Partial evolution based local adiabatic quantum search  

作　　者：Sun Jie Lu Song-Feng Liu Fang Yang Li-Ping 孙杰;路松峰;刘芳;杨莉萍(School of Computer Science,Huazhong University of Science and Technology,Wuhan 430074,China;Department of Computer Science,Huazhong Agricultural University,Wuhan 430074,China)

机构地区：[1]School of Computer Science,Huazhong University of Science and Technology,Wuhan 430074,China [2]Department of Computer Science,Huazhong Agricultural University,Wuhan 430074,China

出　　处：《Chinese Physics B》2012年第1期87-90,共4页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.61173050)

摘　　要：Recently, Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution, which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one. Later, they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database. In the present paper, following the idea of Roland and Cerf [Roland J and Cerf N J 2002 Phys. Rev. A 65 042308], if within the small symmetric evolution interval defined by Zhang et al., a local adiabatic evolution is performed instead of the original ＂global＂ one, this ＂new＂ algorithm exhibits slightly better performance, although they are progressively equivalent with M increasing. In addition, the proof of the optimality for this partial evolution based local adiabatic search when M = 1 is also presented. Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search, which are found to have the same phenomenon above, are also discussed.Recently, Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution, which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one. Later, they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database. In the present paper, following the idea of Roland and Cerf [Roland J and Cerf N J 2002 Phys. Rev. A 65 042308], if within the small symmetric evolution interval defined by Zhang et al., a local adiabatic evolution is performed instead of the original ＂global＂ one, this ＂new＂ algorithm exhibits slightly better performance, although they are progressively equivalent with M increasing. In addition, the proof of the optimality for this partial evolution based local adiabatic search when M = 1 is also presented. Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search, which are found to have the same phenomenon above, are also discussed.

关 键 词：partial adiabatic evolution local adiabatic evolution quantum search 

分 类 号：O413.1[理学—理论物理]