Higher order quantum reservoir computing for non-intrusive reduced-order models

Forecasting dynamical systems is of importance to numerous real-world applications. When possible, dynamical systems forecasts are constructed based on first-principles-based models such as through the use of differential equations. When these equations are unknown, non-intrusive techniques must be utilized to build predictive models from data alone. Machine learning (ML) methods have recently been used for such tasks. Moreover, ML methods provide the added advantage of significant reductions in time-to-solution for predictions in contrast with first-principle based models. However, many state-of-the-art ML-based methods for forecasting rely on neural networks, which may be expensive to train and necessitate requirements for large amounts of memory. In this work, we propose a quantum mechanics inspired ML modeling strategy for learning nonlinear dynamical systems that provides data-driven forecasts for complex dynamical systems with reduced training time and memory costs. This approach, denoted the quantum reservoir computing technique (QRC), is a hybrid quantum-classical framework employing an ensemble of interconnected small quantum systems via classical linear feedback connections. By mapping the dynamical state to a suitable quantum representation amenable to unitary operations, QRC is able to predict complex nonlinear dynamical systems in a stable and accurate manner. We demonstrate the efficacy of this framework through benchmark forecasts of the NOAA Optimal Interpolation Sea Surface Temperature dataset and compare the performance of QRC to other ML methods.