标题： 具有灵活步长的量子卷积神经网络 显示英文标题

标题： Quantum Convolutional Neural Network with Flexible Stride

摘要： 卷积神经网络是机器学习的重要工具，尤其是在计算机视觉领域。 其独特的结构和特性在特征提取方面提供了显著优势。 然而，随着数据规模的指数增长，经典计算架构在时间效率和内存需求方面面临严重挑战。 在本文中，我们提出了一种新型的量子卷积神经网络算法。 它能够在确保所需量子比特不随滑动窗口大小成比例增加的情况下，灵活调整步长以适应不同的任务。 首先，提出了一种基于量子叠加的数据加载方法，能够指数级减少空间需求。 随后，设计了用于卷积层、池化层和全连接层的量子子程序，全面复制了经典卷积神经网络的核心功能。 其中，引入了量子算术技术，通过特征的位置信息恢复相应感受野的数据位置信息，使步长选择更加灵活。 此外，采用了并行量子幅度估计和交换测试技术，实现了并行特征提取。 分析表明，与经典方法相比，该方法在更少内存的情况下能够实现数据规模的指数级加速。 最后，所提出的方法在Qiskit框架上进行了数值模拟，使用MNIST数据集中的手写数字图像。 实验结果为该模型的有效性提供了证据。 显示英文摘要

摘要： Convolutional neural network is a crucial tool for machine learning, especially in the field of computer vision. Its unique structure and characteristics provide significant advantages in feature extraction. However, with the exponential growth of data scale, classical computing architectures face serious challenges in terms of time efficiency and memory requirements. In this paper, we propose a novel quantum convolutional neural network algorithm. It can flexibly adjust the stride to accommodate different tasks while ensuring that the required qubits do not increase proportionally with the size of the sliding window. First, a data loading method based on quantum superposition is presented, which is able to exponentially reduce space requirements. Subsequently, quantum subroutines for convolutional layers, pooling layers, and fully connected layers are designed, fully replicating the core functions of classical convolutional neural networks. Among them, the quantum arithmetic technique is introduced to recover the data position information of the corresponding receptive field through the position information of the feature, which makes the selection of step size more flexible. Moreover, parallel quantum amplitude estimation and swap test techniques are employed, enabling parallel feature extraction. Analysis shows that the method can achieve exponential acceleration of data scale in less memory compared with its classical counterpart. Finally, the proposed method is numerically simulated on the Qiskit framework using handwritten digital images in the MNIST dataset. The experimental results provide evidence for the effectiveness of the model.