Abstract—In this paper, we discuss a quantum control algorithm, devised by the authors, inspired in Rabitz and Krotov algorithms and applied to Nuclear Magnetic Resonance (NMR) That algorithm is based on a numerical method for iterative optimization. Specifically, we address 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 controls in the case of two external electromagnetic fields, integrating the associated equations of the Pontryagin Maximum Principle. That algorithm unifies and generalizes the Rabitz and Krotov algorithms. We compare the efficiency of these algorithms with the solutions found by analytical methods.

Index Terms—Lie algebra, nuclear magnetic resonance, optimal control, quantum control systems, iterative optimization.

Cutberto Romero-Meléndez is with Department of Basic Sciences. Autonomous Metropolitan University, Avenida San Pablo 180, colonia Reynosa T. Ciudad de México. 02200. México (email: cutberto@correo.azc.uam.mx).
Leopoldo González-Santos is with Institute of Neurobiology. National Autonomous University of México, México.

Cite: Cutberto Romero-Meléndez, Leopoldo González-Santos, "A Numerical Approximation Approach for Quantum Optimal Control of Two-Level Systems," International Journal of Applied Physics and Mathematics vol. 7, no. 4, pp. 268-274, 2017.