Rotation- and Permutation-equivariant Quantum Graph Neural Network for 3D Graph Data

Equivariant quantum graph neural networks (EQGNNs) offer a potentially powerful method to process graph data. However, existing EQGNN models only consider the permutation symmetry of graphs, and failing to fully exploit the geometric and non-geometric information in graphs, resulting in suboptimal performance when processing 3D graph data. To address these limitations, we derive constraints of rotation and permutation equivariance, and then propose a novel rotation- and permutation-equivariant quantum graph neural network (RP-EQGNN). An equivariant module is designed to extract the geometric information. Then, a convolution and entanglement module is constructed to extract non-geometric information. To improve performance of our model, an edge entanglement strategy is designed to perform distinguishable entanglement operations based on edge heterogeneity. The experiment results demonstrate that RP-EQGNN is significantly better for graph regression on the QM9 dataset and the OC20 dataset than Q3DGL and EQC in MAE and achieves results comparable to those of EquiformerV2 , Geoformer , SO3KRATES and HEGNN. It also has advantage for point cloud classification on the ModelNet40 dataset over quantum models, including sQCNN-3D and PI-QSVM. RP-EQGNN introduces an innovative approach for processing 3D graph data, establishing a basis for future investigations into symmetries within graph neural networks.