Quantum adiabatic computation and adiabatic conditions

• Published in: Physical review. A, Atomic, molecular, and optical physics Vol. 76; no. 2
• Main Authors: Wei, Zhaohui, Ying, Mingsheng
• Format: Journal Article
• Language: English
• Published: United States 01-08-2007
• Subjects: ADIABATIC APPROXIMATION; ALGORITHMS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; INFORMATION THEORY; QUANTUM COMPUTERS; QUANTUM INFORMATION; QUANTUM MECHANICS
• ISSN: 1050-2947; 1094-1622
• DOI: 10.1103/PhysRevA.76.024304

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 et al. [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.