Effects of initial states on the quantum correlations in the generalized Grover search algorithm

doi:10.1088/1674-1056/ac05a9

中国物理B ›› 2021, Vol. 30 ›› Issue (8): 80303-080303.doi: 10.1088/1674-1056/ac05a9

Effects of initial states on the quantum correlations in the generalized Grover search algorithm

Zhen-Yu Chen(陈祯羽)¹, Tian-Hui Qiu(邱田会)¹, Wen-Bin Zhang(张文彬)², and Hong-Yang Ma(马鸿洋)^1,†

1 School of Science, Qingdao University of Technology, Qingdao 266033, China;
2 School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China

收稿日期:2021-04-07 修回日期:2021-05-17 接受日期:2021-05-27 出版日期:2021-07-16 发布日期:2021-07-23
通讯作者: Hong-Yang Ma E-mail:hongyang_ma@aliyun.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132 and 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and Shandong Province Higher Educational Science and Technology Program, China (Grant No. J18KZ012).

Effects of initial states on the quantum correlations in the generalized Grover search algorithm

Zhen-Yu Chen(陈祯羽)¹, Tian-Hui Qiu(邱田会)¹, Wen-Bin Zhang(张文彬)², and Hong-Yang Ma(马鸿洋)^1,†

1 School of Science, Qingdao University of Technology, Qingdao 266033, China;
2 School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China

Received:2021-04-07 Revised:2021-05-17 Accepted:2021-05-27 Online:2021-07-16 Published:2021-07-23
Contact: Hong-Yang Ma E-mail:hongyang_ma@aliyun.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132 and 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and Shandong Province Higher Educational Science and Technology Program, China (Grant No. J18KZ012).

摘要/Abstract

摘要： We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation. Using a set of suitable bases, we construct the reduced density matrix and give the numerical expression of correlations relating to the iterations. For different initial states, we obtain the concurrence and quantum discord compared with the success probability in the algorithm. The results show that the initial states affect the correlations and the limit point of the correlations in the searching process. However, the initial states do not influence the whole cyclical trend.

关键词: Grover search algorithm, quantum correlations, initial states, the success probability

Abstract: We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation. Using a set of suitable bases, we construct the reduced density matrix and give the numerical expression of correlations relating to the iterations. For different initial states, we obtain the concurrence and quantum discord compared with the success probability in the algorithm. The results show that the initial states affect the correlations and the limit point of the correlations in the searching process. However, the initial states do not influence the whole cyclical trend.

Key words: Grover search algorithm, quantum correlations, initial states, the success probability

中图分类号: (Quantum algorithms, protocols, and simulations)

03.67.Ac

03.67.Hk (Quantum communication)

Zhen-Yu Chen(陈祯羽), Tian-Hui Qiu(邱田会), Wen-Bin Zhang(张文彬), and Hong-Yang Ma(马鸿洋). Effects of initial states on the quantum correlations in the generalized Grover search algorithm[J]. 中国物理B, 2021, 30(8): 80303-080303.

参考文献

[1] Shor P 1995 Phys. Rev. A 52 R2493
[2] Grover L 1996 Proceedings of the 28th Annual ACM Symposium on Theory of Computing (New York:ACM Press) p. 212
[3] Castagnoli G 2016 Found. Phys. 46 360
[4] Castagnoli G 2016 Quanta 5 34
[5] Li T, Zhang S, Fu X Q, Wang X, Wang Y, Lin J and Bao W S 2019 Chin. Phys. B 28 120301
[6] Jin S, Wu S, Zhou G, Li Y, Li L, Li B and Wang X 2020 Quantum Engineering 2 e49
[7] Li H S, Fan P, Xia H, Peng H and Long G L 2020 Sci. China. Phys. Mech. 63 280311
[8] Vidal G 2003 Phys. Rev. Lett. 91 147902
[9] Knill E and Laflamme R 1998 Phys. Rev. Lett. 81 5672
[10] Lanyon B P, Barbieri M, Almeida M P and White A G 2008 Phys. Rev. Lett. 101 200501
[11] Merali Z 2011 Nature 474 24
[12] Teng J K and Ma H Y 2019 IET Information Security 13 703
[13] Shi P, Li N C, Wang S M, Liu Z, Ren M R and Ma H Y 2019 Sensors 19 5257
[14] Yang H, Qin L G, Tian L J and Ma H Y 2020 Chin. Phys. B 29 040303
[15] He Z X, Fan X K, Chu P C and Ma H Y 2020 Acta Phys. Sin. 69 160301 (in Chinese)
[16] Chen G, Zhang W H, Yin P, Li C F and Guo G C 2021 Fundamental Research 1 27
[17] Li B M, Hu M L and Fan H 2019 Acta Phys. Sin. 68 030304 (in Chinese)
[18] Zhang C, Cao H, Huang Y F, Liu B H and Guo G C 2021 Fundamental Research 1 22
[19] Yan Z, Qin J L, Qin Z Z, Su X L and Peng K C 2021 Fundamental Research 1 43
[20] Bruβ D and Macchiavello C 2011 Phys. Rev. A 83 052313
[21] Bennett C H, Bernstein H J, Popescu S and Schumacher B 1996 Phys. Rev. A 53 2046
[22] Popescu S and Rohrlich D 1996 Phys. Rev. A 56 R3319
[23] Zhang M, Zhou L, Zhong W and Sheng Y B 2019 Chin. Phys. B 28 010301
[24] Holweck F, Jaffali H and Nounouh I 2016 Quantum Inf. Process. 15 4391
[25] Pan M H, Qiu D W and Zheng S G 2017 Quantum Inf. Process. 16 211
[26] Qu R, Shang B J, Bao Y R, Song D W, Teng C M and Zhou Z W 2015 Nat. Comput. 14 683
[27] Pan M H, Qiu D W, Mateus P and Gruska J 2018 Theoret. Comput. Sci. 733 138
[28] Shimoni Y, Shapira D and Biham O 2003 Phys. Rev. A 69 666
[29] Cui J and Fan H 2010 J. Phys. A-Math Theor. 43 045305
[30] Batle J, Raymond Ooi C H, Farouk A, Alkhambash M S and Abdalla S 2016 Quantum Inf. Process 15 833
[31] Rossi M, Bruβ D and Macchiavello C 2013 Phys. Rev. A 87 022331
[32] Rungta P 2009 Phys. Lett. A 373 2652
[33] Chakraborty S, Banerjee S, Adhikari S and Kumar A 2013 Quantum Phys. 1305 4454
[34] Bruβ D 2002 J. Math. Phys. 43 4237
[35] Eltschka C and Siewert J 2014 J. Phys. A Math. Theor 47 424005
[36] Zhang S S, Qi S, Zhou L and Sheng Y B 2017 Chin. Phys. B 26 060307
[37] Jozsa R and Linden N 2003 Proc. R. Soc. Lond. A 459 2011
[38] Wootters W K 1998 Phys. Rev. Lett 80 2245
[39] Fang Y Y, Kaszlikowski D, Chin C M, Tay K, Kwek L C and Oh C H 2005 Phys. Lett. A 345 265
[40] Long G L 2001 Phys. Rev. A 64 022307
[41] Long G L, Li X and Sun Y 2002 Phys. Lett. A 294 143
[42] Toyama F M, Dijk W V and Nogami Y 2013 Quantum Inf. Process 12 1897
[43] Biham E, Biham O, Biron D, Grassl M, Lidar D A and Shapira D 2000 Phys. Rev. A 63 5384
[44] Zhu S, Liu C Y, Zhao B K, Zhou L, Zhong W and Sheng Y B 2020 Europhys. Lett. 129 50004
[45] Sheng Y B, Guo R, Pan J, Zhou L and Wang X F 2015 Quantum Inf. Process 14 963
[46] Zhou L and Sheng Y B 2014 Phys. Rev. A 90 024301
[47] Groisman B, Popescu S and Winter A 2005 Phys. Rev. A 72 032317
[48] Henderson L and Vedral V 2000 Phys. Rev. Lett. 84 2263

Effects of initial states on the quantum correlations in the generalized Grover search algorithm

Effects of initial states on the quantum correlations in the generalized Grover search algorithm

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