HQC-MCDCNN: a novel hybrid quantum–classical multi-path denoising convolutional neural network

Image denoising is a longstanding and enduring visual problem, and with the continuous rise of quantum computing in the field of machine learning, its role in image processing has become increasingly important. This paper introduces for the first time the use of multiscale variational quantum circuits in the field of image denoising, aiming to enhance the performance of classical convolutional neural networks and explore the potential advantages of combining quantum and classical approaches. In this work, we propose a novel Hybrid Quantum-Classical Multi-Path Denoising Convolutional Neural Network, abbreviated as HQC-MCDCNN. The HQC-MCDCNN is composed of a hybrid of quantum and classical elements, with the quantum part using multiscale variational quantum circuits instead of classical convolutional layers for feature extraction, and the classical part employing a newly designed multi-path denoising convolutional neural network for supervised learning. Together, these components synergistically achieve image denoising. It is worth noting that this paper aims to build readers’ intuition for quantum computing, presenting all internal details of this work with rich images and visualizations. To demonstrate the denoising capability of HQC-MCDCNN, we conducted rigorous comparative experiments. Due to the constraints of Noisy Intermediate-Scale Quantum (NISQ) devices and the limited number of quantum bits, the experiments were based on the MNIST and Fashion-MNIST datasets with varying degrees of noise (noise factors ranging from 0.3 to 0.7), employing a 6-fold stratified sampling strategy for cross-validation. The experimental results indicate that HQC-MCDCNN is promising across all evaluation metrics, particularly outperforming other models by 56.5% in the average UIQ index. This suggests that our hybrid model exhibits outstanding feature extraction capabilities and excellent denoising performance, providing a promising path for addressing image denoising challenges.