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Chin. Phys. B, 2015, Vol. 24(6): 060304    DOI: 10.1088/1674-1056/24/6/060304
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Effects of systematic phase errors on optimized quantum random-walk search algorithm

Zhang Yu-Chao (张宇超)a b, Bao Wan-Su (鲍皖苏)a b, Wang Xiang (汪翔)a b, Fu Xiang-Qun (付向群)a b
a Zhengzhou Information Science and Technology Institute, Zhengzhou 450004, China;
b Synergetic Innovation Center of Quantum Information and Quantum Physics,University of Science and Technology of China, Hefei 230026, China
Abstract  This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover's algorithm.
Keywords:  quantum search algorithm      quantum random walk      phase errors      robustness  
Received:  31 October 2014      Revised:  02 February 2015      Accepted manuscript online: 
PACS:  03.67.Lx (Quantum computation architectures and implementations)  
  03.67.Ac (Quantum algorithms, protocols, and simulations)  
Fund: Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).
Corresponding Authors:  Bao Wan-Su     E-mail:
About author:  03.67.Lx; 03.67.Ac

Cite this article: 

Zhang Yu-Chao (张宇超), Bao Wan-Su (鲍皖苏), Wang Xiang (汪翔), Fu Xiang-Qun (付向群) Effects of systematic phase errors on optimized quantum random-walk search algorithm 2015 Chin. Phys. B 24 060304

[1] Grover L 1996 Proceedings of the 28th Annual ACM Symposium on Theory of Computing (New York: ACM Press) p. 212
[2] Long G L 2001 Phys. Rev. A 64 022307
[3] Li T, Bao W S, Lin W Q, Zhang H and Fu X Q 2014 Chin. Phys. Lett. 31 050301
[4] Wang X, Bao W S and Fu X Q 2011 Chin. Sci. Bull. 56 484
[5] Chuang I L, Gershenfeld N and Kubinec M 1998 Phys. Rev. Lett. 80 3408
[6] Zhang J F, Lu Z H, Deng Z W and Shan L 2003 Chin. Phys. 12 700
[7] Zheng S B 2005 Chin. Phys. 14 2222
[8] Sun J, Lu S F, Liu F and Yang L P 2012 Chin. Phys. B 21 010306
[9] Zhang Y Y, Hu H P and Lu S F 2014 Chin. Phys. B 23 040309
[10] Long G L, Li Y S, Zhang W L and Tu C C 2000 Phys. Rev. A 61 042305
[11] Shenvi N, Brown K R and Whaley K B 2003 Phys. Rev. A 68 052313
[12] Shenvi N, Kempe J and Whaley K B 2003 Phys. Rev. A 67 052307
[13] Potocek V, Gábris A, Kiss T and Jex I 2009 Phys. Rev. A 79 012325
[14] Childs A M and Goldstone J 2004 Phys. Rev. A 70 022314
[15] Ambainis A 2008 SIAM J. Comput. 37 210
[16] Tulsi A 2008 Phys. Rev. A 78 012310
[17] Magniez F, Nayak A, Roland J and Santha M 2011 SIAM J. Comput. 40 142
[18] Li Y, Ma L and Zhou J 2006 J. Phys. A: Math. Gen. 39 9309
[19] Moore C and Russell A 2002 Randomization and Approximation Techniques in Computer Science (Berlin/Heidelberg: Springer) p. 164
[20] Li Y 2006 "Investigations on Quantum Random-Walk Search Algorithm", MS Thesis (Shanghai: East China Normal University) p. 34 (in Chinese)
[21] Ma L, Du J F, Li Y and L H 2006 Chin. Phys. Lett. 23 779
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