  In this paper, we propose a concept to use a quantum speed limit (QSL) as a
measure of robustness of states, defining that a state with bigger QSL is more
robust. In this perspective, it is important to have an explicitly-computable
QSL, because then we can formulate an engineering problem of Hamiltonian that
makes a target state robust against decoherence. Hence we derive a new
explicitly-computable QSL that is applicable to general Markovian open quantum
systems. This QSL is tighter than another explicitly-computable QSL, in an
important setup such that decoherence is small. Also the Hamiltonian
engineering problem with this QSL is a quadratic convex optimization problem,
and thus it is efficiently solvable. The idea of robust state characterization
and the Hamiltonian engineering, in terms of QSL, is demonstrated with several
examples.
