Quantum Generative Adversarial Autoencoders: Learning latent representations for quantum data generation

Over the past decade, machine learning has undergone transformative advancements, primarily fueled by the development of sophisticated deep learning architectures and training methodologies. In parallel, Quantum Machine Learning (QML) has emerged as a field dedicated to exploring how quantum algorithms and quantum computing platforms can be utilized to process, model, and extract meaningful insights from data [9, 14, 65], and also generate new data [26, 59]. While efforts in QML primarily focused on leveraging quantum computing to accelerate classical machine learning tasks [19, 34], a significant and increasingly important direction involves the development of quantum models that operate directly on quantum data [7, 9, 41]. These models, tailored specifically to quantum data, are essential for realizing the full potential of quantum technologies, enabling applications in quantum information processing that are intractable with classical methods [25]. A notable model within QML for handling quantum data is the Quantum Autoencoder (QAE), which draws inspiration from its classical counterpart, the Autoen-coder (AE) [5, 58]. QAE has been applied to demonstrate how quantum circuits can be trained to compress quantum states, with applications to quantum simulation and quantum information [13, 29, 42, 44, 57]. Further developments extend these architectures to the denoising of entangled quantum states under realistic noise models [1, 10, 62, 63], along with proposals for error mitigation strategies tailored to Noisy Intermediate-Scale Quantum (NISQ) devices [46, 66]. Practical realizations of QAE in quantum hardware, such as nitrogen-vacancy centers, demonstrated robust compression and the preservation of entanglement, while significantly lengthening the coherence times of Bell states [67]. These two authors contributed equally.