Analysis of Learnability of a Novel Hybrid Quantum-Classical Convolutional Neural Network in Image Classification

We design a new hybrid quantum-classical convolutional neural network (HQCCNN) model based on parameter quantum circuits. In this model, we use parameterized quantum circuits (PQC) to redesign the convolutional layer in classical convolutional neural networks (CNN), forming a new quantum convolutional layer to achieve unitary transformation of quantum states, enabling the model to more accurately extract hidden information from images. At the same time, we combine the classical fully connected layer with PQC to form a new hybrid quantum-classical fully connected layer to further improve the accuracy of classification. Finally, we used the MNIST dataset to test the potential of HQCCNN. The results indicate that HQCCNN has good performance in solving classification problems. In binary classification tasks, the classification accuracy of numbers 5 and 7 is as high as 99.71%. And in multivariate classification, the accuracy rate also reached 98.51%. Finally, we compare the performance of HQCCNN with other models and find that HQCCNN has better classification performance and convergence speed.