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Center for Nonlinear Studies |
A gapped quantum system that is adiabatically perturbed remains in its eigenstate after the perturbation. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a minimum time proportional to the ratio of the length of the eigenstate path to the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We also give a necessary condition for the adiabatic approximation that is suitable for those cases where the gap varies.
Host: Diego Dalvit