An iterative algorithm for optimal control of two-level quantum systems
This paper addresses the numerical resolution of a state transfer problem in a single spin qubit using three different Optimal Control algorithms: Krotov algorithm, Rabitz algorithm, used on Quantum Molecular Dynamics, and a new algorithm that we propose. In the problem of finding the optimal control in the spin transference between two given states with a minimal cost in Nuclear Magnetic Resonance (NMR), we present the application of the two algorithms mentioned above to control a quantum system with one varying external electromagnetic field. Then, we propose a new algorithm, inspired in the Maday-Turinici algorithm, to compute the optimal controls for a system with two varying external electromagnetic fields, integrating the adjoint equations of the Pontryagin Maximum Principle (PMP). We compare the numerical results with the analytic solutions known for both problems and analyze the performance of these algorithms.
CYBERNETICS AND PHYSICS, Vol. 6, No. 4, pp.231-238