Prediction of chaotic dynamics and extreme events: A recurrence-free quantum reservoir computing approach

TL;DR

This paper introduces a quantum reservoir computing approach that uses compact quantum circuits to predict chaotic dynamics and extreme events more efficiently than classical methods, with potential for hardware implementation.

Contribution

The paper proposes the recurrence-free quantum reservoir computer (RF-QRC) architecture, leveraging quantum features and entanglement to improve prediction accuracy with smaller reservoirs.

Findings

RF-QRC requires smaller reservoirs than classical counterparts.

RF-QRC achieves longer predictability of extreme events.

Quantum features enhance nonlinear expressivity and scalability.

Abstract

In chaotic dynamical systems, extreme events manifest in time series as unpredictable large-amplitude peaks. Although deterministic, extreme events appear seemingly randomly, which makes their forecasting difficult. By learning the dynamics from observables (data), reservoir computers can time-accurately predict extreme events and chaotic dynamics, but they may require many degrees of freedom (large reservoirs). In this paper, by exploiting quantum-computer ans\"atze and entanglement, we design reservoir computers with compact reservoirs and accurate prediction capabilities. First, we propose the recurrence-free quantum reservoir computer (RF-QRC) architecture. By developing ad-hoc quantum feature maps and removing recurrent connections, the RF-QRC has quantum circuits with small depths. This allows the RF-QRC to scale well with higher-dimensional chaotic systems, which makes it suitable for hardware implementation. Second, we forecast the temporal chaotic dynamics and their long-term statistics of low- and higher-dimensional dynamical systems. We find that RF-QRC requires smaller reservoirs than classical reservoir computers. Third, we apply the RF-QRC to the time prediction of extreme events in a model of a turbulent shear flow with turbulent bursts. We find that the RF-QRC has a longer predictability than the classical reservoir computer. The results and analyses indicate that quantum-computer ans\"atze offer nonlinear expressivity and computational scalability, which are useful for forecasting chaotic dynamics and extreme events. This work opens new opportunities for using quantum machine learning on near-term quantum computers.