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量子通信是经典通信和量子力学相结合的一门新兴交叉学科.量子纠错编码是实现量子通信的关键技术之一.构造量子纠错编码的主要方法是借鉴经典纠错编码技术,许多经典的编码技术在量子领域中都可以找到其对应的编码方法.针对经典纠错码中最好码之一的Turbo乘积码,提出一种以新构造的CSS型量子卷积码为稳定子码的量子Turbo乘积码.首先,运用群的理论及稳定子码的基本原理构造出新的CSS型量子卷积码稳定子码生成元,并描述了其编码网络.接着,利用量子置换SWAP门定义推导出量子Turbo乘积码的交织编码矩阵.最后,推导出量子Turbo乘积码的译码迹距离与经典Turbo乘积码的译码距离的对应关系,并提出量子Turbo乘积码的编译码实现方案.这种编译码方法具有高度结构化,设计思路简单,网络易于实施的特点.
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关键词:
- CSS码 /
- 量子卷积码 /
- 量子Turbo乘积码 /
- 量子纠错编码
Quantum communication is a growing interdisciplinary field which combines classical communications and quantum mechanics. Quantum error correction coding is one of the key techniques in quantum communication. Nearly all of the classical error correction coding schemes have been transplanted to the domain of quantum communication, and the quantum counterparts of classical error correction coding techniques have been found. Based on the classical turbo product codes (TPCs) which is one of the most outstanding schemes in classical coding region, a new structure of the CSS-type quantum convolutional codes (QCC) as stabilizer sub-code of the quantum turbo product codes (QTPC) is presented. Firstly, CSS-type QCC stabilizer generator is constructed with the help of group theory and the basic principle of stabilizer coders, and the corresponding networks are described. Secondly, the interleaved coded matrix of the QTPC is obtained by quantum permutation SWAP gate definition. Finally, the corresponding relation between the quantum trace distance of QTPC decoding and the distance of classical TPCs decoding is obtained, and the scheme of QTPCs coding and decoding is completed. The coding and decoding of QTPCs have a highly regular structure and a simple design idea, and the networks are easy to realize.-
Keywords:
- CSS coding /
- quantum convolutional codes /
- quantum turbo product codes /
- quantum error correcting coding
[1] Bennett C H 1992 Phys. Rev. Lett. 68 3124
[2] Xiao H L, Ouyang S, Nie Z P 2009 Acta Phys. Sin. 58 3685 (in Chinese) [肖海林、欧阳缮、聂在平 2009 物理学报 58 3685]
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[9] Alexei A, Emanuel K 2001 IEEE Trans. Inf. Theory 47 3065
[10] Ashikhim A, Litsyn S, Tsfasman M 2001 IEEE Trans. Inf. Theory 47 1206
[11] David J C, Mitchison G, McFadden P L 2004 IEEE Trans. Inf. Theory 50 2315
[12] Xing L Z, Li Z, Bao B M, Wang X M 2008 Acta Phys. Sin. 57 4695 (in Chinese) [邢莉娟、李 卓、白宝明、王新梅 2008 物理学报 57 4695]
[13] Yue K F, Zhao S M, Li M M 2008 Journal of Nanjing University of Posts and Telecomm 28 44 (in Chinese) [岳克峰、赵生妹、李苗苗 2008 南京邮电大学学报 28 44]
[14] Djordjevic I B 2009 IEEE Photonics Technology Lett. 21 842
[15] Vucetic B, Li Y H, Perez L C, Jiang F 2007 IEEE Proc. 95 1323
[16] Huebner A, Zigangirov K S, Costello D J 2008 IEEE Trans. Inf. Theory 54 3024
[17] Liese F, Vajda I 2006 IEEE Trans. Inf. Theory 52 4394
[18] Chen G T, Cao L, Yu Lun, Chen C W 2009 IEEE Trans. Comm. 57 307
[19] Xu C L, Liang Y C, Leon W S 2008 IEEE Trans. Wire. Comm. 7 43
[20] Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
[21] Steane A M 1999 IEEE Trans. Inf. Theory 45 2492
[22] Fletcher A S, Shor P W, Win M Z 2008 IEEE Trans. Inf. Theory 54 5705
[23] Zhang Q, Tang C J, Gao F 2002 Acta Phys. Sin. 51 15 (in Chinese) [张 权、唐朝京、高 峰 2002 物理学报 51 15]
[24] Jaromir F 2009 Phys. Rev. A 79 012330
[25] Heng F, Vwani R, Thomas S 2005 Phys. Rev. A 72 052323
[26] Zhang Q, Zhang E Y, Tang C J 2002 Acta Phys. Sin. 51 1676 (in Chinese) [张 权、张尔杨、唐朝京 2002 物理学报 51 1676]
[27] Tetsufumi T, Liu Y X, Hu X D, Franco N 2009 Phys. Rev. Lett. 102 100501
[28] Zhang M, Dai H Y, Xi Z R, Xie H W, Hu D W 2007 Phys. Rev. A 76 042335
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[1] Bennett C H 1992 Phys. Rev. Lett. 68 3124
[2] Xiao H L, Ouyang S, Nie Z P 2009 Acta Phys. Sin. 58 3685 (in Chinese) [肖海林、欧阳缮、聂在平 2009 物理学报 58 3685]
[3] Xiao H L, Ouyang S, Nie Z P 2009 Acta Phys. Sin. 58 6779 (in Chinese) [肖海林、欧阳缮、聂在平 2009 物理学报 58 6779]
[4] Kremsky I, Hsieh M H, Brun T A 2008 Phys. Rev. A 78 012341
[5] Shor P W 1995 Phys. Rev. A 52 2493
[6] Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
[7] Dave B 2008 Phys. Rev. A 78 042324
[8] Gottesman D 1996 Phys. Rev. A 54 1862
[9] Alexei A, Emanuel K 2001 IEEE Trans. Inf. Theory 47 3065
[10] Ashikhim A, Litsyn S, Tsfasman M 2001 IEEE Trans. Inf. Theory 47 1206
[11] David J C, Mitchison G, McFadden P L 2004 IEEE Trans. Inf. Theory 50 2315
[12] Xing L Z, Li Z, Bao B M, Wang X M 2008 Acta Phys. Sin. 57 4695 (in Chinese) [邢莉娟、李 卓、白宝明、王新梅 2008 物理学报 57 4695]
[13] Yue K F, Zhao S M, Li M M 2008 Journal of Nanjing University of Posts and Telecomm 28 44 (in Chinese) [岳克峰、赵生妹、李苗苗 2008 南京邮电大学学报 28 44]
[14] Djordjevic I B 2009 IEEE Photonics Technology Lett. 21 842
[15] Vucetic B, Li Y H, Perez L C, Jiang F 2007 IEEE Proc. 95 1323
[16] Huebner A, Zigangirov K S, Costello D J 2008 IEEE Trans. Inf. Theory 54 3024
[17] Liese F, Vajda I 2006 IEEE Trans. Inf. Theory 52 4394
[18] Chen G T, Cao L, Yu Lun, Chen C W 2009 IEEE Trans. Comm. 57 307
[19] Xu C L, Liang Y C, Leon W S 2008 IEEE Trans. Wire. Comm. 7 43
[20] Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
[21] Steane A M 1999 IEEE Trans. Inf. Theory 45 2492
[22] Fletcher A S, Shor P W, Win M Z 2008 IEEE Trans. Inf. Theory 54 5705
[23] Zhang Q, Tang C J, Gao F 2002 Acta Phys. Sin. 51 15 (in Chinese) [张 权、唐朝京、高 峰 2002 物理学报 51 15]
[24] Jaromir F 2009 Phys. Rev. A 79 012330
[25] Heng F, Vwani R, Thomas S 2005 Phys. Rev. A 72 052323
[26] Zhang Q, Zhang E Y, Tang C J 2002 Acta Phys. Sin. 51 1676 (in Chinese) [张 权、张尔杨、唐朝京 2002 物理学报 51 1676]
[27] Tetsufumi T, Liu Y X, Hu X D, Franco N 2009 Phys. Rev. Lett. 102 100501
[28] Zhang M, Dai H Y, Xi Z R, Xie H W, Hu D W 2007 Phys. Rev. A 76 042335
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