Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamics

TL;DR

This paper introduces a quantum algorithm for forecasting many-body quantum dynamics using reservoir computing, achieving computational speedup and accurate long-term predictions without relying on classical simulation methods.

Contribution

It presents the first end-to-end quantum reservoir computing algorithm for quantum dynamics forecasting, leveraging block-encoding for efficiency and bypassing classical computational limitations.

Findings

Accurately predicts quantum dynamics in integrable and chaotic systems.

Achieves quantum computational speedup over classical methods.

Enables long-term forecasting without intermediate state information.

Abstract

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.