Forecasting chaotic dynamics on a quantum computer: A hardware-efficient recurrence-free quantum reservoir computer

Quantum reservoir computing (QRC) has recently emerged as a promising framework in quantum computing to predict chaotic dynamics and extreme events. The main objective of this work is to propose a hardware-efficient quantum reservoir network to predict chaotic dynamics and its stability properties from data only. First, we propose a recurrence-free quantum reservoir computing (RF-QRC) architecture, which avoids exponential circuit depth, scales with higher dimensional chaotic systems, and does not have an additional feedback loop, making it suitable for hardware implementation. Second, we develop a method for optimal training of finitely sampled quantum reservoir computers. The methods are employed for a turbulent shear flow model with extreme events (MFE) on IBM Quantum backends. We demonstrate the feasibility of our methods by training the RF-QRC on multiple parallel QPUs, coupled with denoising techniques. Third, we derive the analytic Jacobian of quantum reservoir computers to infer the stability property of the chaotic system from data only. We correctly infer the Lyapunov spectrum in both the Lorenz-63 and MFE turbulence models. This work opens opportunities for using quantum reservoir computing for time series forecasting of chaotic flows in near- and mid-term quantum hardware.