Parameterized quantum circuits for reinforcement learning of classical rare dynamics

In the study of non-equilibrium or industrial systems, rare events are crucial for understanding the systems' behavior and the effective search for such rare dynamics is frequently the subject of research. Since they are atypical, one requires specific methods for sampling and generating rare event statistics in an automated and statistically meaningful way. Recent publications have shown variational quantum algorithms to be among the most promising candidates for near-term applications on quantum devices. In this article, we propose two quantum reinforcement learning (QRL) approaches to study rare dynamics of time-dependent systems and investigate their benefits over classical approaches based on neural networks. We investigate how architectural choices such as different data encoding strategies and weights influence the successful learning by QRL agents and find a numerical separation in the benefits of data re-uploading for policy-based and value-based quantum approaches. We demonstrate that a quantum agent needs just a single qubit to be capable of learning and representing the rare dynamics of a random walker with a comparable performance of a simple neural network. Furthermore, we are able to numerically demonstrate an improved environment exploration during learning and a better performance in coping with environment scaling by the quantum agents in comparison to their classical counterparts. This is the first study of QRL in rare event statistics and suggests that QRL is a viable method to study rare dynamics of a system.