Necessary condition for the quantum adiabatic approximation

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.032308· OSTI ID:21408387

Boixo, S ^[1]; Somma, R D ^[2]

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1. Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)
2. Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

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.

• OSTI ID: 21408387
• Journal Information: Physical Review. A, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.032308; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ADIABATIC APPROXIMATION
EVOLUTION
LENGTH
YIELDS
APPROXIMATIONS
CALCULATION METHODS
DIMENSIONS