Next Generation Reservoir Computing (NG-RC) is a modern class of model-free
machine learning that enables an accurate forecasting of time series data
generated by dynamical systems. We demonstrate that NG-RC can accurately
predict full many-body quantum dynamics in both integrable and chaotic systems.
This is in contrast to the conventional application of reservoir computing that
concentrates on the prediction of the dynamics of observables. In addition, we
apply a technique which we refer to as skipping ahead to predict far future
states accurately without the need to extract information about the
intermediate states. However, adopting a classical NG-RC for many-body quantum
dynamics prediction is computationally prohibitive due to the large Hilbert
space of sample input data. In this work, we propose an end-to-end quantum
algorithm for many-body quantum dynamics forecasting with a quantum
computational speedup via the block-encoding technique. This proposal presents
an efficient model-free quantum scheme to forecast quantum dynamics coherently,
bypassing inductive biases incurred in a model-based approach.Comment: 15 pages, 5 figures. v2: additional forecasting results for a chaotic
quantum syste