|
|
|
Realization of quantum permutation algorithm in high dimensional Hilbert space |
| Dong-Xu Chen(陈东旭)1, Rui-Feng Liu(刘瑞丰)1, Pei Zhang(张沛)1,2, Yun-Long Wang(王云龙)1, Hong-Rong Li(李宏荣)1, Hong Gao(高宏)1, Fu-Li Li(李福利)1 |
1 Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an 710049, China;
2 Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China |
|
|
|
|
Abstract Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light's orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light's orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup.
|
Received: 05 January 2017
Revised: 24 March 2017
Accepted manuscript online:
|
|
PACS:
|
03.67.Ac
|
(Quantum algorithms, protocols, and simulations)
|
| |
03.67.-a
|
(Quantum information)
|
| |
42.50.-p
|
(Quantum optics)
|
|
| Fund: Project supported by the Fundamental Research Funds for the Central Universities and the National Natural Science Foundation of China (Grant Nos. 11374008, 11374238, 11374239, and 11534008). |
Corresponding Authors:
Pei Zhang
E-mail: zhangpei@mail.ustc.edu.cn
|
Cite this article:
Dong-Xu Chen(陈东旭), Rui-Feng Liu(刘瑞丰), Pei Zhang(张沛), Yun-Long Wang(王云龙), Hong-Rong Li(李宏荣), Hong Gao(高宏), Fu-Li Li(李福利) Realization of quantum permutation algorithm in high dimensional Hilbert space 2017 Chin. Phys. B 26 060305
|
| [1] |
Feynman R P 1982 Int. J. Theor. Phys. 21 467
|
| [2] |
Montanaro A 2016 npj Quantum Information 2 15023
|
| [3] |
Deutsch D 1985 Proc. R. Soc. Lond. A 400 97
|
| [4] |
Jozsa R and Deutsch D 1994 Proc. R. Soc. A 439 553
|
| [5] |
Zhang P, Liu R F, Huang Y F, Gao H and Li F L 2012 Phys. Rev. A 82 064302
|
| [6] |
Shor P W 1994 IEEE Comp. Soc. 11 124
|
| [7] |
Martin-Lopez E, Laing A, Lawson T, Alvarez R, Zhou X Q and O'Brien J L 2012 Nat. Photon. 6 773
|
| [8] |
Grover L K 1997 Phys. Rev. Lett. 79 325
|
| [9] |
Li T, Bao W, Lin W, Zhang H and Fu X 2014 Chin. Phys. Lett. 31 050301
|
| [10] |
Zhang Y, Bao W, Wang X and Fu X 2015 Chin. Phys. B 24 110309
|
| [11] |
Lloyd S 1996 Science 273 1073
|
| [12] |
Buluta I and Nori F 2009 Science 326 108
|
| [13] |
Harrow A W, Hassidim A and Lloyd S 2009 Phys. Rev. Lett. 103 150502
|
| [14] |
Cai X D, Weedbrook C, Su Z E, Chen M C, Gu M, Zhu M J, Li L, Liu N L, Lu C Y and Pan J W 2013 Phys. Rev. Lett. 110 230501
|
| [15] |
Pan J, Cao Y, Yao X, Li Z, Ju C, Chen H, Peng X, Kais S and Du J 2014 Phys. Rev. A 89 022313
|
| [16] |
Bian Z, Chudak F, Israel R, Lackey B, Macready W G and Roy A 2016 arXiv: 1603.03111 [quan-ph]
|
| [17] |
Amin M 2015 Phys. Rev. A 92 052323
|
| [18] |
Howard M, Wallman J, Veitch V and Emerson J 2014 Nature 510 351
|
| [19] |
Gedik Z, Silva I A, Çakmak B, Karpat G, Gé Vidoto E L, Soares-Pinto D O, deAzevedo E R and Fanchini F F 2015 Sci. Rep. 5 14671
|
| [20] |
Dogra S, Arvind and Dorai K 2014 Phys. Lett. A 378 3452
|
| [21] |
Zhan X, Li J, Qin H, Bian Z and Xue P 2015 Opt. Express 23 18422
|
| [22] |
Wang F, Wang Y, Liu R, Chen D, Zhang P, Gao H and Li F 2015 Sci. Rep. 5 10995
|
| [23] |
Nielsen M A and Chuang I L 2013 2000 Quantum computation and quantum information (Cambridge: Cambridge University Press)
|
| [24] |
Mirhosseini M, Mangna-Loaiza O S, Chen C, Rodenburg B, Malik M and Boyd R W Opt. Express 21 30196
|
| [25] |
Nagali E, Sciarrino F, De Martini F, Marrucci L, Piccirillo B, Karimi E and Santamato E 2009 Phys. Rev. Lett. 103 013601
|
| [26] |
Mair A, Vaziri A, Weihs G and Zeilinger A 2001 Nature 412 313
|
| [27] |
Xu Y, Huang Y, Hu L, Zhang P, Wei D, Li H, Gao H and Li F 2013 Chin. Phys. Lett. 30 100304
|
| [28] |
Liu R, Zhang P, Gao H and Li F 2012 Chin. Phys. Lett. 29 124203
|
| [29] |
Wang L, Zhao S, Gong L and Cheng W 2015 Chin. Phys. B 24 120307
|
| [30] |
Allen L, Beijersbergen M W, Spreeuw R J C and Woerdman J P 1992 Phys. Rev. A 45 8185
|
| [31] |
Leach J, Padgett M J, Barnett S M, Franke-Arnold S and Courtial J 2002 Phys. Rev. Lett. 88 257901
|
| [32] |
Fu D, Jia J, Zhou Y, Chen D, Gao H, Li F and Zhang P 2015 Acta Phys. Sin 64 130704 (in Chinese)
|
| [33] |
Schlederer F, Krenn M, Fickler R, Malik M and Zeilinger A 2016 New J. Phys. 18 043019
|
| [34] |
Krenn M, Malik M, Fickler R, Lapkiewicz R and Zeilinger A 2016 Phys. Rev. Lett. 116 090405
|
| 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
|
|
|
