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Average position in quantum walks with a U(2) coin |
Li Min (李敏), Zhang Yong-Sheng (张永生), Guo Guang-Can (郭光灿) |
Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Science, Hefei 230026, China |
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Abstract We investigated discrete-time quantum walks with an arbitary unitary coin. Here we discover that the average position〈x〉=max(〈x〉)sin(α+γ), while the initial state is 1/√2(|0L〉+ i|0R〉). We verify the result, and obtain some symmetry properties of quantum walks with a U(2) coin with |0L〉 and |0R〉 as the initial state.
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Received: 01 November 2012
Revised: 30 November 2012
Accepted manuscript online:
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PACS:
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03.65.Yz
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(Decoherence; open systems; quantum statistical methods)
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03.67.-a
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(Quantum information)
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03.67.Ac
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(Quantum algorithms, protocols, and simulations)
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Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10974192 and 61275122), the National Basic Research Program of China (Grant Nos. 2011CB921200 and 2011CBA00200), and K. C. Wong Education Foundation and the Chinese Academy of Sciences. |
Corresponding Authors:
Zhang Yong-Sheng
E-mail: yszhang@ustc.edu.cn
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Cite this article:
Li Min (李敏), Zhang Yong-Sheng (张永生), Guo Guang-Can (郭光灿) Average position in quantum walks with a U(2) coin 2013 Chin. Phys. B 22 030310
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[1] |
Aharonov Y, Davidovich L and Zagury N 1993 Phys. Rev. A48 1687
|
[2] |
Farhi E and Gutmann S 1998 Phys. Rev. A58 915
|
[3] |
Childs A M 2009Phys. Rev. Lett. 102 180501
|
[4] |
Lovett N B, Cooper S, Everitt M, Trevers M and Kendon V 2010 Phys. Rev. A81 042330
|
[5] |
Childs A M, Cleve R, Deotto E, Farhi E,Gutmann S and Spielman D A 2003 Proceedings of the 35th ACM Symposiumon Theory of Computing (New York: ACM Press) p.59
|
[6] |
Shenvi N, Kempe J and Whaley K B 2003Phys. Rev. A 67 052307
|
[7] |
Childs A M, Farhi E and Gutmann S 2002 Quantum InformationProcessing 1 35
|
[8] |
Childs A M and Goldstone J 2004 Phys. Rev. A70 022314
|
[9] |
Ambainis A 2003 Int. J. Quantum Inform. 1 507
|
[10] |
Ambainis A and Kempe J 2005 Proceedingsof the 16th ACM-SIAM Symposium on Discrete Algorithms p.1099
|
[11] |
Aharonov D, Ambainis A, Kempe J and Vazirani U 2001 Proceedings of the Thirty-third Annual ACM Symposium on Theory of Computingp.50
|
[12] |
Kwek L C and Setiawan 2011Phys. Rev. A 84 032319
|
[13] |
Brun T A, Carteret H A and Ambainis A 2003 Phys. Rev. A67 052317
|
[14] |
Brun T A, Carteret H A and Ambainis A 2003 Phys. Rev. A67 032304
|
[15] |
Chandrashekar C M, Srikanth R and Laflamme R 2008 Phy. Rev. A77 032306
|
[16] |
Nayak A and Vishwanath A 2000 Technical Report,Center for Discrete Mathematics & Theoretical Computer Science
|
[17] |
Tregenna B, Flanagan W, Maile R and Kendon V 2003 New J. Phys.5 83
|
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