Implementation of a one-dimensional quantum walk in both position and phase spaces

doi:10.1088/1674-1056/23/1/010301

Abstract Quantum walks have been investigated as they have remarkably different features in contrast to classical random walks. We present a quantum walk in a one-dimensional architecture, consisting of two coins and a walker whose evolution is in both position and phase spaces alternately controlled by the two coins respectively. By analyzing the dynamics evolution of the walker in both the position and phase spaces, we observe an influence on the quantum walk in one space from that in the other space, which behaves like decoherence. We propose an implementation of the two-coin quantum walk in both position and phase spaces via cavity quantum electrodynamics (QED).

Keywords: quantum walks cavity quantum electrodynamics

Received: 29 June 2013
Revised: 28 August 2013
Accepted manuscript online:

PACS:	03.67.Ac	(Quantum algorithms, protocols, and simulations)
	42.50.Pq	(Cavity quantum electrodynamics; micromasers)
	74.50.+r	(Tunneling phenomena; Josephson effects)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11004029 and 11174052), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010422), the Ph.D. Program of the Ministry of Education of China, the Excellent Young Teachers Program of Southeast University, China, the National Basic Research Program of China (Grant No. 2011CB921203), and the Open Fund from the State Key Laboratory of Precision Spectroscopy of East China Normal University, China.

Corresponding Authors: Xue Peng
E-mail: gnep.eux@gmail.com

Cite this article:

Qin Hao (秦豪), Xue Peng (薛鹏) Implementation of a one-dimensional quantum walk in both position and phase spaces 2014 Chin. Phys. B 23 010301

[1]	Ambainis A 2003 Int. J. Quantum Inf. 1 507
[2]	Childs A M, Cleve R, Deotto E, Farhi E, Gutmann S and Spielman D A 2003 Proc. 35th ACM Symposium on Theory of Computing, pp. 59–68
[3]	Shenvi N, Kempe J and Whaley K B 2003 Phys. Rev. A 67 052307
[4]	Kempe J 2003 Contemp. Phys. 44 307
[5]	Brun T A, Carteret H A and Ambainis A 2003 Phys. Rev. Lett. 91 130602
[6]	Kitagawa T, Rudner M S, Berg E and Demler E 2010 Phys. Rev. A 82 033429
[7]	Oliveira A C, Portugal R and Donangelo R 2006 Phys. Rev. A 74 012312
[8]	Xue P and Wu J Z 2012 Chin. Phys. B 21 010308
[9]	Xue P 2012 Chin. Phys. B 21 100306
[10]	Xue P 2011 Chin. Phys. B 20 100310
[11]	Childs A M 2009 Phys. Rev. Lett. 102 180501
[12]	Childs A M, Gosset D and Webb Z 2013 Science 339 791
[13]	Cote R, Russell A, Eyler E E and Gould P L 2006 New J. Phys. 8 156
[14]	Zähringer F, Kirchmair G, Gerritsma R, Solano E, Blatt R and Roos C F 2010 Phys. Rev. Lett. 104 100503
[15]	Schmitz H, Matjeschk R, Schneider C, Glueckert J, Enderlein M, Huber T and Schaetz T 2009 Phys. Rev. Lett. 103 090504
[16]	Karski M, Forster L, Choi J M, Steffen A, Alt W, Meschede D and Widera A 2009 Science 325 174
[17]	Du J, Li H, Xu X, Shi M, Wu J, Zhou X and Han R 2003 Phys. Rev. A 67 042316
[18]	Peruzzo A, Lobino M, Matthews J C F, Matsuda N, Politi A, Poulios K, Zhou X, Lahini Y, Ismail N, Worhoff K, Bromberg Y, Silberberg Y, Thompson M G and O’Brien J L 2010 Science 329 1500
[19]	Perets H B, Lahini Y, Pozzi F, Sorel M, Morandotti R and Silberberg Y 2008 Phys. Rev. Lett. 100 170506
[20]	Schreiber A, Gábris A, Rohde P P, Laiho K, Štefaňák M, Potoček V, Hamilton C, Jex I and Silberhorn C 2012 Science 336 55
[21]	Broome M A, Fedrizzi A, Lanyon B P, Kassal I, Aspuru-Guzik A and White A G 2010 Phys. Rev. Lett. 104 153602
[22]	Schreiber A, Cassemiro K N, Potoček V, Gábris A, Mosley P J, Andersson E, Jex I and Silberhorn C 2010 Phys. Rev. Lett. 104 050502
[23]	Sansoni L, Sciarrino F, Vallone G, Mataloni P, Crespi A, Ramponi R and Osellame R 2012 Phys. Rev. Lett. 108 010502
[24]	Xue P and Sanders B C 2008 New J. Phys. 10 053025
[25]	Xue P, Sanders B C and Leibfried D 2009 Phys. Rev. Lett. 103 183602
[26]	Xue P, Sanders B C, Blais A and Lalumiére K 2008 Phys. Rev. A 78 042334
[27]	Xue P and Sanders B C 2013 Phys. Rev. A 87 022334
[28]	Xue P and Zhang Y S 2013 Chin. Phys. B 22 070302
[29]	Xu Y Y, Zhou F, Chen L, Xie Y, Xue P and Feng M 2012 Chin. Phys. B 21 040304
[30]	Sanders B C, Bartlett S D, Tregenna B and Knight P L 2003 Phys. Rev. A 67 042305
[31]	Xue P 2013 J. Comput. Theor. Nanosci. 10 1606
[32]	Pellizzari T, Gardiner S A, Cirac J I and Zoller P 1995 Phys. Rev. Lett. 75 3788
[33]	Imamoglu A, Awschalom D D, Burkard G, DiVincenzo D P, Loss D, Sherwin M and Small A 1999 Phys. Rev. Lett. 83 4204
[34]	Zheng S B and Guo G C 2000 Phys. Rev. Lett. 85 2392
[35]	Xiao Y F, Lin X M, Gao J, Yang Y, Han Z F and Guo G C 2004 Phys. Rev. A 70 042314
[36]	Xue P, Ficek Z and Sanders B C 2012 Phys. Rev. A 86 043826
[37]	Xue P 2010 Chin. Phys. Lett. 27 060301
[38]	Xue P and Xiao Y F 2006 Phys. Rev. Lett. 97 140501
[39]	Xiao Y F, Zou C L, Xue P, Xiao L X, Li Y, Dong C H, Han Z F and Gong Q H 2010 Phys. Rev. A 81 053807
[40]	Xue P, Han C, Yu B, Lin X M and Guo G C 2004 Phys. Rev. A 69 052318
[41]	Xiao Y F, Han Z F, Gao J and Guo G C 2006 J. Phys. B 39 485
[42]	Chen C Y, Zhang X L, Deng Z J, Gao K L and Feng M 2006 Phys. Rev. A 74 032328

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