Quantum Optimal Control for Bose-Einstein-Condensates at Complex Space

Quantum control of Bose-Einstein-Condensates is interesting topic in the areas of control and physics. In this work, Gross-Pitaevskii equation expressed Bose-Einstein-Condensates is considered as control target. Full theoretical proof for the existence of quantum optimal control is provided for cubical Schrodinger equation in complex Hilbert spaces.