  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.
