Point cloud symmetry encoding and multi-channel rotational equivariant quantum neural networks

Abstract Equivariant Quantum Neural Networks can mitigate the barren plateau problem by embedding inductive bias into variational quantum circuits, making them well-suited for processing symmetric point clouds. However, existing point cloud to quantum state encoding methods fail to preserve inherent symmetries of point clouds, and research on compatible equivariant quantum circuits remains inadequate. To address these limitations, this paper proposes cylindrical and spherical voxelization encoding for point clouds, which retains rotational and vertical cyclic symmetry about the Z-axis. Concurrently, Multi-Channel Rotational Equivariant Quantum Neural Networks are designed, where symmetries across different dimensions are treated as distinct channels. Experimental results demonstrate that cylindrical voxelization achieves superior performance in encoding point clouds. Specifically, this work attains a comparable level of accuracy with a smaller parameter scale than Hardware Efficient Ansatz and Rotational Equivariant Quantum Neural Networks, while also alleviating the barren plateau problem. These findings demonstrate the applicability of proposed encoding method, reveal the adaptive relationship between encoding characteristics and model architecture, and provide a potentially feasible solution for processing complex point clouds with large-scale qubits.