Classical SU(2) Models Match or Exceed Shallow Variational Quantum Circuits on Vision Benchmarks

arXiv:2608.07822v1 Announce Type: cross Abstract: Quaternion-valued neural networks and variational quantum circuits (VQCs) both derive local transformations from SU(2) geometry, yet their performance on classical supervised learning remains poorly understood. We compare real-valued, quaternion-valued, and quantum classification heads on identical frozen features across MNIST, FashionMNIST, and CIFAR-10. CIFAR-10 uses a learned 16-dimensional bottleneck and frozen ImageNet-pretrained ResNet18 features to separate architecture from representation quality. Quaternion classifiers match or approach real-valued baselines while outperforming shallow VQCs. On MNIST and FashionMNIST, quaternion networks nearly equal real-valued MLPs, whereas product-state VQCs show lower accuracy and higher cost. On CIFAR-10, quaternion networks retain 94--97% of real-valued performance and remain stable under a 32-fold increase in dimensionality. Product-state circuits underperform quaternion classifiers, while entanglement gives modest grayscale gains but reverses under pretrained CNN features (9.25 pp degradation vs. product-state). Fubini--Study/QFI natural gradients improve geometric alignment but not short-horizon loss reduction vs. Adam. A Friedman test on five-seed MNIST detects model differences (hi^2=12.796, p=0.0051, n=5), with Wilcoxon tests yielding large effect sizes (d>5) for QuatNet vs. quantum comparisons. For FashionMNIST and CIFAR-10, large effects (d>2.0) are the primary statistic given n=3. These results indicate that quaternion networks provide efficient, stable SU(2) alternatives to shallow VQCs on tasks lacking intrinsic quantum structure. Shared local SU(2) geometry and shallow entanglement are insufficient, within the regime studied, to confer practical quantum advantage. Conclusions are limited to shallow, measurement-limited circuits on such tasks.

Source: arXiv cs.LG | 2026-08-11