Potential quantum machine learning applications for classical nonlinear dynamical systems and fluid flows

Quantum machine learning (QML) combines two recently emerging new paradigms of classifying, generating and analyzing data – quantum computing and machine learning. In quantum machine learning, data processing follows the laws of the unitary dynamics of quantum mechanics as described by the linear Schrödinger equation. This requires new ways of computation in comparison to the classical counterparts, which already exist for most of the machine learning algorithms. We provide a compact overview of potential applications of QML to classical nonlinear physics, such as the modeling of (turbulent) flows, all of which are still in an early proof-of-concept stage and have not demonstrated a quantum advantage over corresponding classical methods. This includes QML algorithms for clustering and classification of observational data, anomaly detection in time series, the generation of super-resolution data by generative algorithms, and the construction of dynamical reduced-order models for nonlinear dynamical processes. All the presented methods are not restricted to fluid flow problems, but also found their way into neighboring research fields, such as plasma and astrophysics or atmospheric science. I will provide example cases for each algorithm and discuss potential advantages.