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 (PQCs) to redesign the convolutional layer in classical convolutional neural networks, 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 PQCs to form a new hybrid quantum–classical fully connected layer to further improve the accuracy of classification. Finally, we use the MNIST dataset to test the potential of the HQCCNN. The results indicate that the 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%. In multivariate classification, the accuracy rate also reaches 98.51%. Finally, we compare the performance of the HQCCNN with other models and find that the HQCCNN has better classification performance and convergence speed.