Free-time and Fixed End-point Multi-target Optimal Control Theory: Application to Quantum Computing

An extension of monotonically convergent free-time and fixed end-point optimal control theory (FRFP-OCT) to monotonically convergent free-time and fixed end-point \textit{multi-target} optimal control theory (FRFP-MTOCT) is presented. The features of our theory include optimization of the laser pulses with high transition probabilities, that of the temporal duration, the monotonic convergence, and the ability to optimize multiple-laser pulses simultaneously. The advantage of the theory and a comparison with conventional fixed-time and fixed end-point multi-target optimal control theory (FIFP-MTOCT) are presented by comparing data calculated using the present theory with those published previously [K. Mishima and K. Yamashita, Chem. Phys. \textbf{361}, 106 (2009)], where qubit system of interest consists of two polar NaCl molecules coupled by dipole-dipole interaction.