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Chin. Phys. B, 2022, Vol. 31(4): 040305    DOI: 10.1088/1674-1056/ac3817
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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
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.
Keywords:  fault-tolerant error correction      quantum stabilizer code      gate fault      quantum circuit  
Received:  21 October 2021      Revised:  08 November 2021      Accepted manuscript online:  10 November 2021
PACS:  03.67.Pp (Quantum error correction and other methods for protection against decoherence)  
  03.67.-a (Quantum information)  
  03.67.Hk (Quantum communication)  
Fund: 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).
Corresponding Authors:  Xiu-Bo Chen     E-mail:

Cite this article: 

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 2022 Chin. Phys. B 31 040305

[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
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