Journal
PHYSICAL REVIEW A
Volume 81, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.81.032308
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Funding
- National Science Foundation through the Institute for Quantum Information at the California Institute of Technology [PHY-0803371]
- Direct For Mathematical & Physical Scien
- Division Of Physics [0803371] Funding Source: National Science Foundation
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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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