Enhancing a Convolutional Autoencoder with a Quantum Approximate Optimization Algorithm for Image Noise Reduction

TL;DR

This paper tackles image denoising by introducing a hybrid quantum–classical approach, the quantum convolutional autoencoder (QCAE), which replaces the classical latent space of a convolutional autoencoder with a QAOA-inspired quantum circuit. It combines a classical encoder/decoder with a depth-$p$ QAOA latent space and trains using a parameter-shift rule (PSR) to efficiently compute gradients on quantum hardware. Across MNIST with Gaussian noise, QCAE achieves lower training loss and higher SSIM than a classical CAE, including up to ~40% SSIM improvement, while ablation studies show a ~25% average SSIM gain when using the QAOA circuit with PSR. The work demonstrates the potential of quantum latent representations for image denoising on NISQ devices, while acknowledging hardware noise limitations and outlining directions for real-world images, noise-mitigation strategies, and latent-space design optimization.

Abstract

Image denoising is essential for removing noise in images caused by electric device malfunctions or other factors during image acquisition. It ensures the preservation of image quality and accurate interpretation. Many convolutional autoencoder algorithms have proven effective in image denoising. Owing to their promising efficiency, quantum computers have gained popularity. This paper proposes a method, the quantum convolutional autoencoder (QCAE), which enhances traditional convolutional autoencoders by replacing their latent space with a quantum counterpart implemented via a QAOA-inspired ansatz circuit. To enhance efficiency, we leveraged the advantages of the quantum approximate optimization algorithm (QAOA)-incorporated parameter-shift rule to identify an optimized cost function, facilitating effective learning from data and gradient computation on an actual quantum computer. The proposed QCAE method outperformed its classical counterpart as it exhibited lower training loss and a higher structural similarity index (SSIM) value. QCAE also outperformed its classical counterpart in denoising the MNIST dataset by up to 40% in terms of SSIM value, confirming its enhanced capabilities in real-world applications. Evaluation of QAOA performance across different circuit configurations and layer variations showed that our technique outperformed other circuit designs by 25% on average.

Figures (12)

• Figure 1: Angle encoding quantum circuit.
• Figure 2: Architecture of classical convolutional autoencoder: The core design of a convolutional autoencoder consists of classical encoder and decoder components, each featuring crucial convolutional layers. These layers play a pivotal role in transforming the input image data $x$ into a reconstructed representation $\hat{X}$ through the latent space $Z$.
• Figure 3: Architecture of quantum convolutional autoencoder, where the classical latent space is replaced with a QAOA circuit to efficiently denoise images.
• Figure 4: Schematic depicting the quantum approximate optimization algorithm, which integrates a quantum circuit and classical optimization to iteratively optimize variational parameters for enhanced performance.
• Figure 5: Parameterizing the rotation gates of QAOA circuit with the optimized value of the encoded input image data.