Jointly-check iterative decoding algorithm for quantum sparse graph codes

doi:10.1088/1674-1056/19/8/080307

Abstract For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with a standard belief-propagation (BP) algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms the standard BP algorithm with an obvious performance improvement.

Keywords: quantum error correction sparse graph code iterative decoding belief-propagation algorithm

Received: 12 October 2009
Revised: 22 March 2010
Accepted manuscript online:

PACS:	03.65.Ca	(Formalism)
	02.10.Ox	(Combinatorics; graph theory)
	02.60.Cb	(Numerical simulation; solution of equations)
	03.67.Pp	(Quantum error correction and other methods for protection against decoherence)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60972046) and Grant from the National Defense Pre-Research Foundation of China.

Cite this article:

Shao Jun-Hu(邵军虎), Bai Bao-Ming(白宝明), Lin Wei(林伟), and Zhou Lin(周林) Jointly-check iterative decoding algorithm for quantum sparse graph codes 2010 Chin. Phys. B 19 080307

[1]	Divincenzo D P and Shor P W 1996 Phys. Rev. Lett. 77 3260
[2]	Brito D B, Nascimento J C and Ramos R V 2007 IEEE J. Quantum Electron. 44 113
[3]	Ambainis A and Gottesman D 2006 IEEE Trans. Information Theory 52 748
[4]	Li Z and Xing L J 2007 Acta Phys. Sin. 56 5602 (in Chinese)
[5]	Wu S, Liang L M and Li C Z 2007 Chin. Phys. 16 1229
[6]	MacKay J C D, Mitchison G and McFadden P 2004 IEEE Trans. Information Theory 50 2315
[7]	David J C MacKay 1999 IEEE Trans. Information Theory 45 399
[8]	Li Z and Xing L J 2008 Acta Phys. Sin. 57 28 (in Chinese)
[9]	Calderbank A R and Shor P W 1996 Phys. Rev. A 54 1098
[10]	Forney G D and Costello D J 2007 Proceedings of the IEEE 95 1150
[11]	Poulin D and Bilgin E 2008 Phys. Rev. A 77 052318
[12]	Zhang Q, Tang C J and Gao F 2002 Acta Phys. Sin. 51 15 (in Chinese)
[13]	Xing L J, Li Z, Bai B M and Wang X M 2008 Acta Phys. Sin. 57 4695 (in Chinese)
[14]	John A S, Smith G and Wehner S 2007 Phys. Rev. Lett. 99 130505
[15]	Hagiwara M and Imai H 2007 IEEE International Symposium on Information Theory France June 24--29 p. 806
[16]	Aly S A 2008 IEEE Global Telecommunications Conference New Orleans 30 November--4 December p. 1097
[17]	Brun T, Devetak I and Hsieh M H 2006 Science 314 1464
[18]	Poulin D 2005 Phys. Rev. Lett. 95 230504
[19]	Vontobel P O 2008 The 5th International Symposium on Turbo Codes and Related Topics Lausanne, September 1--5 p. 215
[20]	Camara T, Ollivier H and Tillich J P 2005 arXiv quant-ph/0502086 [hep-ph]
[21]	Tan P Y and Li J 2007 IEEE International Symposium on Information Theory Nice June 24--29 p. 2106
[22]	Tan P Y and Li J 2008 IEEE International Conference on Communications Ontario July 6--11 p. 1166
[23]	Poulin D and Chung Y 2008 International Journal of Quantum Information and Computation 8 987
[24]	Chung K and Heo J 2006 IEEE 63rd on Vehicular Technology Conference Melbourne May 7--10 p. 1464
[25]	Gottesman D 1997 Stabilizer Codes and Quantum Error Correction (Ph.D. Thesis) (California: California Institute of Technology)
[26]	Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) pp. 454--468
[27]	Calderbank A R, Rains E M and Shor P W 1998 IEEE Trans. Information Theory 44 1369

[1]	Feedback control and quantum error correction assisted quantum multi-parameter estimation Hai-Yuan Hong(洪海源), Xiu-Juan Lu(鲁秀娟), and Sen Kuang(匡森). Chin. Phys. B, 2023, 32(4): 040603.
[2]	An overview of quantum error mitigation formulas Dayue Qin(秦大粤), Xiaosi Xu(徐晓思), and Ying Li(李颖). Chin. Phys. B, 2022, 31(9): 090306.
[3]	Determination of quantum toric error correction code threshold using convolutional neural network decoders Hao-Wen Wang(王浩文), Yun-Jia Xue(薛韵佳), Yu-Lin Ma(马玉林), Nan Hua(华南), and Hong-Yang Ma(马鸿洋). Chin. Phys. B, 2022, 31(1): 010303.
[4]	Quantum computation and error correction based on continuous variable cluster states Shuhong Hao(郝树宏), Xiaowei Deng(邓晓玮), Yang Liu(刘阳), Xiaolong Su(苏晓龙), Changde Xie(谢常德), and Kunchi Peng(彭堃墀). Chin. Phys. B, 2021, 30(6): 060312.
[5]	Encoding entanglement-assisted quantum stabilizer codes Wang Yun-Jiang(王云江), Bai Bao-Ming(白宝明), Li Zhuo(李卓), Peng Jin-Ye(彭进业), and Xiao He-Ling(肖鹤玲) . Chin. Phys. B, 2012, 21(2): 020304.
[6]	Secure deterministic communication in a quantum loss channel using quantum error correction code Wu Shuang(吴双), Liang Lin-Mei(梁林梅), and Li Cheng-Zu(李承祖). Chin. Phys. B, 2007, 16(5): 1229-1232.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Jointly-check iterative decoding algorithm for quantum sparse graph codes

Cite this article:

Online attention