Control-enhanced quantum parameter estimation through reinforcement learning*

Measurement and estimation of parameters are indispensable for science and engineering. One of the main goals in parameter estimation is to find systematic schemes achieving high precision. Schemes for quantum parameter estimation could focus on optimizing the probe, its interaction with the system and measurements. Recently, schemes that add controls during the evolution are realized for significantly improving the precision. However, the identification of the control-enhanced scheme is usually computationally demanding, because the controls depend on the parameter value and need to be re-optimized after each update of the estimation. Here we show an efficient way to identify the controls through reinforcement learning that can improve the precision for both single-parameter estimation and multi-parameter estimation. Reinforcement learning also shows great generalizability, namely the neural network trained under a particular value of the parameter can work for different values within a broad range. These results suggest that reinforcement learning can be an efficient alternative to conventional optimal quantum control methods.