Predicting three-dimensional chaotic systems with four qubit quantum systems

TL;DR

This paper demonstrates that a minimal four-qubit quantum reservoir can effectively predict three-dimensional chaotic systems, advancing quantum reservoir computing for complex system forecasting.

Contribution

It introduces an optimized quantum reservoir computing approach using four qubits for predicting 3D chaotic systems, highlighting minimal quantum resources needed.

Findings

Successful prediction of three-dimensional chaotic systems

Effective reproduction of system 'climate' over long-term predictions

Validation across eight prototypical chaotic systems

Abstract

Reservoir computing (RC) is among the most promising approaches for AI-based prediction models of complex systems. It combines superior prediction performance with very low CPU-needs for training. Recent results demonstrated that quantum systems are also well-suited as reservoirs in RC. Due to the exponential growth of the Hilbert space dimension obtained by increasing the number of quantum elements small quantum systems are already sufficient for time series prediction. Here, we demonstrate that three-dimensional systems can already well be predicted by quantum reservoir computing with a quantum reservoir consisting of the minimal number of qubits necessary for this task, namely four. This is achieved by optimizing the encoding of the data, using spatial and temporal multiplexing and recently developed read-out-schemes that also involve higher exponents of the reservoir response. We outline, test and validate our approach using eight prototypical three-dimensional chaotic systems. Both, the short-term prediction and the reproduction of the long-term system behavior (the system's "climate") are feasible with the same setup of optimized hyperparameters. Our results may be a further step towards the realization of a dedicated small quantum computer for prediction tasks in the NISQ-era.