经典SU(2)模型在视觉基准测试中与浅度变分量子电路性能相当或更优
Classical $\mathrm{SU}(2)$ Models Match or Exceed Shallow Variational Quantum Circuits on Vision Benchmarks
浏览论文内容
中文总结 AI 辅助
该研究对比实值、四元数值分类头与浅度变分量子电路在视觉基准上的性能，发现四元数网络是浅度VQCs的高效SU(2)替代方案，未观测到实用量子优势。
中文摘要 AI 辅助
四元数值神经网络和变分量子电路（VQCs）均从SU(2)几何中衍生出局部变换，但它们在经典监督学习中的性能仍鲜为人知。我们在MNIST、FashionMNIST和CIFAR-10数据集上，对相同冻结特征下的实值、四元数值和量子分类头进行了比较。CIFAR-10使用学习得到的16维瓶颈和冻结的ImageNet预训练ResNet18特征，以分离架构与表示质量。四元数分类器与实值基线性能相当或接近，同时优于浅度VQCs。在MNIST和FashionMNIST上，四元数网络几乎与实值MLPs性能相当，而乘积态VQCs准确率更低、开销更高。在CIFAR-10上，四元数网络保留了实值性能的94%-97%，且在维度增加32倍时仍保持稳定。乘积态电路性能劣于四元数分类器，而纠缠在灰度任务上带来适度增益，但在预训练CNN特征下会逆转（相比乘积态出现9.25个百分点的性能下降）。Fubini-Study/QFI自然梯度可改善几何对齐，但与Adam相比无法缩短短期损失。对5个随机种子的MNIST进行Friedman检验，检测到模型差异（χ²=12.796，p=0.0051，n=5），Wilcoxon检验显示QuatNet与量子模型对比具有大效应量（d>5）。对于FashionMNIST和CIFAR-10，由于n=3，大效应量（d>2.0）为主要统计结果。这些结果表明，在缺乏固有量子结构的任务上，四元数网络是浅度VQCs的高效、稳定的SU(2)替代方案。在本研究范围内，共享局部SU(2)几何和浅度纠缠不足以带来实用量子优势，结论仅限于此类任务上的浅度、受测量限制的电路。
英文摘要
Quaternion-valued neural networks and variational quantum circuits (VQCs) both derive local transformations from $\mathrm{SU}(2)$ 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 ($χ^2=12.796$, $p=0.0051$, $n=5$), 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 $\mathrm{SU}(2)$ alternatives to shallow VQCs on tasks lacking intrinsic quantum structure. Shared local $\mathrm{SU}(2)$ 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.
发表机构
- United States Air Force Test Pilot School（美国空军试飞员学校）
- National University（美国国家大学）
- Boston College（波士顿学院）
机构由 AI 辅助整理，请以论文原文为准。
