Learning quantum dynamics with latent neural ODEs

Abstract: The core objective of machine-assisted scientific discovery is to learn physical laws from experimental data without prior knowledge of the systems in question. In the area of quantum physics, making progress towards these goals is significantly more challenging due to the curse of dimensionality as well as the counter-intuitive nature of quantum mechanics. Here, we present the QNODE, a latent neural ODE trained on expectation values of closed and open quantum systems dynamics. It can learn to generate such measurement data and extrapolate outside of its training region that satisfies the von Neumann and time-local Lindblad master equations for closed and open quantum systems respectively in an unsupervised means. Furthermore, the QNODE rediscovers quantum mechanical laws such as the Heisenberg's uncertainty principle in a data-driven way, without any constraint or guidance. Additionally, we show that trajectories that are generated from the QNODE that are close in its latent space have similar quantum dynamics while preserving the physics of the training system.