针对X-Z型Pauli信道的量子稀疏图码的反馈式和积译码算法

王云江; 白宝明; 彭进业; 王新梅

doi:10.7498/aps.60.030306

摘要

本文针对X-Z型Pauli量子信道构建了一个量子稀疏图码的反馈式和积译码算法.相比较之前的基本和积算法,该反馈式译码策略利用了错误图样的比较, 稳定子中相关元素的值,特别的还根据信道的特征充分考虑了各变量所占错误的比重,并由此来调整信息节点的概率分布.该反馈式策略起到了经典译码中的软判决技术的作用,不但克服了对称简并问题带来的不利影响,更重要的是还给译码器提供了更多的有效信息,从而大大提高了译码器的纠错译码能力.另外,反馈式译码和积译码算法是基于GF(4)的,大大拓展了和积译码器关于量子译码

关键词:

Abstract

In this paper, a feedback sum-product decoding algorithm of sparse quantum codes for X-Z Pauli channels is developed. Compared with the previous decoding algorithm, our feedback strategy exploits not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the character of the channel model with the portion of each error to adjust the probability distribution of information nodes. Due to the smart adjustment, our decoding algorithm, on one hand, can break the symmetric degeneracy, and on the other hand, can feed back more useful information to the SPA decoder to help the decoder determine a valid output, thereby significantly improving the decoding ability of the decoder. Moreover, our algorithm, which is based on GF(4), overcomes the limitation caused by decoding in GF(2). Finally, we want to point out that, our method does not increase the measurement overhead in comparison wioth the previous methods, as the extra information comes for free from the requisite stabilizer measurement.

Keywords:

作者及机构信息

(1)西安电子科技大学综合业务网理论与关键技术国家重点实验室,西安 710071; (2)西北工业大学电子信息学院,西安 710072

基金项目: 国家重点基础研究发展计划(973计划)(批准号: 2010CB328300),国家预研项目(纠缠量子编码调制技术),国家自然科学基金委员会-广东省联合基金(批准号: U0635003),111基地项目(批准号: B08038)、国家留学基金委员会国家公派专项研究生奖学金项目(批准号: [2008] 3019)资助的课题.

Authors and contacts

(1)School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China; (2)State Key Lab of Integrated Service Networks, Xidian University, Xi’an 710071, China

参考文献

[1]	Liu W J, Chen H W, Ma T H, Li Z Q, Liu Z H, Hu W B 2009 Chin. Phys. B 18 4105
[2]	Wang X B 2004 Phys. Rev. Lett. 92 077902
[3]	Li C Y, Li X H, Deng F G, Zhou H Y 2008 Chin. Phys. B 17 2352
[4]	Zhou N C, Zeng G H, Gong L H, Liu S Q 2007 Acta Phys. Sin. 56 9 (in Chinese) [周南润、曾贵华、龚黎秋、刘三秋2007 物理学报 56 9]
[5]	Zhang S, Wang J, Zhang Q, Tang C J 2009 Acta Phys. Sin. 58 1 (in Chinese)[张盛、王剑、张权、唐朝京 2009 物理学报 58 1]
[6]	Gallager R G 1962 IRE Trans. Inform. Theory 8 21
[7]	Li Z, Xing L J 2008 Acta Phys. Sin. 57 28 (in Chinese) [李卓、邢莉娟 2008 物理学报 57 28]
[8]	MacKay D J C, Mitchison G J, McFadden P L 2004 IEEE Trans. Inform. Theory 50 2315
[9]	Wang Y J, Bai B M, Zhao W B, Wang X M 2009 Int. J. Quantum Inf. 7 1373
[10]	Li Y, Zeng G H, Moon H L 2009 Chin. Phys. B 18 4154
[11]	Poulin D, Chung Y 2008 Quantum Inform. Comput. 8 987
[12]	Wang Y J, Sanders B C, Bai B M, Wang X M 2009 Proceedings of the 9th Asian Conference on Quantum Information Science Nanjing, P.R. China, August 2009 p79
[13]	Gottesman D 1996 Phys. Rev. A 54 1862
[14]	Camara T, Ollivier H, Tillich J P 2007 Proceedings of the International Symposium on Information Theory Nice, France, June 2007 p811
[15]	Steane A M 1996 Phys. Rev. Lett. 77 793
[16]	Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
[17]	Preskill J 2001 Lecture Notes for Physics 219: Quantum Computation. Chap 7 p5
[18]	Wang Y J, Sanders B, Bai B M, Wang X M 2009 arxiv.org/abs/0912.4546
[19]	Calderbank A R, Rains E M, Shor P W, Sloane N J A 1997 Phys. Rev. Lett. 78 405

施引文献

[1]	Liu W J, Chen H W, Ma T H, Li Z Q, Liu Z H, Hu W B 2009 Chin. Phys. B 18 4105
[2]	Wang X B 2004 Phys. Rev. Lett. 92 077902
[3]	Li C Y, Li X H, Deng F G, Zhou H Y 2008 Chin. Phys. B 17 2352
[4]	Zhou N C, Zeng G H, Gong L H, Liu S Q 2007 Acta Phys. Sin. 56 9 (in Chinese) [周南润、曾贵华、龚黎秋、刘三秋2007 物理学报 56 9]
[5]	Zhang S, Wang J, Zhang Q, Tang C J 2009 Acta Phys. Sin. 58 1 (in Chinese)[张盛、王剑、张权、唐朝京 2009 物理学报 58 1]
[6]	Gallager R G 1962 IRE Trans. Inform. Theory 8 21
[7]	Li Z, Xing L J 2008 Acta Phys. Sin. 57 28 (in Chinese) [李卓、邢莉娟 2008 物理学报 57 28]
[8]	MacKay D J C, Mitchison G J, McFadden P L 2004 IEEE Trans. Inform. Theory 50 2315
[9]	Wang Y J, Bai B M, Zhao W B, Wang X M 2009 Int. J. Quantum Inf. 7 1373
[10]	Li Y, Zeng G H, Moon H L 2009 Chin. Phys. B 18 4154
[11]	Poulin D, Chung Y 2008 Quantum Inform. Comput. 8 987
[12]	Wang Y J, Sanders B C, Bai B M, Wang X M 2009 Proceedings of the 9th Asian Conference on Quantum Information Science Nanjing, P.R. China, August 2009 p79
[13]	Gottesman D 1996 Phys. Rev. A 54 1862
[14]	Camara T, Ollivier H, Tillich J P 2007 Proceedings of the International Symposium on Information Theory Nice, France, June 2007 p811
[15]	Steane A M 1996 Phys. Rev. Lett. 77 793
[16]	Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
[17]	Preskill J 2001 Lecture Notes for Physics 219: Quantum Computation. Chap 7 p5
[18]	Wang Y J, Sanders B, Bai B M, Wang X M 2009 arxiv.org/abs/0912.4546
[19]	Calderbank A R, Rains E M, Shor P W, Sloane N J A 1997 Phys. Rev. Lett. 78 405

[1]	朱孝先, 高亦谈, 王羡之, 王一鸣, 王佶, 王兆华, 赵昆, 魏志义. 阿秒脉冲串产生和相位信息重构的对比研究. 物理学报, 2024, 0(0): . doi: 10.7498/aps.73.20240292

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板