  This article presents a robust control strategy using Time-Optimal Model
Predictive Control (TOMPC) for a two-level quantum system subject to bounded
uncertainties. In this method, the control field is optimized over a finite
horizon using a nominal quantum system as the reference and then the optimal
control for the first time interval is applied and a projective measurement is
implemented on the uncertain system. The new control field for the next time
interval will be iteratively optimized based on the measurement result. We
present theoretical results to guarantee the stability of the TOMPC algorithm.
We also characterize the robustness and the convergence rate of the TOMPC
strategy for the control of two-level systems. Numerical simulations further
demonstrate that, in the presence of uncertainties, our quantum TOMPC algorithm
enhances robustness and steers the state to the desired state with high
fidelity. This work contributes to the progress of Model Predictive Control in
quantum control and explores its potential in practical applications of quantum
technology.
