HyQuRP: Hybrid quantum-classical neural network with rotational and permutational equivariance
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911653988139008 |
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| author | Park, Semin Park, Chae-Yeun |
| author_facet | Park, Semin Park, Chae-Yeun |
| contents | 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$1.5K parameters) achieves 76.13% accuracy on the 5-class ModelNet benchmark, compared with 72.54%, 71.09%, and 71.03% for Tensor Field Network, PointNet, and PointMamba with similar parameter counts. These results highlight HyQuRP's strong data efficiency and suggest the potential of equivariant quantum machine learning approaches in symmetry-sensitive tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06381 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | HyQuRP: Hybrid quantum-classical neural network with rotational and permutational equivariance Park, Semin Park, Chae-Yeun Quantum Physics Machine Learning Group-equivariant quantum machine learning has emerged as a promising paradigm by incorporating symmetry into quantum models. However, constructing models simultaneously equivariant to both rotational and permutational symmetries in a principled manner remains a bottleneck. In this work, we develop a general framework for dual-equivariant gates under rotations and permutations and analyze the dimension of the resulting gate space using group representation theory. Based on this, we introduce HyQuRP, a hybrid quantum-classical neural network with dual equivariance. On 3D point cloud classification benchmarks in the sparse-point regime, HyQuRP outperforms strong classical and quantum baselines. For example, when six subsampled points are used, HyQuRP ($\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. |
| title | HyQuRP: Hybrid quantum-classical neural network with rotational and permutational equivariance |
| topic | Quantum Physics Machine Learning |
| url | https://arxiv.org/abs/2602.06381 |