Nuclear magnetic resonance for quantum computing: Techniques and recent achievements

doi:10.1088/1674-1056/27/2/020308

Abstract

Rapid developments in quantum information processing have been made, and remarkable achievements have been obtained in recent years, both in theory and experiments. Coherent control of nuclear spin dynamics is a powerful tool for the experimental implementation of quantum schemes in liquid and solid nuclear magnetic resonance (NMR) system, especially in liquid-state NMR. Compared with other quantum information processing systems, the NMR platform has the advantages such as the long coherence time, the precise manipulation, and well-developed quantum control techniques, which make it possible to accurately control a quantum system with up to 12-qubits. Extensive applications of liquid-state NMR spectroscopy in quantum information processing such as quantum communication, quantum computing, and quantum simulation have been thoroughly studied over half a century. This article introduces the general principles of NMR quantum information processing, and reviews the new-developed techniques. The review will also include the recent achievements of the experimental realization of quantum algorithms for machine learning, quantum simulations for high energy physics, and topological order in NMR. We also discuss the limitation and prospect of liquid-state NMR spectroscopy and the solid-state NMR systems as quantum computing in the article.

Keywords: nuclear magnetic resonance quantum control techniques machine learning topological quantum computing

Received: 21 November 2017
Revised: 14 January 2018
Accepted manuscript online:

PACS:	03.65.-w	(Quantum mechanics)
	03.67.Ac	(Quantum algorithms, protocols, and simulations)
	03.67.Lx	(Quantum computation architectures and implementations)

Fund:

Project supported by the National Natural Science Foundation of China (Grants Nos. 11175094 and 91221205) and the National Basic Research Program of China (Grant No. 2015CB921002).

Corresponding Authors: Gui-Lu Long
E-mail: gllong@mail.tsinghua.edu.cn

About author: 03.65.-w; 03.67.Ac; 03.67.Lx

Cite this article:

Tao Xin(辛涛), Bi-Xue Wang(王碧雪), Ke-Ren Li(李可仁), Xiang-Yu Kong(孔祥宇), Shi-Jie Wei(魏世杰), Tao Wang(王涛), Dong Ruan(阮东), Gui-Lu Long(龙桂鲁) Nuclear magnetic resonance for quantum computing: Techniques and recent achievements 2018 Chin. Phys. B 27 020308

[1]	Bennett C H and DiVincenzo D P 2000 Nature 404 6775
[2]	Schwindt P D D, Kwiat P G and Englert B G 1999 Phys. Rev. A 60 4285
[3]	Long G L 2006 Commun. Theor. Phys. 45 825
[4]	Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[5]	Guo R, Zhou L, Gu S P, et al. 2016 Chin. Phys. B 25 030302
[6]	Friedman J R, Patel V, Chen W, Tolpygo S K and Lukens J E 2000 Nature 406 6791
[7]	Li T and Yin Z Q 2016 Sci. Bull. 61 163
[8]	Benioff P 1980 J. Stat.Phys. 22 563
[9]	Deutsch D 1985 Proc. R. Soc. Lond. A 400 97
[10]	Feynman R P 1982 Int. J. Theor. Phys. 21 476
[11]	Deng F G, Long G L and Liu X S 2003 Phys. Rev. A 68 042317
[12]	Deng F G and Long G L 2004 Phys. Rev. A 69 052319
[13]	Zhao X L, Li J L, Niu P H, et al. 2017 Chin. Phys. B 26 030302
[14]	Yan C, Shi Z, Li Y, et al. 2016 Chin. Phys. B 24 050307
[15]	Shor P W 1999 SIAM Rev. 41 303
[16]	Knill E 2010 Nature 463 441
[17]	Ahn J, Weinacht T C and Bucksbaum P H 2000 Science 287 5452
[18]	DiVincenzo D P 2000 arXiv:0002077[quant-ph]
[19]	Jones J A, Vedral V, Ekert A and Castagnoli G 1999 arXiv:9910052[quant-ph]
[20]	Shnirman A, Schon G and Hermon Z 1997 Phys. Rev. Lett. 79 2371
[21]	Chiorescu I, Nakamura Y, Harmans C M and Mooij J E 2003 Science 299 56141869
[22]	Cirac J I and Zoller P 1995 Phys. Rev. Lett. 74 4091
[23]	Kielpinski D, Monroe C and Wineland D J 2002 Nature 417 709
[24]	Imamog A, Awschalom D D, Burkard G, DiVincenzo D P, Loss D, Sherwin M and Small A 1999 Phys. Rev. Lett. 83 4204
[25]	Pellizzari T, Gardiner S A, Cirac J I and Zoller P 1995 Phys. Rev. Lett. 75 3788
[26]	Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P and Milburn G J 2007 Rev. Mod. Phys. 79 135
[27]	Obrien J L 2007 Science 318 1567
[28]	Li A X, Duan S Q and Zhang W 2016 Chin. Phys. B 25 108506
[29]	Loss D and DiVincenzo D P 1998 Phys. Rev. A 57 120
[30]	Petta J R, Johnson A C, Taylor J M, Laird E A, Yacoby A, Lukin M D and Gossard A C 2007 Science 309 2180
[31]	Rigden J S 1986 Rev. Mod. Phys. 58 433
[32]	Chuang I L, Gershenfeld N, Kubinec M G and Leung D W 1998 Proc. R. Soc. Lond. A 454 447
[33]	Knill E and Laflamme R 1998 Phys. Rev. Lett. 81 5672
[34]	Cory D G, Fahmy A F and Havel T F 1997 Proc. R. Soc. A 94 1634
[35]	Cory D G, Laflamme R, Knill E, Viola L, Havel T F and Boulant N 2000 Fortschritte der Physik 48 875
[36]	Cory D G, Price M D and Havel T F 1998 Physica D 120 82
[37]	Vandersypen L M and Chuang I L 2005 Rev. Mod. Phys. 76 1037
[38]	Zhen X L, Xin T, Zhang F H and Long G L 2016 Sci. China-Phys., Mech. & Astron. 59 690312
[39]	Pan X Y 2016 Sci. China-Phys., Mech. & Astron. 60 020333
[40]	Brown K R, Harrow A W and Chuang I L 2004 Phys. Rev. A 70 052318
[41]	Alway W G and Jones J A 2007 Phys. Rev. A 189 114
[42]	Fung B M, Khitrin A K and Ermolaev K 2000 J. Magn. Reson. 142 97
[43]	Waugh J S, Huber L M and Haeberlen U 1968 Phys. Rev. Lett. 20 180
[44]	Shaka A J, Keeler J, Frenkiel T and Freeman R A Y 1983 J. Magn. Reson. 52 335
[45]	Viola L, Knill E and Lloyd S 1999 Phys. Rev. Lett. 82 2417
[46]	Souza A M, Alvarez G A and Suter D 2011 Phys. Rev. Lett. 106 240501
[47]	Zhen X L, Zhang F H, Feng G, Li, H and Long G L 2016 Phys. Rev. A 93 022304
[48]	Zhang J, Souza A M, Brandao F D and Suter D 2014 Phys. Rev. Lett. 112 050502
[49]	West J R, Lidar D A, Fong B H and Gyure M F 2010 Phys. Rev. Lett. 105 230503
[50]	Aharonov D, Van Dam,W, Kempe J, Landau Z, Lloyd S and Regev O 2008 SIAM Rev. 50 755
[51]	Childs A M, Farhi E and Preskill J 2001 Phys. Rev. A 65 012322
[52]	Gaitan F and Clark L 2012 Phys. Rev. Lett. 108 010501
[53]	Stoustrup J, Schedletzky O, Glaser S J, Griesinger C, Nielsen N C and Sorensen O W 1995 Phys. Rev. Lett. 74 2921
[54]	Fortunato E M, Pravia M A, Boulant N, Teklemariam G, Havel T F and Cory D G 2002 J. Chem. Phys. 116 7599
[55]	Boulant N, Edmonds K, Yang J, Pravia M A and Cory D G 2002 Phys. Rev. A 68 032305
[56]	Khaneja N, Reiss T, Kehlet C, Schulte-Herbruggen T and Glaser S J 2005 J. Magn. Reson. 172 296
[57]	Li J, Yang X, Peng X and Sun C P 2016 arXiv:1608.00677
[58]	Lu D, Li K, Li J, Katiyar H, Park A J and Feng G 2017 arXiv:1701.01198
[59]	Rebentrost P, Schuld M, Petruccione F and Lloyd S 2016 arXiv:1612.01789
[60]	Egger D J and Wilhelm F K 2014 Supercond. Sci. & Technol. 27 014001
[61]	Ryan C A, Negrevergne C, Laforest M, Knill E and Laflamme R 2008 Phys. Rev. A 78 012328
[62]	Knill E, Laflamme R, Martinez R and Tseng C H 2000 Nature 404 368
[63]	Li J, Cui J, Laflamme R and Peng X 2016 Phys. Rev. A 94 032316
[64]	Xin T, Lu D, Klassen J, Yu N, Ji Z and Chen J 2017 Phys. Rev. Lett. 118 020401
[65]	Jonathan A. Jones J A, Mosca M and Hansen R H 1998 Nature 393 344
[66]	Long G L 2001 Phys. Rev. A 64 022307
[67]	Liu Y and Zhang F 2015 Sci. China-Phys., Mech. & Astron. 58 1
[68]	Vandersypen L M, Steffen M, Breyta G, Yannoni C S, Sherwood M H and Chuang I L 2001 Nature 414 883
[69]	Chuang I L, Vandersypen L M K, Zhou X, Leung D W and Lloyd S 1998 Nature 393 143
[70]	Vandersypen L M, Steffen M, Breyta G, Yannoni C S, Cleve R and Chuang I L 2000 Phys. Rev. Lett. 85 5452
[71]	Peng X, Zhu X, Fang X, Feng M, Liu M and Gao K 2002 Phys. Rev. A 65 042315
[72]	Pan J, Cao Y, Yao X, Li Z, Ju C and Chen H 2014 Phys. Rev. A 89 022313
[73]	Georgescu I M, Ashhab S and Nori F 2014 Rev. Mod. Phys. 86 153
[74]	Zhang J, Long G L, Deng Z, Liu W and Lu Z 2004 Phys. Rev. A 70 062322
[75]	Du J, Xu N, Peng X, Wang P, Wu S and Lu D 2010 Phys. Rev. Lett. 104 030502
[76]	Peng X, Zhang J, Du J and Suter D 2009 Phys. Rev. Lett. 103 140501
[77]	Alvarez G A and Suter D 2010 Phys. Rev. Lett. 104 230403
[78]	Alvarez G A, Suter D and Kaiser R 2015 Science 349 846
[79]	Peng X, Du J and Suter D 2005 Phys. Rev. A 71 012307
[80]	Zhang J, Peng X, Rajendran N and Suter D 2008 Phys. Rev. Lett. 100 100501
[81]	Feng G R, Lu Y, Hao L, Zhang F H and Long G L 2013 Sci. Rep. 3
[82]	Zheng C, Hao L and Long G L 2013 Phil. Trans. R. Soc. A 371 20120053
[83]	Nielsen M A, Knill E and Laflamme R 1998 Nature 396 52
[84]	Fang X, Zhu X, Feng M, Mao X A and Du F 2000 Phys. Rev. A 61 022307
[85]	Roy S S, Shukla A and Mahesh T S 2012 Phys. Rev. A 85 022109
[86]	Souza A M, Magalhaes A, Teles J, Bonagamba T J, Oliveira I S and Sarthour R S 2008 New J. Phys. 10 033020
[87]	Souza A M, Oliveira I S and Sarthour R S 2011 New J. Phys. 13 053023
[88]	Xin T, Li H, Wang B X and Long G L 2015 Phys. Rev. A 92 022126
[89]	Wei S J and Long G L 2016 Quantum Inf. Process. 15 1189
[90]	Hou S Y, Li H and Long G L 2015 Sci. Bull. 62 497
[91]	Li H, Gao X, Xin T, Yung M H and Long G L 2015 Sci. Bull. 62 497
[92]	Lu D, Li H, Trottier D A, Li J, Brodutch A and Krismanich A P 2015 Phys. Rev. Lett. 114 140505
[93]	Lu D, Xin T, Yu N, Ji Z, Chen J and Long G 2016 Phys. Rev. Lett. 116 230501
[94]	Feng G, Xu G and Long G 2013 Phys. Rev. Lett. 110 190501
[95]	Li H, Liu Y and Long G 2017 Sci. China-Phys., Mech. & Astron. 60 080311
[96]	Levitt M H 2008 Spin Dynamics:Basics of NMR
[97]	Suter D and Mahesh T S 2008 J. Chem. Phys. 128 052206
[98]	Wiseman H M and Milburn G J 2009 Quantum Measurement and Control (Cambridge:Cambridge University Press)
[99]	Nielsen M and Chuang I 2000 Quantum Information and Computation
[100]	Mansfield P 1970 Phys. Lett. A 32 485
[101]	Khodjasteh K, Sastrawan J, Hayes D, et al. 2013 Nat. Commun. 4
[102]	Biercuk M J, Doherty A C and Uys H 2011 J. Phys. B:At. Mol. Opt. Phys. 44 154002
[103]	Hahn E L 1950 Phys. Rev. 80 580
[104]	Viola L and Lloyd S 1998 Phys. Rev. A 58 2733
[105]	Carr H Y and Purcell E M 1954 Phys. Rev. 94 630
[106]	Meiboom S and Gill D 1958 Rev. Sci. Instrum. 29 688
[107]	Uhrig G S 2007 Phys. Rev. Lett. 98 100504
[108]	Uhrig G S 2008 New J. Phys. 10 083024
[109]	Du J, Rong Z, Zhao N, Wang Y, Yang J and Liu R 2009 Nature 461 1265
[110]	Biercuk M J, Uys H, VanDevender A P, et al. 2009 Nature 458 996
[111]	Biercuk M J, Uys H, VanDevender A P, et al. 2009 Phys. Rev. A 79 062324
[112]	Khodjasteh K and Lidar D 2005 Phys.Rev. Lett. 95 180501
[113]	West J R, Fong B H and Lidar D A 2010 Phys. Rev. Lett. 104 130501
[114]	Kuo W and Lidar D A 2011 Phys. Rev. A 84 042329
[115]	Jiang L and Imambekov A 2011 Phys. Rev. A 84 060302
[116]	Ai Q, Yen T, Jin B and Cheng Y 2013 J. Phys. Chem. Lett. 4 2577
[117]	Jing J, Wu L, Yu T, You J, Wang Z and Garcia L 2014 Phys. Rev. A 89 032110
[118]	Soare A, Ball H, Hayes D, Sastrawan J, Jarratt M C, McLoughlin J J, Zhen X, Green T J and Biercuk M J 2014 Nat. Phys. 10 825
[119]	Soare A, Ball H, Hayes D, Zhen X, Jarratt M C, Sastrawan J, Uys H and Biercuk M J 2014 Phys. Rev. A 89 042329
[120]	Shor P W 1999 SIAM Rev. 41 303
[121]	Lu C Y, Browne D E, Yang T and Pan J W 2007 Phys. Rev. Lett. 99 250504
[122]	Lanyon B P, Weinhold T J, Langford N K, Barbieri M, James D F V, Gilchrist A and White A G 2007 Phys. Rev. Lett. 99 250505
[123]	Politi A, Matthews J C and Obrien J L 2009 Science 325 1221
[124]	Monz T, Nigg D, Martinez E A, Brandl M F, Schindler P and Rines R 2016 Science 351 1068
[125]	Shor P W 2012 Nat. Photon. 6 773
[126]	Xu N, Zhu J, Lu D, Zhou X, Peng X and Du J 2012 Phys. Rev. Lett. 108 130501
[127]	Martin-Lopez E, Laing A, Lawson T, Alvarez R, Zhou X Q and Obrien J L 2009 Phys. Rev. Lett. 103 150502
[128]	Harrow A W, Hassidim A and Lloyd S 2009 Phys. Rev. Lett. 103 150502
[129]	Michalski R S, Carbonell J G and Mitchell T M 2015 Contemporary Physics 56 172
[130]	Schuld M, Sinayskiy I and Petruccione F 2015 Contemporary Physics 56 172
[131]	Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N and Lloyd S 2015 Quantum Inf. Comput. 15
[132]	Lloyd S, Mohseni M and Rebentrost P 2013 arXiv:1307.0411[quantph]
[133]	Wiebe N, Kapoor A and Svore K M 2015 Quantum Inf. Comput. 15
[134]	Cai X D, Wu D, Su Z E, Chen M C, Wang X L and Li L 2015 Phys. Rev. Lett. 114 110504
[135]	Dunjko V, Taylor J M and Briegel H J 2016 Phys. Rev. Lett. 117 130501
[136]	Rebentrost P, Mohseni M and Lloyd S 2014 Phys. Rev. Lett. 113 130503
[137]	Li Z, Liu X, Xu N and Du J 2015 Phys. Rev. Lett. 114 140504
[138]	Gershenfeld N A and Chuang I L 1997 Science 275 350
[139]	Lu Y, Feng G R, Li Y S and Long G L 2015 Sci. Bull. 60 241
[140]	Pearson J, Feng G, Zheng C and Long G 2015 Sci. China-Phys., Mech. & Astron. 59 120312
[141]	Jin F, Chen H, Rong X, Zhou H, Shi M and Zhang Q 2015 Sci. China-Phys., Mech. & Astron. 59 630302
[142]	Lu D, Xu N, Xu R, Chen H, Gong J, Peng X and Du J 2011 Phys. Rev. Lett. 107 020501
[143]	Alvarez-Rodriguez U, Sanz M, Lamata L and Solano E 2016 Sci. Rep. 6
[144]	Alvarez-Rodriguez U, Sanz M, Lamata L and Solano E 2014 Sci. Rep. 4
[145]	Nayak C, Simon S H, Stern A, Freedman M and Sarma S D 2008 Rev. Mod. Phys. 80 1083
[146]	Kitaev A Y 2003 Ann. Phys. 303 2
[147]	Park A J, McKay E, Lu D and Laflamme R 2016 New J. Phys. 18 043043
[148]	Li J, Fan R, Wang H, Ye B, Zeng B and Zhai H 2017 Phys. Rev. X 7 031011
[149]	Swingle B, Bentsen G, Schleier-Smith M and Hayden P 2016 Phys. Rev. A 94 040301
[150]	Li K, Wan Y, Hung L Y, Lan T, Long G and Lu D 2017 Phys. Rev. Lett. 118 080502
[151]	Luo Z, Li J, Li Z, Hung L Y, Wan Y, Peng X and Du J 2016 arXiv:1608.06978[quant-ph]
[152]	Martinez E A, Muschi C A, Schindler P, Nigg D, Erhard A, Heyl M, Hauke P, Dalmonte M, Monz T, Zoller P and Blatt R 2016 Nature 534 516
[153]	Li K, Han M, Long G, Wan Y, Lu D, Zeng B and Laflamme R 2017 arXiv:1705.00365[quant-ph]
[154]	Maldacena J, Shenker S H and Stanford D 2016 J. High Energy Phys. 2016 106
[155]	Hosur P, Qi X L, Roberts D A and Yoshida B 2016 J. High Energy Phys. 2016 4
[156]	Sachdev S and Ye J 1993 Phys. Rev. Lett. 70 3339
[157]	Ryu S and Takayanagi T 2006 Phys. Rev. Lett. 96 181602

[1]	Prediction of lattice thermal conductivity with two-stage interpretable machine learning Jinlong Hu(胡锦龙), Yuting Zuo(左钰婷), Yuzhou Hao(郝昱州), Guoyu Shu(舒国钰), Yang Wang(王洋), Minxuan Feng(冯敏轩), Xuejie Li(李雪洁), Xiaoying Wang(王晓莹), Jun Sun(孙军), Xiangdong Ding(丁向东), Zhibin Gao(高志斌), Guimei Zhu(朱桂妹), Baowen Li(李保文). Chin. Phys. B, 2023, 32(4): 046301.
[2]	Variational quantum simulation of thermal statistical states on a superconducting quantum processer Xue-Yi Guo(郭学仪), Shang-Shu Li(李尚书), Xiao Xiao(效骁), Zhong-Cheng Xiang(相忠诚), Zi-Yong Ge(葛自勇), He-Kang Li(李贺康), Peng-Tao Song(宋鹏涛), Yi Peng(彭益), Zhan Wang(王战), Kai Xu(许凯), Pan Zhang(张潘), Lei Wang(王磊), Dong-Ning Zheng(郑东宁), and Heng Fan(范桁). Chin. Phys. B, 2023, 32(1): 010307.
[3]	The coupled deep neural networks for coupling of the Stokes and Darcy-Forchheimer problems Jing Yue(岳靖), Jian Li(李剑), Wen Zhang(张文), and Zhangxin Chen(陈掌星). Chin. Phys. B, 2023, 32(1): 010201.
[4]	Data-driven modeling of a four-dimensional stochastic projectile system Yong Huang(黄勇) and Yang Li(李扬). Chin. Phys. B, 2022, 31(7): 070501.
[5]	Machine learning potential aided structure search for low-lying candidates of Au clusters Tonghe Ying(应通和), Jianbao Zhu(朱健保), and Wenguang Zhu(朱文光). Chin. Phys. B, 2022, 31(7): 078402.
[6]	Quantum algorithm for neighborhood preserving embedding Shi-Jie Pan(潘世杰), Lin-Chun Wan(万林春), Hai-Ling Liu(刘海玲), Yu-Sen Wu(吴宇森), Su-Juan Qin(秦素娟), Qiao-Yan Wen(温巧燕), and Fei Gao(高飞). Chin. Phys. B, 2022, 31(6): 060304.
[7]	Evaluation of performance of machine learning methods in mining structure—property data of halide perovskite materials Ruoting Zhao(赵若廷), Bangyu Xing(邢邦昱), Huimin Mu(穆慧敏), Yuhao Fu(付钰豪), and Lijun Zhang(张立军). Chin. Phys. B, 2022, 31(5): 056302.
[8]	Quantum partial least squares regression algorithm for multiple correlation problem Yan-Yan Hou(侯艳艳), Jian Li(李剑), Xiu-Bo Chen(陈秀波), and Yuan Tian(田源). Chin. Phys. B, 2022, 31(3): 030304.
[9]	Tri-hexagonal charge order in kagome metal CsV₃Sb₅ revealed by ¹²¹Sb nuclear quadrupole resonance Chao Mu(牟超), Qiangwei Yin(殷蔷薇), Zhijun Tu(涂志俊), Chunsheng Gong(龚春生), Ping Zheng(郑萍), Hechang Lei(雷和畅), Zheng Li(李政), and Jianlin Luo(雒建林). Chin. Phys. B, 2022, 31(1): 017105.
[10]	Dynamical learning of non-Markovian quantum dynamics Jintao Yang(杨锦涛), Junpeng Cao(曹俊鹏), and Wen-Li Yang(杨文力). Chin. Phys. B, 2022, 31(1): 010314.
[11]	Quantitative structure-plasticity relationship in metallic glass: A machine learning study Yicheng Wu(吴义成), Bin Xu(徐斌), Yitao Sun(孙奕韬), and Pengfei Guan(管鹏飞). Chin. Phys. B, 2021, 30(5): 057103.
[12]	Nodal superconducting gap in LiFeP revealed by NMR: Contrast with LiFeAs A F Fang(房爱芳), R Zhou(周睿), H Tukada, J Yang(杨杰), Z Deng(邓正), X C Wang(望贤成) , C Q Jin(靳常青), and Guo-Qing Zheng(郑国庆). Chin. Phys. B, 2021, 30(4): 047403.
[13]	Spin correlations in the S=1 armchair chain Ni₂NbBO₆ as seen from NMR Kai-Yue Zeng(曾凯悦), Long Ma(马龙), Long-Meng Xu(徐龙猛), Zhao-Ming Tian(田召明), Lang-Sheng Ling(凌浪生), and Li Pi(皮雳). Chin. Phys. B, 2021, 30(4): 047503.
[14]	Quantum annealing for semi-supervised learning Yu-Lin Zheng(郑玉鳞), Wen Zhang(张文), Cheng Zhou(周诚), and Wei Geng(耿巍). Chin. Phys. B, 2021, 30(4): 040306.
[15]	Quantum simulations with nuclear magnetic resonance system Chudan Qiu(邱楚丹), Xinfang Nie(聂新芳), and Dawei Lu(鲁大为). Chin. Phys. B, 2021, 30(4): 048201.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Nuclear magnetic resonance for quantum computing: Techniques and recent achievements

Cite this article:

Online attention