A quantum search algorithm based on the partial adiabatic evolution [Phys. Rev. A 80, 052328 (2009)] is provided. We calculate its time complexity and find that the algorithm improves the time complexity, which is $O(\sqrt{N/M})$ , of the local adiabatic search algorithm [Phys. Rev. A 65, 042308 (2002)] to $O(\sqrt{N}/M)$ .A quantum search algorithm based on the partial adiabatic evolution [Phys. Rev. A 80, 052328 (2009)] is provided. We calculate its time complexity and find that the algorithm improves the time complexity, which is $O(\sqrt{N/M})$, of the local adiabatic search algorithm [Phys. Rev. A 65, 042308 (2002)] to $O(\sqrt{N}/M)$.

arXiv:1007.1528Physical Review ASep 22, 201016 citations

Partial evolution based local adiabatic quantum search

Jie Sun, Songfeng Lu, Fang Liu +1 more

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.

Chinese Physics BJan 1, 201212 citations

O(\sqrt{N/M})

, of the local adiabatic search algorithm [Phys. Rev. A 65, 042308 (2002)] to

O(\sqrt{N}/M)