Necessary condition for the quantum adiabatic approximation

S. Boixo and R. D. Somma
Phys. Rev. A 81, 032308 – Published 9 March 2010

Abstract

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.

  • Figure
  • Received 4 December 2009

DOI:https://doi.org/10.1103/PhysRevA.81.032308

©2010 American Physical Society

Authors & Affiliations

S. Boixo1,* and R. D. Somma2,†

  • 1Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA
  • 2Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • *boixo@caltech.edu
  • somma@lanl.gov

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Vol. 81, Iss. 3 — March 2010

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