Variational Shadow Quantum Circuits Assisted Quantum Convolutional Neural Network

Convolutional neural network (CNN), as a prominent machine learning model, is crucial in image classification and feature extraction by completely utilizing the correlation information of data. Currently, the CNN is facing the challenges of slow computing speed, expanding data scale and poor interpretation for rapidly increasing Hilbert space. Fortunately, quantum convolutional neural network (QCNN) promises an elegant solution to improve the efficiency of data processing by combining the superiority of quantum computing and the feature extraction capability of the CNN. However, most of the existing QCNNs have the problem that they are feeble to extract global features effectively and coincidentally variational shadow quantum circuit (VSQC) can preferably figure out it. Accordingly, an enhanced QCNN assisted by the VSQC (VSQC-QCNN) is developed. To be specific, the input data is primarily preprocessed by the VSQC module to establish global entanglement and extract effective features. Then the output shadow features are further processed by encoding, quantum circuit evolution and decoding through quantum convolutional layer and the dimensionality of the feature results is reduced through the pooling layer. When the data dimension is small enough, it is fed into a fully connected neural network to make classification predictions via activation functions. Experiments conducted on the MNIST dataset through the VQNet quantum framework demonstrate that the VSQC-QCNN model is with performance surpassing the original QCNN in terms of loss function, classification accuracy and training speed. In addition, it is proved that the VSQC-QCNN model has good astringency and stability under different circuit depths, widths and learning rates. Remarkably, the classification average accuracy of the model can reach up to 99% (even 100% for a few cases). Finally, experiments are also performed on Fashion-MNIST and Iris datasets, indicating that the designed model has good universality.