Controlling Unknown Quantum States via Data-Driven State Representations

Accurate control of quantum states is crucial for quantum computing and other quantum technologies. In the basic scenario, the task is to steer a quantum system towards a target state through a sequence of control operations. Determining the appropriate operations, however, generally requires information about the initial state of the system. When the initial state is not {\em a priori} known, gathering this information is generally challenging for quantum systems of increasing size. To address this problem, we develop a machine-learning algorithm that uses a small amount of measurement data to construct a representation of the system's state. The algorithm compares this data-driven representation with the representation of the target state, and uses reinforcement learning to output the appropriate control operations.We illustrate the effectiveness of the algorithm showing that it achieves accurate control of unknown many-body quantum states and non-Gaussian continuous-variable states using data from a limited set of quantum measurements.