Control of Stochastic Quantum Dynamics with Differentiable Programming

摘要: Controlling stochastic dynamics of a quantum system is an indispensable task in fields such as information processing and metrology. Yet, there no general ready-made approach to design efficient control strategies. Here, we propose framework for the automated schemes based on differentiable programming ($\partial \mathrm{P}$). We apply this state preparation stabilization qubit subjected homodyne detection. To end, formulate optimization problem where loss function quantifies distance from target employ neural networks (NNs) controllers. The system's time evolution governed by differential equation (SDE). implement training, backpropagate gradient through SDE solver using adjoint sensitivity methods. As first example, feed controller focus different methods obtain gradients. second directly detection signal controller. instantaneous value current contains only very limited actual system, covered unavoidable photon-number fluctuations. Despite resulting poor signal-to-noise ratio, can train our prepare stabilize with mean fidelity around 85%. also compare solutions found NN hand-crafted strategy.