Quantum Convolutional Neural Network with Flexible Stride

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.