Quantum-inspired activation functions in the convolutional neural network

Driven by the significant advantages offered by quantum computing, research in quantum machine learning has increased in recent years. While quantum speed-up has been demonstrated in some applications of quantum machine learning, a comprehensive understanding of its underlying mechanisms for improved performance remains elusive. Our study fills this gap by examining the expressibility of quantum circuits integrated within a convolutional neural network (CNN). Through numerical training on the MNIST dataset, our hybrid quantum-classical CNN model exhibited superior feature selection capabilities and significantly reduced the required training steps compared to the classical CNN. To understand the root of this enhanced performance, we conducted an analytical investigation of the functional expressibility of quantum circuits and derived a quantum activation function. We demonstrated that this quantum activation is more efficient in selecting important features and discarding unimportant information of input images. These findings not only deepen our comprehension of quantum-enhanced machine-learning models but also advance the classical machine-learning technique by introducing the quantum-inspired activation function.