Necessary Condition for the Quantum Adiabatic Approximation

Details Necessary Condition for the Quantum Adiabatic Approximation Necessary Condition for the Quantum Adiabatic Approximation

2009-11-07

arxiv.org/abs/0911.1362v1

Phys. Rev. A 81, 032308 (2010)

Physics

Quantum Physics

5 pages, 1 figure

Scientific paper

10.1103/PhysRevA.81.032308

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.

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