AI 中文总结
研究量子卷积神经网络训练难题，提出基于能量学习框架，经卷积操作、量子采样，由特定能量项构成网络能量，借平衡传播机制免显式梯度计算实现参数更新，增强可解释性，为量子卷积神经网络训练及与人工智能集成提供统一视角。
AI 中文摘要
量子卷积神经网络由于涉及量子测量和离散量子态演化，面临与不可微操作和离散优化动力学相关的固有训练挑战，使得传统基于梯度的学习难以有效应用。在此背景下，基于能量的学习提供了一种有前景的替代方案，将网络训练重新表述为无显式梯度的能量最小化过程。在该框架中，输入数据通过卷积操作处理，然后进行量子采样以生成中间二进制表示，输出层也依赖量子采样产生最终预测。整体网络能量由卷积特征匹配项、输出层的线性耦合项和全局输出约束项组成，通过物理可解释的能量动力学描述参数更新和特征演化。此外，在平衡传播机制下，利用自由相和弱钳位相之间的能量差驱动参数更新而无需显式梯度计算，从而在不可微和离散空间中实现稳定且一致的学习。该框架在与经典卷积学习理论保持一致的同时，通过量子能量建模增强了可解释性和可观测性，为高效的量子卷积神经网络训练以及量子计算与人工智能的集成提供了统一的物理视角。
英文摘要
Quantum convolutional neural networks, due to the involvement of quantum measurements and discrete quantum state evolution, face inherent training challenges associated with non-differentiable operations and discrete optimization dynamics, which make conventional gradient-based learning difficult to apply effectively. In this context, energy-based learning provides a promising alternative by reformulating network training as an energy minimization process without explicit gradient backpropagation.In this framework, input data are processed through convolutional operations, followed by quantum sampling to generate intermediate binary representations, while the output layer also relies on quantum sampling to produce final predictions. The overall network energy is composed of convolutional feature matching terms, linear coupling terms at the output layer, and global output constraint terms, enabling both parameter updates and feature evolution to be described through physically interpretable energy dynamics. Furthermore, under the equilibrium propagation mechanism, the energy difference between the free phase and the weakly clamped phase is exploited to drive parameter updates without explicit gradient computation, thereby enabling stable and consistent learning in non-differentiable and discrete spaces. While remaining consistent with classical convolutional learning theory, the proposed framework enhances interpretability and observability through quantum energy modeling, offering a unified physical perspective for efficient QCNN training and the integration of quantum computing with artificial intelligence.
