Determination of quantum toric error correction code threshold using convolutional neural network decoders

doi:10.1088/1674-1056/ac11e3

中国物理B ›› 2022, Vol. 31 ›› Issue (1): 10303-010303.doi: 10.1088/1674-1056/ac11e3

Determination of quantum toric error correction code threshold using convolutional neural network decoders

Hao-Wen Wang(王浩文)², Yun-Jia Xue(薛韵佳)², Yu-Lin Ma(马玉林)², Nan Hua(华南)², and Hong-Yang Ma(马鸿洋)^1,†

1 School of Sciences, Qingdao University of Technology, Qingdao 266033, China;
2 School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China

收稿日期:2021-06-07 修回日期:2021-06-25 接受日期:2021-07-07 出版日期:2021-12-03 发布日期:2021-12-14
通讯作者: Hong-Yang Ma E-mail:hongyang_ma@aliyun.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132 and 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and the Project of Shandong Province Higher Educational Science and Technology Program, China (Grant No. J18KZ012).

Determination of quantum toric error correction code threshold using convolutional neural network decoders

Hao-Wen Wang(王浩文)², Yun-Jia Xue(薛韵佳)², Yu-Lin Ma(马玉林)², Nan Hua(华南)², and Hong-Yang Ma(马鸿洋)^1,†

1 School of Sciences, Qingdao University of Technology, Qingdao 266033, China;
2 School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China

Received:2021-06-07 Revised:2021-06-25 Accepted:2021-07-07 Online:2021-12-03 Published:2021-12-14
Contact: Hong-Yang Ma E-mail:hongyang_ma@aliyun.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132 and 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and the Project of Shandong Province Higher Educational Science and Technology Program, China (Grant No. J18KZ012).

摘要/Abstract

摘要： Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers. In order to find the best syndrome of the stabilizer code in quantum error correction, we need to find a fast and close to the optimal threshold decoder. In this work, we build a convolutional neural network (CNN) decoder to correct errors in the toric code based on the system research of machine learning. We analyze and optimize various conditions that affect CNN, and use the RestNet network architecture to reduce the running time. It is shortened by 30%-40%, and we finally design an optimized algorithm for CNN decoder. In this way, the threshold accuracy of the neural network decoder is made to reach 10.8%, which is closer to the optimal threshold of about 11%. The previous threshold of 8.9%-10.3% has been slightly improved, and there is no need to verify the basic noise.

关键词: quantum error correction, toric code, convolutional neural network (CNN) decoder

Abstract: Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers. In order to find the best syndrome of the stabilizer code in quantum error correction, we need to find a fast and close to the optimal threshold decoder. In this work, we build a convolutional neural network (CNN) decoder to correct errors in the toric code based on the system research of machine learning. We analyze and optimize various conditions that affect CNN, and use the RestNet network architecture to reduce the running time. It is shortened by 30%-40%, and we finally design an optimized algorithm for CNN decoder. In this way, the threshold accuracy of the neural network decoder is made to reach 10.8%, which is closer to the optimal threshold of about 11%. The previous threshold of 8.9%-10.3% has been slightly improved, and there is no need to verify the basic noise.

Key words: quantum error correction, toric code, convolutional neural network (CNN) decoder

中图分类号: (Quantum error correction and other methods for protection against decoherence)

03.67.Pp

03.67.-a (Quantum information) 87.64.Aa (Computer simulation)

Hao-Wen Wang(王浩文), Yun-Jia Xue(薛韵佳), Yu-Lin Ma(马玉林), Nan Hua(华南), and Hong-Yang Ma(马鸿洋). Determination of quantum toric error correction code threshold using convolutional neural network decoders[J]. 中国物理B, 2022, 31(1): 10303-010303.

参考文献

[1] Kitaev A Y 1997 Russ. Math. Surv. 52 1191
[2] Long G L 2001 Phys. Rev. A 64 022307
[3] Fowler A G, Mariantoni M, Martinis J M and Cleland A N 2012 Phys. Rev. A 86 032324
[4] Xu P A, He Z X, Qiu T H and Ma H Y 2020 Opt. Express 28 12508
[5] Bravyi S B and Kitaev A Y 1998 arXiv:9811052[quant-ph]
[6] Hu X M, Huang C X, Sheng Y B, et al. 2021 Phys. Rev. Lett. 126 010503
[7] Li K, Wan Y, Hung L Y, Lan T, Long G, Lu D, Zeng B and Laflamme R 2017 Phys. Rev. Lett. 118 080502
[8] Castagnoli G 2016 Found. Phys. 46 360
[9] Kang Y H, Shi Z C, Song J and Xia Y 2020 Opt. Lett. 45 4952
[10] Keyserlingk C W V, Burnell F J and Simon S H 2013 Phys. Rev. B 87 045107
[11] Rist D, Poletto S, Huang M Z, Bruno A, Vesterinen V, Saira O P and DiCarlo L 2015 Nat. Commun. 6 6983
[12] Li H H, Gong L H and Zhou N R 2020 Chin. Phys. B 29 010304
[13] Li T, Zhang S, Fu X Q et al. 2019 Chin. Phys. B 28 120301
[14] Andrianov A V, Korobeynikova A P 2020 Quantum Eng. 50 742
[15] Schindler F, Regnault N and Neupert T 2017 Phys. Rev. B 95 245134
[16] Qi L, Yan Y, Xing Y, Zhao X D, Liu S T, Cui W X, Han X, Zhang S and Wang H F 2021 Phys. Rev. Res. 3 023037
[17] Kitaev A Y 2003 Ann. Phys. 303 2
[18] Liu F, Zhang X and Xu P A 2020 Int. J. Theor. Phys. 59 3491
[19] Zhou L, Sheng Y B and Long G L 2020 Sci. Bull. 65 12
[20] Kitaev A Y 1997 Ann. Phys. 303 1
[21] Katzgraber H G, Bombin H and Martin-Delgado M A 2009 Phys. Rev. Lett. 103 090501
[22] Zheng R H, Xiao Y, Su S L, Chen Y H, Shi Z C, Song J, Xia Y and Zheng S B 2021 Phys. Rev. A 103 052402
[23] Dennis E, Kitaev A Y, Landahl A and Preskill J 2002 J. Math. Phys. 43 4452
[24] Chen G, Zhang W H, Yin P et al. 2021 Fund. Res. 1 27
[25] Vandersypen L M K and Chuang I L 2005 Rev. Mod. Phys. 76 1037
[26] Zhou N R, Zhu K N, Bi W and Gong L H 2019 Quantum Inf. Process. 18 197
[27] Wilczek F 1982 Phys. Rev. Lett. 49 957
[28] Zhou Z R, Sheng Y B, Niu P H et al. 2020 Sci. Chin. Phys. Mech. Astron. 63 230362
[29] Zhao J B, Zhang W B, Ma Y L, Zhang X H and Ma H Y 2020 Appl. Sci. 10 1935
[30] Zhang C, Cao H, Huang Y F et al. 2021 Fund. Res. 1 22
[31] Kang Y H, Shi Z C, Huang B H, Song J and Xia Y 2020 Phys. Rev. A 101 032322
[32] Dauphinais G and Poulin D 2017 Commun. Math. Phys. 355 519
[33] Qi L, Xing Y, Zhao X D, Liu S T, Zhang S, Hu S and Wang H F 2021 Phys. Rev. B 103 085129
[34] Duclos-Cianci G and Poulin D 2010 Phys. Rev. Lett. 104 050504
[35] Qiu T H, Li H and Xie M 2019 Phys. Rev. A 100 013844
[36] Lo H K and Preskill J 1993 Phys. Rev. D 48 4821
[37] Bravyi S, Suchara M and Vargo A 2014 Phys. Rev. A 90 032326
[38] Dennis E, Kitaev A, Landahl A and Preskill J 2002 J. Math. Phys. 43 4452
[39] Liu F, Zhang X and Xu P A 2019 Int. J. Theor. Phys. 58 4241
[40] Starobor A V it et al. 2020 Quantum Eng. 50 414
[41] Delfosse N 2014 Phys. Rev. A 89 012317
[42] Varsamopoulos S, Criger B and Bertels K 2017 Quantum Sci. Technol. 3 015004
[43] Magesan E, Gambetta J M, Crcoles A D and Chow J M 2015 Phys. Rev. Lett. 114 200501
[44] Gong L H, Li J F and Zhou N R 2018 Laser Phys. Lett. 15 105204
[45] Yokoyama J 2021AAPPS Bull. 31 17
[46] Qi L, Wang G L, Liu S T, Zhang S and Wang H F 2020 Phys. Rev. Appl. 13 064016
[47] Wen X G 2002 Phys. Rev. B 65 165113
[48] Haldane F D M 1983 Phys. Lett. A 93 464
[49] Levin M and Wen X G 2006 Phys. Rev. Lett. 96 110405
[50] Ma H Y, He Z X, Xu P A, Dong Y M and Fan X K 2020 Quantum Inf. Process. 19 52
[51] Qi L, Wang G L, Liu S T, Zhang S and Wang H F 2020 Phys. Rev. A 102 022404
[52] Gottesman D 1996 Phys. Rev. A 54 1862
[53] Cai W Z et al. 2021 Fund. Res. 1 50
[54] Ren Z X, Zhang S Q, Zhao P W et al. 2019 Sci. Chin. Phys. Mech. Astron. 62 112062
[55] Sheth M, Jafarzadeh S Z, Gheorghiu V 2020 Phys. Rev. A 101 032338
[56] Kojo T 2021AAPPS Bull. 31 11
[57] Torlai G and Melko R G 2017 Phys. Rev. Lett. 119 030501
[58] Duclos-Cianci G and Poulin D 2010 Phys. Rev. Lett. 104 050504
[59] Li B M, Hu M L and Fan H 2019 Acta Phys. Sin. 68 030304 (in Chinese)
[60] Hao S H et al. 2021 Chin. Phys. B 30 060312

Determination of quantum toric error correction code threshold using convolutional neural network decoders

Determination of quantum toric error correction code threshold using convolutional neural network decoders

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 5

Metrics

本文评价

推荐阅读 0

[1]	Hai-Yuan Hong(洪海源), Xiu-Juan Lu(鲁秀娟), and Sen Kuang(匡森). Feedback control and quantum error correction assisted quantum multi-parameter estimation[J]. 中国物理B, 2023, 32(4): 40603-040603.
[2]	Dayue Qin(秦大粤), Xiaosi Xu(徐晓思), and Ying Li(李颖). An overview of quantum error mitigation formulas[J]. 中国物理B, 2022, 31(9): 90306-090306.
[3]	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). Quantum computation and error correction based on continuous variable cluster states[J]. 中国物理B, 2021, 30(6): 60312-060312.
[4]	邵军虎, 白宝明, 林伟, 周林. Jointly-check iterative decoding algorithm for quantum sparse graph codes[J]. 中国物理B, 2010, 19(8): 80307-080307.
[5]	吴双, 梁林梅, 李承祖. Secure deterministic communication in a quantum loss channel using quantum error correction code[J]. 中国物理B, 2007, 16(5): 1229-1232.