提出兼具旋转与排列对称性的量子-经典神经网络，提升点云分类效率。
HyQuRP: Hybrid quantum-classical neural network with rotational and permutational equivariance
- 设计双重对称性量子门，基于群表示理论构建可解释框架。
- 在稀疏点云下，6个采样点时模型准确率达76.13%，优于多个基线。
- 适合处理具有几何对称性的数据任务，如3D点云分析。
群等变量子机器学习通过将对称性融入量子模型，展现出巨大潜力。然而，如何在理论上一致地构建同时具备旋转与排列对称性的模型仍是瓶颈。本文提出一种双重对称性量子门的通用框架，并利用群表示理论分析其门空间维度。基于此，我们构建了HyQuRP——一种兼具旋转与排列等变性的混合量子-经典神经网络。在稀疏点云场景下的3D点云分类基准测试中，HyQuRP表现优异：当仅使用6个子采样点时，在5类ModelNet数据集上达到76.13%的准确率，显著优于参数量相近的Tensor Field Network（72.54%）、PointNet（71.09%）和PointMamba（71.03%）。结果表明，该模型具有强数据效率，验证了等变量子机器学习在对称敏感任务中的应用前景。
原文摘要 · Abstract (English)
Group-equivariant quantum machine learning has emerged as a promising paradigm by incorporating symmetry into quantum models. However, constructing models simultaneously equivariant to both rotational and permutational symmetries in a principled manner remains a bottleneck. In this work, we develop a general framework for dual-equivariant gates under rotations and permutations and analyze the dimension of the resulting gate space using group representation theory. Based on this, we introduce HyQuRP, a hybrid quantum-classical neural network with dual equivariance. On 3D point cloud classification benchmarks in the sparse-point regime, HyQuRP outperforms strong classical and quantum baselines. For example, when six subsampled points are used, HyQuRP ($\sim$1.5K parameters) achieves 76.13% accuracy on the 5-class ModelNet benchmark, compared with 72.54%, 71.09%, and 71.03% for Tensor Field Network, PointNet, and PointMamba with similar parameter counts. These results highlight HyQuRP's strong data efficiency and suggest the potential of equivariant quantum machine learning approaches in symmetry-sensitive tasks.
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