Forecasting Long-Time Dynamics in Quantum Many-Body Systems by Dynamic Mode Decomposition

Numerically computing physical quantities of time-evolved states in quantum many-body systems is a challenging task in general. Here, we propose a method that utilizes reliable short-time data of physical quantities to accurately forecast long-time behavior. The method is based on the dynamic mode decomposition (DMD), which is commonly used in fluid dynamics. The effectiveness and applicability of the DMD in quantum many-body systems such as the Ising model in the transverse field at the critical point are studied, even when the input data exhibits complicated features such as multiple oscillatory components and a power-law decay with long-ranged quantum entanglements unlike fluid dynamics. It is demonstrated that the present method enables accurate forecasts at time as long as nearly an order of magnitude longer than that of the short-time training data. Effects of noise on the accuracy of the forecast are also investigated, because they are important especially when dealing with the experimental data. We find that a few percent of noise does not affect the prediction accuracy destructively.