|
|
|
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 |
|
|
|
|
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.
|
Received: 07 April 2021
Revised: 17 May 2021
Accepted manuscript online: 27 May 2021
|
|
PACS:
|
03.67.Ac
|
(Quantum algorithms, protocols, and simulations)
|
| |
03.67.Hk
|
(Quantum communication)
|
|
| Fund: 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). |
Corresponding Authors:
Hong-Yang Ma
E-mail: hongyang_ma@aliyun.com
|
Cite this article:
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 2021 Chin. Phys. B 30 080303
|
[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 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
