HyQuRP: Hybrid quantum-classical neural network with rotational and permutational equivariance

TL;DR

HyQuRP is a novel hybrid quantum-classical neural network that incorporates dual rotational and permutational equivariance, demonstrating superior performance on 3D point cloud classification tasks with high data efficiency.

Contribution

This work introduces a general framework for dual-equivariant gates and develops HyQuRP, the first hybrid quantum-classical model with combined rotational and permutational equivariance.

Findings

HyQuRP achieves 76.13% accuracy on ModelNet with 6 points, outperforming classical baselines.

HyQuRP has approximately 1.5K parameters, showing high data efficiency.

The framework enables principled construction of dual-equivariant quantum models.

Abstract

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.