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Published March 2010 | Published
Journal Article Open

Necessary condition for the quantum adiabatic approximation

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.

Additional Information

© 2010 The American Physical Society. Received 4 December 2009; published 9 March 2010. We thank H. Barnum, R. Cleve, A. Childs, and E. Knill for discussions, and the Perimeter Institute where part of this work was done. SB thanks the National Science Foundation for support under grant PHY-0803371 through the Institute for Quantum Information at the California Institute of Technology. RS thanks the Laboratory Directed Research and Development Program at Los Alamos National Laboratory for support.

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August 19, 2023
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