Continuous monitoring and feedback control of qubit dynamics using differentiable programming

In quantum state control, protocols that allow one to prepare desired target states are developed. Starting from a distribution of initial states, we aim to find the optimal control scheme to fulfill the control task over a certain time interval. The dynamics of a (dissipative) quantum system can be described by a (stochastic) Schrödinger equation. Thus, given an initial state and a sequence of all measurement results, it is conceptually straightforward to determine the time evolution of the system. However, solving the control problem by deriving a performant control scheme is generally hard.
To solve this inverse problem, we simulate the dynamics of the quantum system as part of a fully differentiable program [1]. Specifically, we employ a neural network that selects control parameters to be applied in the next time-step based on the current state of the qubit or the observed sequence of measurement results. These control parameters modify the equation of motion of the system. The parameters of the neural network are optimized in a series of epochs based on gradient information obtained efficiently by (adjoint) sensitivity methods. We verify the robustness of our method in different scenarios.

[1] F. Schäfer et al., Mach. Learn.: Sci. Technol.,*1* 035009 (2020)