  Image denoising is essential for removing noise in images caused by electric
device malfunctions or other factors during image acquisition. It helps
preserve image quality and interpretation. Many convolutional autoencoder
algorithms have proven effective in image denoising. Owing to their promising
efficiency, quantum computers have gained popularity. This study introduces a
quantum convolutional autoencoder (QCAE) method for improved image denoising.
This method was developed by substituting the representative latent space of
the autoencoder with a quantum 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.
