Transition graph-based control of quantum eigenstates

Based on the analysis of the invariant set in quantum Lyapunov control under a performance index with degrees of freedom, the population control of eigenstates is studied. For isolated target eigenstates, this paper shows the existence of the degrees of freedom that guarantee exact convergence and obtains rigorous construction relation of those degrees of freedom. For non-isolated target eigenstates, we propose a path-planning-based method. The method considers transition paths of controlled systems, so can achieve intuitive and high-probability transition to desired target eigenstate accompanied with appropriate design of those degrees of freedom.