HyQuRP：具有旋转和置换等价性的混合量子-经典神经网络
HyQuRP: Hybrid quantum-classical neural network with rotational and permutational equivariance
AI总结：
本文提出HyQuRP，一种具有旋转和置换等价性的混合量子-经典神经网络，通过组表示理论分析门空间维度，实验证明其在稀疏点云分类中优于经典和量子基线模型。
摘要：
基于群表示理论分析门空间维度，本文提出HyQuRP，一种具有旋转和置换等价性的混合量子-经典神经网络，通过组表示理论分析门空间维度，实验证明其在稀疏点云分类中优于经典和量子基线模型。
英文摘要：
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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