Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability

TL;DR

This paper demonstrates that quantum reservoir computers, both recurrent and recurrence-free, are effective and robust tools for learning and forecasting chaotic dynamics, with stability and noise resilience analyzed through generalized synchronization.

Contribution

It introduces a novel interpretation of quantum reservoir computers as generalized-synchronization systems and establishes design criteria ensuring robustness and stability, including the $GS=ESP$ condition.

Findings

Quantum reservoir computers can learn Lyapunov spectra and attractor properties.

Dissipation from noise enhances robustness of quantum reservoir computers.

RF-QRCs fulfill the $GS=ESP$ criterion, ensuring stability.

Abstract

We show that recurrent quantum reservoir computers (QRCs) and their recurrence-free architectures (RF-QRCs) are robust tools for learning and forecasting chaotic dynamics from time-series data. First, we formulate and interpret quantum reservoir computers as coupled dynamical systems, where the reservoir acts as a response system driven by training data; in other words, quantum reservoir computers are generalized-synchronization (GS) systems. Second, we show that quantum reservoir computers can learn chaotic dynamics and their invariant properties, such as Lyapunov spectra, attractor dimensions, and geometric properties such as the covariant Lyapunov vectors. This analysis is enabled by deriving the Jacobian of the quantum reservoir update. Third, by leveraging tools from generalized synchronization, we provide a method for designing robust quantum reservoir computers. We propose the criterion $GS=ESP$: GS implies the echo state property (ESP), and vice versa. We analytically show that RF-QRCs, by design, fulfill $GS=ESP$. Finally, we analyze the effect of simulated noise. We find that dissipation from noise enhances the robustness of quantum reservoir computers. Numerical verifications on systems of different dimensions support our conclusions. This work opens opportunities for designing robust quantum machines for chaotic time series forecasting on near-term quantum hardware.