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With the development of quantum information and quantum computation science, quantum information processor has been widely used in different areas such as quantum simulation, quantum computation and quantum metrology and so on. To make quantum computer come true, we need to increase the number of controllable qubits of the system and improve the controllability to perform complex quantum manipulation. As a good experimental testbed for quantum information processing, nuclear magnetic resonance (NMR) spin system provides rich and sophisticated quantum control methods. In recent years a lot of multi-qubit experiments have been performed on the platform and a series of experimental technologies have been developed. In this paper, we firstly explain the difficulties of multi-qubit NMR experiments. Then by focusing on the experiment of 7-qubit labelled pseudo-pure state preparation and other relevant experiments, we review the technologies in multi-qubit experiments. Using the radio frequency selective method, the inhomogeneities of the radio frequency pulses are reduced and the spectral resolution is improved. After performing 1/2 spin selective sequence, we can regard the three methyl protons in the sample of crotonic acid as a single 1/2 spin nucleus and treat the whole molecule as a 7-qubit quantum information processor. We utilize Gauss pulses, Hermite pulses, composite pulses and gradient ascent pulse engineering (GRAPE) pulses to implement basic /2 and rotation operations. The GRAPE pulses are calculated by subspace GRAPE program to speed up the computation greatly. The errors of the basic pulses caused by chemical shift and J-coupling evolution can be estimated by the program of pulse compilation. It divides the errors of the pulses into a series of post-errors and pre-errors. A program of sequence compilation is used to eliminate the accumulated error of the whole pulse sequence, reduce the number of pulses and optimize the experimental duration. A variety of methods of quantum state tomography have been proposed to improve the efficiency of reading out information about quantum state. As an experimental example, we combine the above experimental technologies and perform the experiment of 7-qubit labelled pseudo-pure state preparation by using the method of cat state preparation. The sequence of cat state preparation consists of three steps:encoding procedure, phase cycling and decoding procedure. We use 14 experiments to realize the phase cycling and acquire the final 7-qubit labelled pseudo-pure state. The total duration of experimental sequence is about 132 ms. All the readout spectra have the similar shapes to the theoretical expectations. Finally we give an outlook for further research in this direction.
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Keywords:
- nuclear magnetic resonance /
- quantum computation /
- quantum control /
- multi-qubit experiment
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[1] Nielsen M A, Chuang I 2002 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press India) pp1-12
[2] Bennett C H, DiVincenzo D P 2000 Nature 404 247
[3] Deutsch D, Jozsa R 1992 Proc. R. Soc. A 439 553
[4] Shor P W 1994 Proceedings of the 35th Annual Symposium on Foundations of Computer Science Washington, DC, USA, November 20-22, 1994 p24
[5] Grover L K 1996 Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing Philadelphia, USA, May 22-24, 1996 p212
[6] Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502
[7] Li J, Peng X, Du J, Suter D 2012 Sci. Rep. 2 260
[8] Somaroo S, Tseng C, Havel T, Laflamme R, Cory D G 1999 Phys. Rev. Lett. 82 5381
[9] Bennett C H, DiVincenzo D P, Smolin J A, Wootters W K 1996 Phys. Rev. A 54 3824
[10] Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photon. 5 222
[11] Monz T, Schindler P, Barreiro J T, Chwalla M, Nigg D, Coish W A, Harlander M, Hänsel W, Hennrich M, Blatt R 2011 Phys. Rev. Lett. 106 130506
[12] Mariantoni M, Wang H, Yamamoto T, Neeley M, Bialczak R C, Chen Y, Lenander M, Lucero E, O'Connell A D, Sank D, Weides M, Wenner J, Yin Y, Zhao J, Korotkov A N, Cleland A N, Martinis J M 2011 Science 334 61
[13] Knill E, Laflamme R, Martinez R, Tseng C H 2000 Nature 404 368
[14] Vandersypen L M, Steffen M, Breyta G, Yannoni C S, Sherwood M H, Chuang I L 2001 Nature 414 883
[15] Chuang I L, Vandersypen L M, Zhou X, Leung D W, Lloyd S 1998 Nature 394 143
[16] Jones J A, Mosca M, Hansen R H 1998 Nature 393 344
[17] Souza A M, Zhang J, Ryan C A, Laflamme R 2011 Nature Commun. 2 169
[18] Zhang J, Yung M H, Laflamme R, Aspuru-Guzik A, Baugh J 2012 Nature Commun. 3 880
[19] Negrevergne C, Mahesh T, Ryan C, Ditty M, Cyr-Racine F, Power W, Boulant N, Havel T, Cory D, Laflamme R 2006 Phys. Rev. Lett. 96 170501
[20] Li J, Yang X D, Peng X H, Sun C P 2017 Phys. Rev. Lett. 118 150503
[21] Lu D, Li K, Li J, Katiyar H, Park A J, Feng G, Xin T, Li H, Long G, Brodutch A, Baugh J, Zeng B, Laflamme R 2017 arXiv: 1701.01198 [quant-ph]
[22] Warren W S 1997 Science 277 1688
[23] Khaneja N, Reiss T, Kehlet C, Schulte-Herbrggen T, Glaser S J 2017 J. Magn. Reson. 172 296
[24] Cory D G, Price M D, Havel T F 1998 Physica D 120 82
[25] Knill E, Chuang I, Laflamme R 1998 Phys. Rev. A 57 3348
[26] Peng X, Zhu X, Fang X, Feng M, Gao K, Yang X, Liu M 2001 Chem. Phys. Lett. 340 509
[27] Ma X, Jackson T, Zhou H, Chen J, Lu D, Mazurek M D, Fisher K A, Peng X, Kribs D, Resch K J, Ji Z, Zeng B, Laflamme R 2016 Phys. Rev. A 93 032140
[28] Gross D, Liu Y K, Flammia S T, Becker S, Eisert J 2010 Phys. Rev. Lett. 105 150401
[29] Maffei P, Elbayed K, Brondeau J, Canet D 1991 J. Magn. Reson. 95 382
[30] Freeman R, Morris G A 1978 J. Magn. Reson. 29 173
[31] Li J, Cui J Y, Yang X D, Luo Z H, Pan J, Yu Q, Li Z K, Peng X H, Du J F 2015 Acta Phys. Sin. 64 167601 (in Chinese) [李俊, 崔江煜, 杨晓东, 罗智煌, 潘健, 余琦, 李兆凯, 彭新华, 杜江峰 2015 64 167601]
[32] Bauer C, Freeman R, Frenkiel T, Keeler J, Shaka A 1984 J. Magn. Reson. 58 442
[33] Warren W S 1984 J. Chem. Phys. 81 5437
[34] Wimperis S 1994 J. Magn. Reson. Ser. A 109 221
[35] Ryan C, Negrevergne C, Laforest M, Knill E, Laflamme R 2008 Phys. Rev. A 78 012328
[36] Pan J, Cao Y, Yao X, Li Z, Ju C, Chen H, Peng X, Kais S, Du J 2014 Phys. Rev. A 89 022313
[37] Li J, Cui J, Laflamme R, Peng X 2016 Phys. Rev. A 94 032316
[38] Levitt M H 2008 Spin Dynamics: Basics of Nuclear Magnetic Resonance (England: John Wiley & Sons Ltd) pp93-99
[39] D'Ariano G, Presti P L 2001 Phys. Rev. Lett. 86 4195
[40] Zheng W, Yu Y, Pan J, Zhang J, Li J, Li Z, Suter D, Zhou X, Peng X, Du J 2015 Phys. Rev. A 91 022314
[41] Vandersypen L M, Chuang I L 2005 Rev. Mod. Phys. 76 1037
[42] Cory D G, Fahmy A F, Havel T F 1997 Proc. Natl. Acad. Sci. USA 94 1634
[43] Zhang J, Laflamme R, Suter D 2012 Phys. Rev. Lett. 109 100503
[44] Boykin P O, Mor T, Roychowdhury V, Vatan F, Vrijen R 2002 Proc. Natl. Acad. Sci. USA 99 3388
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