Predicting long-time quantum dynamics from short-time experimental or theoretical data via dynamic mode decomposition

Computing physical quantities for time-evolved states in quantum many-body systems is generally challenging. We apply a method that effectively leverages reliable short-time data to predict long-time behavior [1]. This method is grounded in dynamic mode decomposition (DMD), often used in fluid dynamics. We explore the effectiveness and applicability of DMD in quantum many-body systems, explicitly examining the transverse-field Ising model at the critical point, even in cases where the input data presents intricate features like multiple oscillatory components and power-law decay associated with long-range quantum entanglements, which differ from fluid dynamics. Our findings demonstrate that this approach allows for accurate predictions extending nearly an order of magnitude beyond the duration of the short-time training data. Additionally, we analyze the effect of noise on prediction accuracy, which is particularly relevant for experimental data. Our results indicate that a small amount of noise, around a few percent, does not significantly impair prediction accuracy.