Abstract
Wei et al. have shown an accurate relation between the running time and the distance of the initial state and the final state of a local adiabatic evolution, that is, the adiabatic running time can be completely determined by the distance between the states. They also asked whether more complicated adiabatic evolutions have similar simple relation. We show that the adiabatic evolution with a general class of models of interpolation path proposed by Das et al. is just such another kind of adiabatic evolution which enjoys the relation discussed by Wei et al.
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