Phys. Rev. A 81, 032308 (2010) [4 pages]Necessary condition for the quantum adiabatic approximationReceived 4 December 2009; published 9 March 2010 A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. 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 depends on local properties of the path, which is appropriate when the gap varies. © 2010 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.81.032308
DOI:
10.1103/PhysRevA.81.032308
PACS:
03.67.Lx, 03.65.Xp, 03.67.Ac, 64.70.Tg
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