Preparation of cavity-Fock-state superpositions by reinforcement learning exploiting measurement backaction

Preparation of bosonic and general cavity quantum states usually relies on using open-loop control to reach a desired target state. In this work, a measurement-based feedback approach is used instead, exploiting the nonlinearity of weak measurements alongside a coherent drive to prepare these states. The extension of previous work on Lyapunov-based control is shown to fail for this task. This prompts for a different approach, and reinforcement learning (RL) is resorted to here for this purpose. With such an approach, cavity-eigenstate superpositions can be prepared with fidelities over $98%$ using only the measurements backaction as the nonlinearity, while naturally incorporating detection of cavity photon jumps. Two different RL frameworks are analyzed: an off-policy approach recently introduced called truncated quantile critic (TQC) and the on-policy method commonly used in quantum control, namely proximal policy optimization. It is shown that TQC performs better at reaching higher target state fidelity preparation.