Approximate time-optimal control of quantum ensembles based on sampling and learning

For a general quantum ensemble with Hamiltonian fluctuations, this paper proposes a sampling-based two-stage approximate time-optimal control algorithm with momentum terms and achieves a high-fidelity state transition of all member systems to a common target state within an approximate minimum time. The fidelity and the control time are respectively optimized in the two stages. In particular, the introduction of momentum terms greatly improves the convergence rate of the algorithm. Simulation experiments on a two-level quantum ensemble verify the effectiveness of the proposed algorithm.