Partial evolution based local adiabatic quantum search
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...
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Published in | Chinese physics B Vol. 21; no. 1; pp. 87 - 90 |
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Format | Journal Article |
Language | English |
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2012
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Abstract | 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. |
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AbstractList | 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 042303], 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. |
Author | 孙杰 路松峰 刘芳 杨莉萍 |
AuthorAffiliation | School of Computer Science, Huazhong University of Science and Technology, Wuhan 430074, China Department of Computer Science, Huazhong Agricultural University, Wuhan 430074, China |
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Cites_doi | 10.1103/PhysRevLett.99.070502 10.1088/1674-1056/20/4/040309 10.1103/PhysRevA.65.012322 10.1103/PhysRevLett.79.325 10.1016/j.physleta.2006.01.098 10.1103/PhysRevA.65.062310 10.1103/PhysRevA.65.042308 10.1137/S0097539705447323 10.1103/PhysRevA.82.034304 10.1126/science.1057726 10.1103/PhysRevA.71.060312 10.1103/PhysRevLett.100.160506 10.1088/1674-1056/18/1/004 10.1103/PhysRevA.80.052328 |
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DocumentTitleAlternate | Partial evolution based local adiabatic quantum search |
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Notes | Sun Jie, Lu Song-Feng, Liu Fang, and Yang Li-Ping(a) School of Computer Science, Huazhong University of Science and Technology, Wuhan 430074, China b) Department of Computer Science, Huazhong Agricultural University, Wuhan 430074, China 11-5639/O4 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. partial adiabatic evolution, local adiabatic evolution, quantum search ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
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References | 11 Liu W W (6) 2009; 18 12 13 16 Zhang Y Y (14) 2011; 20 Farhi E (10) 2000 1 2 3 4 5 7 8 9 Messiah A (15) 1999 |
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SubjectTerms | Adiabatic flow Algorithms Evolution Evolutionary algorithms Intervals Search algorithms Searching Tuning 数据库 新泽西州 时间复杂度 时间间隔 算法性能 绝热演化 进化 量子搜索算法 |
Title | Partial evolution based local adiabatic quantum search |
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