  Quantum speed limits for two time-evolved states are introduced and applied
to overlap between true dynamics and approximate dynamics. In particular, we
point out that the present idea is suitable for invariant-based inverse
engineering, i.e., the worst case performance of invariant-based inverse
engineering can be evaluated by using a designed time-evolved state. As
demonstrations, we apply the present method to stimulated Raman adiabatic
passage and quantum annealing, and then we find that the present idea brings
valuable insight to control scheduling.
