Quantum adiabatic computation and adiabatic conditions

Recently, quantum adiabatic computation has attracted more and more attention in the literature. It is a novel quantum computation model based on adiabatic approximation, and the analysis of a quantum adiabatic algorithm depends highly on the adiabatic conditions. However, it has been pointed out that the traditional adiabatic conditions are problematic. Thus, results obtained previously should be checked and sufficient adiabatic conditions applicable to adiabatic computation should be proposed. Based on a result of Tong [Phys. Rev. Lett. 98, 150402 (2007)], we propose a modified adiabatic criterion which is more applicable to the analysis of adiabatic algorithms. As an example, we prove the validity of the local adiabatic search algorithm by employing our criterion.