发表机构
University of Applied Sciences Northwestern Switzerland (FHNW); École Polytechnique Fédérale de Lausanne (EPFL); MatterDecoder（西北瑞士应用科学大学; 洛桑联邦理工学院; MatterDecoder）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过实验证明量子卷积神经网络在小数据 regime 下能有效泛化，仅需少量样本即可超越同等规模经典网络，但扩展到真实图像受限于数据编码和硬件执行。
AI 中文摘要
量子机器学习是一种从有限数据中学习的很有前景的范式，这是医学影像、临床试验和罕见疾病等领域的一个核心瓶颈。量子卷积神经网络（QCNNs）在此背景下尤其具有吸引力，它结合了具有强归纳偏置的层次化架构和仅随系统大小对数增长的参数数量。其吸引力基于 Caro 等人（2022）的泛化界限，该界限表明量子模型的泛化误差随可训练参数数量而非希尔伯特空间维度缩放，使 QCNNs 处于潜在样本高效的 regime。我们开发了一个具有中间电路测量和经典前馈的硬件兼容 QCNN，并在一个二值手写数字任务上表明，仅用 10 个训练样本即可实现强测试性能，且泛化误差随训练集增大而减小。在匹配的 45 参数预算下，QCNN 能学习到同等规模的小型经典卷积网络仍停留在随机水平的问题，尽管一个具有约 25,000 参数的无约束经典基线在数据充足时仍然最强。将幅度和角度编码电路跨图像分辨率从 2x2 到 512x512 像素进行转译，揭示了主导的缩放瓶颈：幅度编码保持量子比特高效但变得极深，而角度编码保持浅层但量子比特需求过高。在医学动机的 BreastMNIST 基准上，QCNN 未超越无约束经典网络，但它使用少几个数量级的参数持续学习到高于随机水平的结果。我们的结果表明，对于 QCNNs，从少量样本学习在实践中是可实现的，而扩展到现实图像数据受限于数据编码和硬件执行，而非优化。
英文摘要
Quantum machine learning is a promising paradigm for learning from limited data, a central bottleneck in domains such as medical imaging, clinical trials, and rare diseases. Quantum convolutional neural networks (QCNNs) are particularly attractive in this setting, combining a hierarchical architecture with strong inductive bias and a parameter count that grows only logarithmically with system size. Their appeal rests on the generalization bounds of Caro et al. (2022), which show that the generalization error of a quantum model scales with the number of trainable parameters rather than with the Hilbert-space dimension, placing QCNNs in a potentially sample-efficient regime. We develop a hardware-compatible QCNN with mid-circuit measurement and classical feed-forward, and show on a binary handwritten-digit task that strong test performance is achievable from as few as 10 training samples, with the generalization error decreasing as the training set grows. At a matched 45-parameter budget the QCNN learns where an equally small classical convolutional network stays at chance, although an unconstrained classical baseline with roughly 25,000 parameters remains strongest when data are plentiful. Transpiling amplitude and angle encoded circuits across image resolutions from 2x2 to 512x512 pixels then exposes the dominant scaling bottleneck: amplitude encoding stays qubit-efficient but grows extremely deep, whereas angle encoding stays shallow but becomes qubit-prohibitive. On the medically motivated BreastMNIST benchmark the QCNN does not surpass the unconstrained classical network, yet it learns consistently above chance using orders of magnitude fewer parameters. Our results indicate that for QCNNs, learning from few samples is attainable in practice, whereas scaling to realistic image data is constrained less by optimization than by data encoding and hardware execution.
