计算机科学 ›› 2020, Vol. 47 ›› Issue (7): 37-41.doi: 10.11896/jsjkx.190600020

• 计算机科学理论 • 上一篇    下一篇

噪声信道下的盲量子计算

罗文俊, 雷爽   

  1. 重庆邮电大学计算机科学与技术学院 重庆400065
  • 收稿日期:2019-06-05 出版日期:2020-07-15 发布日期:2020-07-16
  • 通讯作者: 雷爽(ls889933@163.com)
  • 作者简介:luowj@cqupt.edu.cn

Blind Quantum Computation over Noise Channels

LUO Wen-jun, LEI Shuang   

  1. College of Computer Science and Technology,Chongqing University of Posts and Telecommunications,Chongqing 400065,China
  • Received:2019-06-05 Online:2020-07-15 Published:2020-07-16
  • About author:LUO Wen-jun,born in 1966,professor,Ph.D,is a member of China Computer Federation.His main research interests include cyberspace security and cryptography.
    LEI Shuang,born in 1995,postgra-duate.Her main research interests include cryptography,quantum computing and quantum security.

摘要: 盲量子计算(Blind Quantum Computation,BQC)区别于传统的量子计算(Quantum Metrology),它将客户端的计算任务通过量子信道委托给服务器端完成,解放客户端的计算压力,这就要求在信道的传输过程中,量子尽量精确传输。由于量子信道的噪声问题,理想情况下的无噪传输协议是不可能实现的,需要使用量子纠错码(Quantum Error-Correcting Code,QECC)来纠正由噪声信道引起的量子比特翻转和量子相位翻转错误。在盲量子计算协议的基础上,文中针对噪声比特翻转信道和噪声相位翻转信道分别设计抗噪声的盲量子计算协议,客户端通过不同的方式编码量子比特,利用编码后的量子比特传输量子信息给服务器,服务器利用量子纠错码恢复正确的量子信息与客户端完成盲量子计算。协议分析表明,文中提出的两个盲量子计算协议分别在量子比特翻转和量子相位翻转噪声信道中,通过纠错计算达到了盲量子计算协议对于量子尽量精确传输的要求,并且不改变盲量子计算的正确性和盲特性,不会降低量子计算的无条件安全性。最后展望所提协议可以适用于其他量子纠错码。

关键词: 盲量子计算, 噪声信道, 量子比特翻转, 量子相位翻转, 量子纠错码

Abstract: Blind Quantum Computation (BQC),is a kind of protocol that remarkably distinguishes from traditional quantum computation,delegates computing tasks from clients to the servers through the quantum channels which eventually alleviates the computing pressure generated by the clients.Consequently,BQC requires that the quantum is teleported in an accurate manner of transmission via the channels.Due to the problem of noise of quantum channel,a purely noiseless transmission channel under ideal circumstance cannot be realized without quantum error correction codes that are implemented to rectify the flip errors in terms of quantum bit and phase resulted from noise channels.By the basis of BQC protocol,two anti-noise BQC protocols are proposed from the perspectives of noise bit flip channels and noise phase flip channels,respectively.Explicitly,the client encodes the qubits via various ways,then the encoded qubits are used to transmit the quantum information to the server by which the quantum error correction codes are exploited to recover the correct quantum information for the purpose of completion of BQC with the client.A protocol analysis indicates that via correction computation,the requirement of accurate transmission by BQC protocol can be met during the computation of BQC over the quantum bit flip and quantum phase flip noise channels with neither the sacrifice of correctness and blindness of BQC,nor the reduction in unconditional security of quantum computing.Finally,this paper hopes that the new BQC protocols can be applied to other quantum error correction codes as well.

Key words: Blind quantum computation, Noise channel, Quantum bit flip, Quantum phase flip, Quantum error correcting code

中图分类号: 

  • TP301
[1] GOTTESMAN D.Class of quantum error-correcting codes saturating the quantum Hamming bound [J].Physical Review A,1996,54(3):1862-1868.
[2] CHIAVERINI J,LEIBFRIED D,SCHAETZ T,et al.Realization of quantum error correction [J].Nature,2004,432(7017):602-605.
[3] CÃRCOLES AD,MAGESAN E,SRINIVASAN S J,et al.Demonstration of a quantum error detection code using a square lattice of four superconducting qubits [J].Nature Communications,2015,6:6979.
[4] TÓTH G,APELLANIZI.Quantum metrology from a quantum information science perspective [J].Journal of Physics AMathe-matical & Theoretical,2014,47(42):15-22.
[5] LUO W J.Error Correction Performance of Binary NonlinearEqual Weight Codes [J].Chinese Science Bulletin,2000,45(13):1441-1446.
[6] FU F W,XIA S T.Error detection performance of binary nonlinear equal weight codes [J].Science Bulletin,1997,42(4):343-347.
[7] SHOR P W.Scheme for reducing decoherence in quantum computer memory [J].Physical Review A,1995,52(4):R2493-R2496.
[8] CALDERBANK A R,SHORPW.Good quantum error-correcting codes exist [J].Physical Review A,1996,54(2):1098-1105.
[9] ZHAO S M.Construction of a quantum CSS code based onsparse sequence [J].Journal of Nanjing University of Posts and Telecommunications(Natural Science Edition),2011,31(2):1-5.
[10] FUJIWARA Y,CLARK D,VANDENDRIESSCHE P,et al.Entanglement-assisted quantum low-density parity-check codes [J].Physical Review A,2010,82(4):272-277.
[11] DJORDJEVIC,IVAN B.Quantum LDPC Codes from Balanced Incomplete Block Designs [J].IEEE Communications Letters,2008,12(5):389-391.
[12] WANG X Y,ZHANG Y C,YU S,et al.High speed error correction for continuous-variable quantum key distribution with multi-edge type LDPC code[J].Scientific reports,2018,8(1):1-7.
[13] STEANE,ANDREW M.Error Correcting Codes in QuantumTheory [J].Physical Review Letters,1996,77(5):793-797.
[14] IOFFE L,MEZARD M.Asymmetric quantum error correcting codes [J].Phys. Rev. A,2007,75(3):723-727.
[15] ALY S A,ASHIKHMIN A.Nonbinary quantum cyclic and subsystem codes over asymmetrically-decohered quantum channels [C]//2010 IEEE Information Theory Workshop on Information Theory.Cairo:IEEE,2010:1-5.
[16] WANG L,FENG K,LING S,et al.Asymmetric QuantumCodes:Characterization and Constructions [J].IEEE Transactions on Information Theory,2010,56(6):2938-2945.
[17] DAVID K,LAFLAMME R.Unified and generalized approach to quantum error correction [J].Physical Review Letters,2005,94(18):180501.1-180501.4.
[18] BRUN T,IGOR D,AND MIN-HSIU H.Correcting quantum errors with entanglement [J].Science,2006,314(5798):436-439.
[19] LUO L,ZHI M A,WEI Z,et al.Non-binary entanglement-assisted quantum stabilizer codes[J].Science China(Information Scie-nces),2017,60(4):210-223.
[20] HSIEH M H,YEN W T,HSU L Y.High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement[J].IEEE Transactions on Information Theory,2011,57(3):1761-1769.
[21] NAYAK C,SIMON S H,STERN A,et al.Non-Abelian Anyons and Topological Quantum Computation [J].Review of Modern Physics,2008,80(3):1083-1159.
[22] KASHEFI E,WALLDEN P.Garbled Quantum Computation[J].Cryptography,2017,1(1):6-36.
[23] LOSS D,DIVINCENZO D P.Quantum Computation withQuantum Dots [J].Phys. Rev. A,1997,57(1):120-126.
[24] BRIEGEL H J,BROWNE D E,DüR W,et al.Measurement-based quantum computation[J].Nature Physics,2009,5:19-26.
[25] LAI C Y,BRUN T.Entanglement Increases the Error-Correcting Ability of Quantum Error-Correcting Codes [J].Physical Review A,2010,88(1):2343-2347.
[26] BRUN T A,DEVETAK I,HSIEH M H.Catalytic Quantum Error Correction [J].IEEE Transactions on Information Theory,2006,60(6):3073-3089.
[27] TANG J,LIU J W,CAO Y Q.Cognitive spectrum allocation on demand based on quantum coding and mimic physical optimization[J].Computer Engineering,2015,41(12):135-139.
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[2] 钱建发,马文平. 量子纠错码的一个统一构造方法[J]. 计算机科学, 2010, 37(3): 70-72.
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