Speedup in Generative Learning of Quantum System Dynamics

Learning and reproducing non-classical probability distributions lie at the heart of demonstrating quantum advantage and remains a computationally challenging task. Inspired by the recent success of generative learning models, we propose a quantum generative learning architecture that overcomes the limitations of traditional quantum machine learning approaches. Our framework employs an adversarial learning paradigm implemented directly on quantum hardware, where a variationally trained generator reconstructs the system's dynamics while the discriminator guides the generator's optimization. Unlike heuristic machine learning models that suffer from "barren plateaus", which are regions where gradients vanish and learning becomes exponentially harder, numerical simulations show that our framework maintains stable, system-size-independent gradients, enabling efficient optimization at scale. Furthermore, by incorporating shared entanglement between the generator and the target system, we enhance the sensitivity of the learning process and significantly reduce the sample complexity, offering a clear advantage over conventional tomographic methods. The framework is platform-independent but will be experimentally realized on a quantum photonic processor using a mesh of programmable interferometers. Together, these features establish a scalable route for the characterization and verification of noisy quantum devices, marking a significant step toward generative quantum models with quantum advantage in learning efficiency.