Model Predictive Control of Two-Level Quantum Systems using Quantum Filtering

This paper explores the application of Model Predictive Control (MPC) strategies to quantum systems undergoing continuous-time measurement. The MPC control law is formulated based on the estimated state obtained from quantum filtering. As quantum filtering is affected by uncertainties, applying MPC for real-time monitoring enhances the stability of the filtering process. Our analysis demonstrates that the MPC framework ensures exponential stability in mean square. Additionally, we establish that a nonlinear MPC model guarantees system stability under specified conditions. Furthermore, the inherent robustness of MPC allows the system to remain exponentially bounded in mean square, even in the presence of environmental disturbances. Numerical simulations are provided to validate these control properties of quantum MPC.