提出新型量子卷积网络，实现像素平移等变性，提升训练稳定性。
Pixel-Translation-Equivariant Quantum Convolutional Neural Networks via Fourier Multiplexers
- 基于傅里叶多路复用器构造满足像素循环平移对称性的量子层
- 深度网络在随机初始化下梯度平方期望恒定，避免深度退化问题
- 适用于图像编码类量子模型，尤其适合近中期量子硬件
卷积神经网络的成功很大程度上源于硬编码的平移等变性。量子卷积神经网络（QCNN）被提出作为近期量子计算的类比，但其对应的平移概念依赖于数据编码方式。对于如FRQI这样的地址/幅度编码，像素位移表现为索引寄存器上的模加法；而许多受MERA启发的QCNN仅在物理量子比特的循环置换下保持等变。本文形式化了这一不匹配，并构建了与编码诱导的像素循环平移（PCS）对称性精确交换的QCNN层。核心技术成果是：所有PCS等变酉操作均可通过量子傅里叶变换（QFT）共轭对角化平移，因此任何PCS等变层都可表示为傅里叶模式多路复用器后接逆量子傅里叶变换（IQFT）。基于此，我们设计了一种深层PCS-QCNN，包含测量诱导池化、延迟条件和层间QFT抵消。此外，我们分析了随机初始化下的可训练性，证明了期望平方梯度范数在深度扩展情形下保持常数，从而排除了深度引发的荒芜峡谷现象。
原文摘要 · Abstract (English)
Convolutional neural networks owe much of their success to hard-coding translation equivariance. Quantum convolutional neural networks (QCNNs) have been proposed as near-term quantum analogues, but the relevant notion of translation depends on the data encoding. For address/amplitude encodings such as FRQI, a pixel shift acts as modular addition on an index register, whereas many MERA-inspired QCNNs are equivariant only under cyclic permutations of physical qubits. We formalize this mismatch and construct QCNN layers that commute exactly with the pixel cyclic shift (PCS) symmetry induced by the encoding. Our main technical result is a constructive characterization of all PCS-equivariant unitaries: conjugation by the quantum Fourier transform (QFT) diagonalizes translations, so any PCS-equivariant layer is a Fourier-mode multiplexer followed by an inverse QFT (IQFT). Building on this characterization, we introduce a deep PCS-QCNN with measurement-induced pooling, deferred conditioning, and inter-layer QFT cancellation. We also analyze trainability at random initialization and prove a lower bound on the expected squared gradient norm that remains constant in a depth-scaling regime, ruling out a depth-induced barren plateau in that sense.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。