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Preparation of bosonic and general cavity quantum states usually relies onusing open-loop control to reach a desired target state. In this work, ameasurement-based feedback approach is used instead, exploiting thenon-linearity of weak measurements alongside a coherent drive to prepare thesestates. The extension of previous work on Lyapunov-based control is shown tofail for this task. This prompts for a different approach, and reinforcementlearning (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 back-action as the non-linearity, while naturallyincorporating detection of cavity photon jumps. Two different RL frameworks areanalyzed: an off-policy approach recently introduced called truncated quantilecritic~(TQC) and the on-policy method commonly used in quantum control, namelyproximal policy optimization~(PPO). It is shown that TQC performs better atreaching higher target state fidelity preparation.

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