On the Generalization Limits of Quantum Generative Adversarial Networks with Pure State Generators

Over the past decade, advancements in model architectures, the availability of larger datasets, and improvements in hardware--among other factors--have significantly enhanced the capabilities of generative machine learning models [1-3]. At the same time, ongoing progress toward scalable quantum hardware has sparked growing interest in the development of quantum machine learning (QML) algorithms [4, 5], which aim to leverage quantum properties--such as superposition and entanglement--to enhance the efficiency and expressivity of classical machine learning approaches. Although large-scale fault-tolerant quantum hardware is not yet realizable, many QML algorithms are specifically designed to operate within the constraints of the noisy intermediate-scale quantum (NISQ) era [6-8]. In image generation tasks, several classical deep learning architectures have demonstrated notable effectiveness. Variational Autoencoders (VAEs) are particularly useful for tasks like image denoising [9] and anomaly detection [10] due to their structured latent spaces.