  The quantum speed limit specifies a universal bound of the fidelity between
the initial state and the time-evolved state. We apply this method to find a
bound of the fidelity between the adiabatic state and the time-evolved state.
The bound is characterized by the counterdiabatic Hamiltonian and can be used
to evaluate the worst case performance of the adiabatic quantum computation.
The result is improved by imposing additional conditions and we examine several
models to find a tight bound. We also derive a different type of quantum speed
limits that is meaningful even when we take the thermodynamic limit. By using
solvable spin models, we study how the performance and the bound are affected
by phase transitions.
