Numerical approximation in Optimal Control of Two-Level Quantum Systems
In this paper, we discuss the application of two quantum control algorithms, the Krotov algorithm and the Rabitz algorithm, to Nuclear Magnetic Resonance (NMR), based on a numerical method for iterative optimization. Specifically, we address the problem of the determination of external optimal pulses (controls), to minimal cost, over a two-level quantum system. We use the numerical approximation to find the optimal control in the case of one control, integrating the adjoint equations of the Pontryagin Maximum Principle (PMP) and we have devised an algorithm based on the algorithms of Rabitz et al. and Krotov et al. which unifies and generalizes them for the case of two controls. We compare the efficiency of these algorithms with the solutions found by analytical methods.