Quantum reservoir computing with many body systems

Abstract

This thesis explores the implementation of Quantum Reservoir Computing (QRC) using random matrices and the Transverse Field Ising Model for time series prediction tasks. Given the limited theoretical understanding of QRC, this work investigates the dependence of reservoir dynamics on the performance of chaotic and memory-intensive time series. Our findings reveal that the optimal reservoir for learning is highly task-dependent, where chaotic time series are best predicted using random matrices, while memory-intensive tasks achieve optimal performance at the boundary between integrable and chaotic regimes. Additionally, we explore the connection between QRC and the Volterra expansion, demonstrating that QRC can be interpreted within this framework. This interpretation offers a deeper insight into chaos-boundary enhancement and, more broadly, the performance of various time series modelled using QRC.