Continuos feedback of a controllable nonlinear cavity with Deep Reinforcement Learning

Many tasks in quantum information processing require numerical methods to identify the best control sequence to achieve a specific goal. Deep Reinforcement Learning (DRL) has been applied with great success to many other fields, thanks to its ability to identify the best strategy in problems involving a competition between short and long-term rewards.
We focus on one of the simplest quantum systems highly relevant for quantum information processing, namely a controllable nonlinear cavity. We show how DRL can find the correct feedback control to stabilize a desired state (e.g. a particular Fock state), subject to dissipation and weak measurements.
The few existing DRL applications in physics rely mostly on discrete action spaces, but we show how continuous control sequences can be easily plugged in in such framework, which is the most natural way to handle feedback control sequences in physics . Finally, we exploit Long short-term memory (LSTM) networks to account for non-Markovianity in the master equation.