Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes

doi:10.1088/1674-1056/ac3817

中国物理B ›› 2022, Vol. 31 ›› Issue (4): 40305-040305.doi: 10.1088/1674-1056/ac3817

Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes

Xiu-Bo Chen(陈秀波)^1,†, Li-Yun Zhao(赵立云)¹, Gang Xu(徐刚)^2,3, Xing-Bo Pan(潘兴博)¹, Si-Yi Chen(陈思怡)¹, Zhen-Wen Cheng(程振文)¹, and Yi-Xian Yang(杨义先)¹

1 Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2 School of Information Science and Technology, North China University of Technology, Beijing 100144, China;
3 Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu 610025, China

收稿日期:2021-10-21 修回日期:2021-11-08 接受日期:2021-11-10 出版日期:2022-03-16 发布日期:2022-03-25
通讯作者: Xiu-Bo Chen E-mail:flyover100@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61671087 and 61962009), the Fundamental Research Funds for the Central Universities, China (Grant No. 2019XD-A02), Huawei Technologies Co. Ltd (Grant No. YBN2020085019), the Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant No. 2018BDKFJJ018).

Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes

Xiu-Bo Chen(陈秀波)^1,†, Li-Yun Zhao(赵立云)¹, Gang Xu(徐刚)^2,3, Xing-Bo Pan(潘兴博)¹, Si-Yi Chen(陈思怡)¹, Zhen-Wen Cheng(程振文)¹, and Yi-Xian Yang(杨义先)¹

1 Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2 School of Information Science and Technology, North China University of Technology, Beijing 100144, China;
3 Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu 610025, China

Received:2021-10-21 Revised:2021-11-08 Accepted:2021-11-10 Online:2022-03-16 Published:2022-03-25
Contact: Xiu-Bo Chen E-mail:flyover100@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61671087 and 61962009), the Fundamental Research Funds for the Central Universities, China (Grant No. 2019XD-A02), Huawei Technologies Co. Ltd (Grant No. YBN2020085019), the Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant No. 2018BDKFJJ018).

摘要/Abstract

摘要： Fault-tolerant error-correction (FTEC) circuit is the foundation for achieving reliable quantum computation and remote communication. However, designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge. In this paper, a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems. Firstly, syndrome ancillas are prepared into Bell states to detect errors caused by channel noise. We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into X-type and Z-type. Additionally, a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults, which may also introduce errors into the code block during the error detection process. Finally, analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth.

关键词: fault-tolerant error correction, quantum stabilizer code, gate fault, quantum circuit

Abstract: Fault-tolerant error-correction (FTEC) circuit is the foundation for achieving reliable quantum computation and remote communication. However, designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge. In this paper, a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems. Firstly, syndrome ancillas are prepared into Bell states to detect errors caused by channel noise. We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into X-type and Z-type. Additionally, a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults, which may also introduce errors into the code block during the error detection process. Finally, analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth.

Key words: fault-tolerant error correction, quantum stabilizer code, gate fault, quantum circuit

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

03.67.Pp

03.67.-a (Quantum information) 03.67.Hk (Quantum communication)

Xiu-Bo Chen(陈秀波), Li-Yun Zhao(赵立云), Gang Xu(徐刚), Xing-Bo Pan(潘兴博), Si-Yi Chen(陈思怡), Zhen-Wen Cheng(程振文), and Yi-Xian Yang(杨义先). Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes[J]. 中国物理B, 2022, 31(4): 40305-040305.

参考文献

[1] Shor P W 1995 Phys. Rev. A 52 R2493
[2] Calderbank A R and Shor P W 1996 Phys. Rev. A 54 1098
[3] Steane A M 1996 Phys. Rev. Lett. 77 793
[4] Gottesman D 1996 Phys. Rev. A 54 1862
[5] Laflamme R, Miquel C, Paz J P and Zurek W H 1996 Phys. Rev. Lett. 77 198
[6] Sung Y, Ding L, Braumüller J, Vepsäläinen A, Kannan B, Kjaergaard M, Greene A, Samach G O, McNally C, Kim D, Melville A, Niedzielski B M, Schwartz M E, Yoder J L, Orlando T P, Gustavsson S and Oliver W D 2021 Phys. Rev. X 11 021058
[7] Greganti C, Demarie T F, Ringbauer M, Jones J A, Saggio V, Calafell I A, Rozema L A, Erhard A, Meth M, Postler L, Stricker R, Schindler P, Blatt R, T. Walther M P and Fitzsimons J F 2021 Phys. Rev. X 11 031049
[8] Google Quantum AI 2021 Nature 595 383
[9] Hao S H, Deng X W, Liu Y, Su X L, Xie C D and Peng K C 2021 Chin. Phys. B 30 060312
[10] Chou K S, Blumoff J Z, Wang C S, Reinhold P C, Axline C J, Gao Y Y, Frunzio L, Devoret M H, Jiang L and Schoelkopf R J 2018 Nature 561 368
[11] Wang Y J, Bai B M, Li Z, Peng J Y and Xiao H L 2021 Chin. Phys. B 21 020304
[12] Lai C Y and Brun T A 2021 Chin. Phys. B 88 012320
[13] Jones C, Fogarty M A, Morello A, Gyure M F, Dzurak A S and Ladd T D 2021 Phys. Rev. X 8 021058
[14] Gottesman D 1998 Phys. Rev. A 57 127
[15] Li J, Chen X B, Xu G, Yang Y X and Li Z P 2015 IEEE Commun. Lett. 19 115
[16] Luo M X, Deng Y, Chen X B, Yang Y X and Li H H 2013 Quantum Inf. Processing 12 1969
[17] Shor P W 1996 Proceedings of 37th Conference on Foundations of Computer Science IEEE pp. 56-65
[18] Steane A M 1997 Phys. Rev. Lett. 78 2252
[19] Knill E 2005 Phys. Rev. A 71 042322
[20] Knill E 2005 Nature 434 39
[21] Salas P J and Sanz A L 2004 Phys. Rev. A 69 052322
[22] Yoder T J and Kim I H 2017 Quantum 1 2
[23] Chao R and Reichardt B W 2018 Phys. Rev. Lett. 121 050502
[24] Chao R and Reichardt B W 2018 npj Quantum Information 4 1
[25] Chao R and Reichardt B W 2018 PRX Quantum 1 010302
[26] Chao R 2020 Flag the Faults for Reliable Quantum Computing (Ph.D. Dissertation) (University of Southern California)
[27] Chao R, Beverland M E, Delfosse N and Jeongwan H 2020 Quantum 4 352
[28] Chamberland C and Beverland M E 2018 Quantum 2 53
[29] Reichardt B W 2020 Quantum Science and Technology 6 015007
[30] Baireuther P, Caio M D, Criger B, Beenakker C W J and O'Brien T E 2019 New J. Phys. 21 013003
[31] Bermudez A, Xu X, Gutiérrez M, Benjamin S C and Müller M 2019 Phys. Rev. A 100 062307
[32] Chamberland C, Kubica A, Yoder T J and Zhu G Y 2020 New J. Phys. 22 023019
[33] Tansuwannont T 2018 Flag fault-tolerant error correction for cyclic CSS codes (M.S. Dissertation) (University of Waterloo)
[34] Tansuwannont T, Chamberland C and Leung D 2020 Phys. Rev. A 101 012342
[35] Chamberland C, Zhu G Y, Yoder T J, Hertzberg J B and Cross A W 2020 Phys. Rev. X 10 011022
[36] Chamberland C and Cross A W 2019 Quantum 3 143
[37] Chamberland C and Noh K 2020 npj Quantum Information 6 1
[38] Pathak A 2013 Elements of quantum computation and quantum communication (CRC Press Boca Raton) p. 222
[39] DiVincenzo D P 2000 Fortschritte der Physik:Progress of Physics 48 771

Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes

Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes

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 15

Metrics

本文评价

推荐阅读 0

[1]	Hou-Rong Zhou(周后荣), Kun-Jie Cheng(程昆杰), Jie Ren(任洁), Li-Xing You(尤立星),Li-Liang Ying(应利良), Xiao-Yan Yang(杨晓燕), Hao Li(李浩), and Zhen Wang(王镇). Photon number resolvability of multi-pixel superconducting nanowire single photon detectors using a single flux quantum circuit[J]. 中国物理B, 2022, 31(5): 57401-057401.
[2]	Jia Luo(罗佳), Ri-Gui Zhou(周日贵), Wen-Wen Hu(胡文文), YaoChong Li(李尧翀), and Gao-Feng Luo(罗高峰). Quantum watermarking based on threshold segmentation using quantum informational entropy[J]. 中国物理B, 2022, 31(4): 40302-040302.
[3]	Jing-Wen Zhang(张静文), Xiu-Bo Chen(陈秀波), Gang Xu(徐刚), and Yi-Xian Yang(杨义先). Universal quantum circuit evaluation on encrypted data using probabilistic quantum homomorphic encryption scheme[J]. 中国物理B, 2021, 30(7): 70309-070309.
[4]	Sai Li(李赛), Tao Chen(陈涛), Jia Liu(刘佳), and Zheng-Yuan Xue(薛正远). Interaction induced non-reciprocal three-level quantum transport[J]. 中国物理B, 2021, 30(6): 60314-060314.
[5]	罗高峰, 周日贵, 胡文文. Novel quantum secret image sharing scheme[J]. 中国物理B, 2019, 28(4): 40302-040302.
[6]	郭学仪, 邓辉, 李贺康, 宋鹏涛, 王战, 苏鹭红, 李洁, 金贻荣, 郑东宁. Modulation of energy spectrum and control of coherent microwave transmission at single-photon level by longitudinal field in a superconducting quantum circuit[J]. 中国物理B, 2018, 27(7): 74206-074206.
[7]	王宇, 尚云. Two-qubit pure state tomography by five product orthonormal bases[J]. 中国物理B, 2018, 27(10): 100306-100306.
[8]	瞿治国, 何煌兴, 李涛. Novel quantum watermarking algorithm based on improved least significant qubit modification for quantum audio[J]. 中国物理B, 2018, 27(1): 10306-010306.
[9]	程广玲, 王一平, 陈爱喜. Phase-controlled coherent population trapping in superconducting quantum circuits[J]. , 2015, 24(4): 44204-044204.
[10]	李海超, 葛国勤. Switching from positive to negative absorption with electromagnetically induced transparency in circuit quantum electrodynamics[J]. 中国物理B, 2014, 23(5): 54206-054206.
[11]	邱田会, 杨国建. Controlling group velocity in a superconductive quantum circuit[J]. 中国物理B, 2012, 21(10): 104205-104205.
[12]	葛国勤, 覃翠, 尹淼, 黄勇华. Structure formation of entanglement entropy in a system of two superconducting qubits coupled with an LC-resonator[J]. 中国物理B, 2011, 20(8): 80304-080304.
[13]	张映玉, 胡和平, 路松峰. A quantum search algorithm based on partial adiabatic evolution[J]. 中国物理B, 2011, 20(4): 40309-040309.
[14]	李文东, 张建立, 顾永建. Quantum circuits for realizing deterministic and exact teleportation via two partially entangled pairs of particles[J]. 中国物理B, 2006, 15(3): 482-487.
[15]	袁洪春, 齐开国. Probabilistic and controlled teleportation of tripartite state in a general form and its quantum networks[J]. 中国物理B, 2005, 14(9): 1716-1723.