experiments on quantum classification (MNIST, FashionMNIST), quantum generative modeling (Bars-and-Stripes), and quantum chemistry (LiH VQE) show that LiePrune achieves over $10\times$ compression with negligible or even improved task performance, while providing provable guarantees on redundancy detection, functional approximation, and computational complexity.
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