Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(4): 040303    DOI: 10.1088/1674-1056/abe296
Special Issue: SPECIAL TOPIC — Quantum computation and quantum simulation
SPECIAL TOPIC—Quantum computation and quantum simulation Prev   Next  

Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions

Qing Yan(闫青)1,2 and Qing-Feng Sun(孙庆丰)1,3,4,†
1 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; 2 CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China; 3 Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; 4 Beijing Academy of Quantum Information Sciences, Beijing 100193, China
Abstract  Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can. Realizing the quantum computation requires the universal quantum gate set {T, H, CNOT} so as to perform any unitary transformation with arbitrary accuracy. Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions. Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures, which enable the braiding operation and the partial exchange operation. After defining a qubit by four chiral Majorana fermions, the single-qubit T and H quantum gates are realized via one partial exchange operation and three braiding operations, respectively. The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions. Besides, we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device. Thus, our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.
Keywords:  quantum computation      T gate      CNOT gate      braiding      chiral Majorana fermions  
Received:  14 October 2020      Revised:  26 December 2020      Accepted manuscript online:  03 February 2021
PACS:  03.67.Lx (Quantum computation architectures and implementations)  
  74.78.-w (Superconducting films and low-dimensional structures)  
  73.21.La (Quantum dots)  
Fund: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0303301), the National Natural Science Foundation of China (Grant No. 11921005), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), and Beijing Municipal Science & Technology Commission, China (Grant No. Z191100007219013).
Corresponding Authors:  Corresponding author. E-mail: sunqf@pku.edu.cn   

Cite this article: 

Qing Yan(闫青) and Qing-Feng Sun(孙庆丰) Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions 2021 Chin. Phys. B 30 040303

1 Nielsen M A and Chuang I L 2010 Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge: Cambridge University Press)
2 Feynman R P 1982 Int. J. Theor. Phys. 21 467
3 Ladd T D, Jelezko F, Laflamme R, Nakamura Y, Monroe C and O'Brien J L 2010 Nature 464 45
4 Benioff P 1982 J. Stat. Phys. 29 515
5 DiVincenzo D P 1995 Phys. Rev. A 51 1015
6 Knill E, Laflamme R and Milburn G J 2001 Nature 409 46
7 Blatt R and Wineland D 2008 Nature 453 1008
8 Xu P, He X D, Liu M, Wang J and Zhan M S 2019 Acta Phys. Sin. 68 030305 (in Chinese)
9 Petta J R, Johnson A C, Taylor J M, Laird E A, Yacoby A, Lukin M D, Marcus C M, Hanson M P and Gossard A C 2005 Science 309 2180
10 Zhang X, Li H O, Wang K, Cao G, Xiao M and Guo G P 2018 Chin. Phys. B 27 020305
11 Wang K, Li H O, Xiao M, Cao G and Guo G P 2018 Chin. Phys. B 27 090308
12 Nakamura Y, Pashkin Y A and Tsai J S 1999 Nature 398 786
13 Chiorescu I, Nakamura Y, Harmans C J and Mooij J E 2003 Science 299 1869
14 Zhong Y P, Li C Y, Wang H H and Chen Y 2013 Chin. Phys. B 22 110313
15 Liu W Y, Zheng D N and Zhao S P 2018 Chin. Phys. B 27 027401
16 Nayak C, Simon S H, Stern A, Freedman M and Das Sarma S 2008 Rev. Mod. Phys. 80 1083
17 Sarma S D, Freedman M and Nayak C 2015 npj Quantum Inf. 1 15001
18 Elliott S R and Franz M 2015 Rev. Mod. Phys. 87 137
19 Bravyi S 2006 Phys. Rev. A 73 042313
20 Kitaev A Y 2003 Ann. Phys. 303 2
21 Ivanov D A 2001 Phys. Rev. Lett. 86 268
22 Beenakker C W J 2013 Annu. Rev. Condens. Matter Phys. 4 113
23 Alicea J 2012 Rep. Prog. Phys. 75 076501
24 Kitaev A Y 2001 Phys.-Usp. 44 131
25 Qi J J, Liu H W, Jiang H and Xie X C 2019 Front. Phys. 14 43403
26 Li Y H, Liu J, Song J T, Jiang H, Sun Q F and Xie X C 2018 Sci. China Phys. Mech. Astron. 61 97411
27 Chen C Z, Jiang H, Xu D H and Xie X C 2020 Sci. China Phys. Mech. Astron. 63 107811
28 Yang Y T, Jia Z Y, Wu Y J, Xiao R C, Hang Z H, Jiang H and Xie X C 2020 Sci. Bull. 65 531
29 Fu L and Kane C L 2008 Phys. Rev. Lett. 100 096407
30 Fu L and Kane C L 2009 Phys. Rev. B 79 161408(R)
31 Lutchyn R M, Sau J D and Das Sarma S 2010 Phys. Rev. Lett. 105 077001
32 Oreg Y, Refael G and von Oppen F 2010 Phys. Rev. Lett. 105 177002
33 Zheng H and Jia J F 2019 Chin. Phys. B 28 067403
34 Liu J, Wu Y, Sun Q F and Xie X C 2019 Phys. Rev. B 100 235131
35 Sau J D, Lutchyn R M, Tewari S and Das Sarma S 2010 Phys. Rev. Lett. 104 040502
36 Tang H Z, Sun Q F, Liu J J and Zhang Y T 2019 Phys. Rev. B 99 235427
37 Law K T, Lee P A and Ng T K 2009 Phys. Rev. Lett. 103 237001
38 Mourik V, Zuo K, Frolov S M, Plissard S, Bakkers E P and Kouwenhoven L P 2012 Science 336 1003
39 Nadj-Perge S, Drozdov I K, Li J, Chen H, Jeon S, Seo J, MacDonald A H, Bernevig B A and Yazdani A 2014 Science 346 602
40 Zhang P, Yaji K, Hashimoto T, Ota Y, Kondo T, Okazaki K, Wang Z J, Wen J S, Gu G D, Ding H and Shin S 2018 Science 360 182
41 Jäck B, Xie Y L, Li J, Jeon S, Bernevig B A and Yazdani A 2019 Science 364 1255
42 Laroche D, Bouman D, van Woerkom D J, Proutski A, Murthy C, Pikulin D I, Nayak C, van Gulik R J J, Nygard J, Krogstrup P, Kouwenhoven L P and Geresdi A 2019 Nat. Commun. 10 245
43 Alicea J, Oreg Y, Refael G, von Oppen F and Fisher M P 2011 Nat. Phys. 7 412
44 Halperin B I, Oreg Y, Stern A, Refael G, Alicea J and von Oppen F 2012 Phys. Rev. B 85 144501
45 Bonderson P, Freedman M and Nayak C 2008 Phys. Rev. Lett. 101 010501
46 Bonderson P, Freedman M and Nayak C 2009 Ann. Phys. 324 787
47 Fu L 2010 Phys. Rev. Lett. 104 056402
48 Vijay S and Fu L 2016 Phys. Rev. B 94 235446
49 Karzig T, Knapp C, Lutchyn R M, Bonderson P, Hastings M B, Nayak C, Alicea J, Flensberg K, Plugge S, Oreg Y, Marcus C M and Freedman M H 2017 Phys. Rev. B 95 235305
50 Campbell E T, Terhal B M and Vuillot C 2017 Nature 549 172
51 Fowler A G, Mariantoni M, Martinis J M and Cleland A N 2012 Phys. Rev. A 86 032324
52 Wang J 2020 Acta Phys. Sin. 69 117302 (in Chinese)
53 Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C and Xue Q K 2013 Science 340 167
54 He K, Ma X C, Chen X, Lu L, Wang Y Y and Xue Q K 2013 Chin. Phys. B 22 067305
55 He K 2020 Physics 49 828
56 Fu L and Kane C L 2009 Phys. Rev. Lett. 102 216403
57 Akhmerov A R, Nilsson J and Beenakker C W J 2009 Phys. Rev. Lett. 102 216404
58 Qi X L, Hughes T L and Zhang S C 2010 Phys. Rev. B 82 184516
59 Zhang J, Zhao B, Zhou T and Yang Z 2016 Chin. Phys. B 25 117308
60 Wang J, Zhou Q, Lian B and Zhang S C 2015 Phys. Rev. B 92 064520
61 Yan Q, Zhou Y F and Sun Q F 2020 Chin. Phys. B 29 097401
62 Zhang Y T, Hou Z, Xie X C and Sun Q F 2017 Phys. Rev. B 95 245433
63 Zhou Y F, Hou Z, Zhang Y T and Sun Q F 2018 Phys. Rev. B 97 115452
64 Yan Q, Zhou Y F and Sun Q F 2019 Phys. Rev. B 100 235407
65 Zhou Y F, Hou Z, Lv P, Xie X and Sun Q F 2018 Sci. China Phys. Mech. Astron. 61 127811
66 He Q L, Pan L, Stern A L, Burks E C, Che X, Yin G, Wang J, Lian B, Zhou Q, Choi E S, Murata K, Kou X, Chen Z, Nie T, Shao Q, Fan Y, Zhang S C, Liu K, Xia J and Wang K L 2017 Science 357 294
67 Huang Y, Setiawan F and Sau J D 2018 Phys. Rev. B 97 100501(R)
68 Ji W and Wen X G 2018 Phys. Rev. Lett. 120 107002
69 Chen C Z, He J J, Xu D H and Law K T 2017 Phys. Rev. B 96 041118
70 Lian B, Wang J, Sun X Q, Vaezi A and Zhang S C 2018 Phys. Rev. B 97 125408
71 Kayyalha M, Xiao D, Zhang R X, Shin J, Jiang J, Wang F, Zhao Y F, Xiao R, Zhang L, Fijalkowski K M, Mandal P, Winnerlein M, Gould C, Li Q, Molenkamp L W, Chan M H W, Samarth N and Chang C Z 2020 Science 367 64
72 Lian B, Sun X Q, Vaezi A, Qi X L and Zhang S C 2018 Proc. Natl. Acad. Sci. USA 115 10938
73 Zhou Y F, Hou Z and Sun Q F 2019 Phys. Rev. B 99 195137
74 Beenakker C W J, Baireuther P, Herasymenko Y, Adagideli I, Wang L and Akhmerov A R 2019 Phys. Rev. Lett. 122 146803
75 Zwanenburg F A, Dzurak A S, Morello A, Simmons M Y, Hollenberg L C L, Klimeck G, Rogge S, Coppersmith S N and Eriksson M A 2013 Rev. Mod. Phys. 85 961
76 Georgiev L S 2006 Phys. Rev. B 74 235112
77 Kaye P, Laflamme R and Mosca M 2007 An introduction to quantum computing (Oxford: Oxford University Press)
78 Beenakker C W J SciPostPhys. Lect. Notes 15
79 Kong X Y, Zhu Y Y, Wen J W, Xin T, Li K R and Long G L 2018 Acta Phys. Sin. 67 220301 (in Chinese)
80 Su F F, Wang Z T, Xu H K, Zhao S K, Yan H S, Yang Z H, Tian Y and Zhao S P 2019 Chin. Phys. B 28 110303
81 Yan L, Yin W and Wang F W 2014 Chin. Phys. B 23 100303
82 Bäuerle C, Glattli D C, Meunier T, Portier F, Roche P, Roulleau P, Takada S and Waintal X 2018 Rep. Prog. Phys. 81 056503
83 Levitov L S, Lee H and Lesovik G B 1996 J. Math. Phys. 37 4845
84 Ivanov D A, Lee H W and Levitov L S 1997 Phys. Rev. B 56 6839
85 Keeling J, Klich I and Levitov L S 2006 Phys. Rev. Lett. 97 116403
86 Dubois J, Jullien T, Portier F, Roche P, Cavanna A, Jin Y, Wegscheider W, Roulleau P and Glattli D C 2013 Nature 502 659
87 Bocquillon E, Freulon V, Berroir J M, Degiovanni P, Pla\c cais B, Cavanna A, Jin Y and F\`eve G 2013 Science 339 1054
[1] Quantum computation and simulation with superconducting qubits
Kaiyong He(何楷泳), Xiao Geng(耿霄), Rutian Huang(黄汝田), Jianshe Liu(刘建设), and Wei Chen(陈炜). Chin. Phys. B, 2021, 30(8): 080304.
[2] Universal quantum control based on parametric modulation in superconducting circuits
Dan-Yu Li(李丹宇), Ji Chu(储继), Wen Zheng(郑文), Dong Lan(兰栋), Jie Zhao(赵杰), Shao-Xiong Li(李邵雄), Xin-Sheng Tan(谭新生), and Yang Yu(于扬). Chin. Phys. B, 2021, 30(7): 070308.
[3] Quantum computation and simulation with vibrational modes of trapped ions
Wentao Chen(陈文涛), Jaren Gan, Jing-Ning Zhang(张静宁), Dzmitry Matuskevich, and Kihwan Kim(金奇奂). Chin. Phys. B, 2021, 30(6): 060311.
[4] Quantum computation and error correction based on continuous variable cluster states
Shuhong Hao(郝树宏), Xiaowei Deng(邓晓玮), Yang Liu(刘阳), Xiaolong Su(苏晓龙), Changde Xie(谢常德), and Kunchi Peng(彭堃墀). Chin. Phys. B, 2021, 30(6): 060312.
[5] Efficient self-testing system for quantum computations based on permutations
Shuquan Ma(马树泉), Changhua Zhu(朱畅华), Min Nie(聂敏), and Dongxiao Quan(权东晓). Chin. Phys. B, 2021, 30(4): 040305.
[6] Quantum algorithm for a set of quantum 2SAT problems
Yanglin Hu(胡杨林), Zhelun Zhang(张哲伦), and Biao Wu(吴飙). Chin. Phys. B, 2021, 30(2): 020308.
[7] Low-temperature environments for quantum computation and quantum simulation
Hailong Fu(付海龙), Pengjie Wang(王鹏捷), Zhenhai Hu(胡禛海), Yifan Li(李亦璠), and Xi Lin(林熙). Chin. Phys. B, 2021, 30(2): 020702.
[8] A concise review of Rydberg atom based quantum computation and quantum simulation
Xiaoling Wu(吴晓凌), Xinhui Liang(梁昕晖), Yaoqi Tian(田曜齐), Fan Yang(杨帆), Cheng Chen(陈丞), Yong-Chun Liu(刘永椿), Meng Khoon Tey(郑盟锟), and Li You(尤力). Chin. Phys. B, 2021, 30(2): 020305.
[9] Quantum adiabatic algorithms using unitary interpolation
Shuo Zhang(张硕), Qian-Heng Duan(段乾恒), Tan Li(李坦), Xiang-Qun Fu(付向群), He-Liang Huang(黄合良), Xiang Wang(汪翔), Wan-Su Bao(鲍皖苏). Chin. Phys. B, 2020, 29(1): 010308.
[10] Novel quantum secret image sharing scheme
Gao-Feng Luo(罗高峰), Ri-Gui Zhou(周日贵), Wen-Wen Hu(胡文文). Chin. Phys. B, 2019, 28(4): 040302.
[11] Error-detected single-photon quantum routing using a quantum dot and a double-sided microcavity system
A-Peng Liu(刘阿鹏), Liu-Yong Cheng(程留永), Qi Guo(郭奇), Shi-Lei Su(苏石磊), Hong-Fu Wang(王洪福), Shou Zhang(张寿). Chin. Phys. B, 2019, 28(2): 020301.
[12] Experimental implementation of a continuous-time quantum random walk on a solid-state quantum information processor
Maimaitiyiming Tusun(麦麦提依明·吐孙), Yang Wu(伍旸), Wenquan Liu(刘文权), Xing Rong(荣星), Jiangfeng Du(杜江峰). Chin. Phys. B, 2019, 28(11): 110302.
[13] Direct measurement of the concurrence of hybrid entangled state based on parity check measurements
Man Zhang(张曼), Lan Zhou(周澜), Wei Zhong(钟伟), Yu-Bo Sheng(盛宇波). Chin. Phys. B, 2019, 28(1): 010301.
[14] Solid-state quantum computation station
Fanming Qu(屈凡明), Zhongqing Ji(姬忠庆), Ye Tian(田野), Shiping Zhao(赵士平). Chin. Phys. B, 2018, 27(7): 070301.
[15] An analytical model for nanowire junctionless SOI FinFETs with considering three-dimensional coupling effect
Fan-Yu Liu(刘凡宇), Heng-Zhu Liu(刘衡竹), Bi-Wei Liu(刘必慰), Yu-Feng Guo(郭宇峰). Chin. Phys. B, 2016, 25(4): 047305.
[1] TANG ZHENG-YUAN, YANG JIAN-LUN, WEN SHU-HUAI, WANG GEN-XING, GUO YU-ZHI, YANG HONG-QIONG, MA CHI. NEUTRON TIME OF FLIGHT ENERGY SPECTROMETER FOR ICF ION TEMPERATURE DIAGNOSTIC[J]. Acta Phys. Sin. (Overseas Edition), 1999, 8(12): 913 -918 .
[2] Zhang Zhong-can, Hu Chen-guo, Fang Zhen-yun. SCREENING EFFECT OF THE SPIN DISTRIBUTION IN THE ATOMS OF HYDROGEN AND ALKALI METALS UNDER THE DISTURBANCE OF A STRONG PERIODIC MAGNETIC FIELD[J]. Acta Phys. Sin. (Overseas Edition), 1999, 8(2): 97 -108 .
[3] Liu Ning, Liu Song-hao, Liao Chang-jun, Guo Qi, Xu Wen-cheng. THE NONLINEAR SCHR?DINGER EQUATION AND THE CROSS-PHASE MODULATION IN ERBIUM-DOPED FIBER AMPLIFIERS[J]. Chin. Phys., 2000, 9(10): 753 -756 .
[4] Peng Jie-Hua, Tang Jia-Shi, Yu De-Jie, Hai Wen-Hua, Yan Jia-Ren. Suppressing chaos by parametric perturbation at doubled frequency of periodic perturbation[J]. Chin. Phys., 2003, 12(1): 17 -21 .
[5] Zhu Feng, Proch D., Hao Jian-Kui. Multipacting phenomenon at high electric fields of superconducting cavities[J]. Chin. Phys., 2005, 14(3): 494 -499 .
[6] Wang Li-Jun, Zhang Yong-Ming, Hao Yong-Qin, Zhong Jing-Chang, Ma Jian-Li. Characteristics of selective oxidation during the fabrication of vertical cavity surface emitting laser[J]. Chin. Phys., 2006, 15(8): 1806 -1809 .
[7] Huang Wei-Qi, Xu Li, Wang Hai-Xu, Jin Feng, Wu Ke-Yue, Liu Shi-Rong, Qin Cao-Jian, Qin Shui-Jie. Stimulated photoluminescence emission and trap states in Si/SiO2 interface formed by irradiation of laser[J]. Chin. Phys. B, 2008, 17(5): 1817 -1820 .
[8] Xu Hong-Yan, Jian Ao-Qun, Xue Chen-Yang, Chen Yang, Zhang Bin-Zhen, Zhang Wen-Dong, Zhang Zhi-Guo, Feng Zhen. Temperature dependence of biaxial strain and its influence on phonon and band gap of GaN thin film[J]. Chin. Phys. B, 2008, 17(6): 2245 -2250 .
[9] Long Yun-Ze, Yin Zhi-Hua, Hui Wen, Chen Zhao-Jia, Wan Mei-Xiang. Rectifying effect of heterojunctions between metals and doped conducting polymer nanostructure pellets[J]. Chin. Phys. B, 2008, 17(7): 2707 -2711 .
[10] Wang Dong, Chen Dai-Bing, Qin Fen, Fan Zhi-Kai. Magnetically insulated transmission line oscillator oscillated in a modified HEM11 mode[J]. Chin. Phys. B, 2009, 18(10): 4281 -4286 .