Low-loss belief propagation decoder with Tanner graph in quantum error-correction 	codes

doi:10.1088/1674-1056/ac11cf

中国物理B ›› 2022, Vol. 31 ›› Issue (1): 10304-010304.doi: 10.1088/1674-1056/ac11cf

Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

Dan-Dan Yan(颜丹丹), Xing-Kui Fan(范兴奎), Zhen-Yu Chen(陈祯羽), and Hong-Yang Ma(马鸿洋)^†

School of Sciences, Qingdao University of Technology, Qingdao 266033, China

收稿日期:2021-05-17 修回日期:2021-06-28 接受日期:2021-07-07 出版日期:2021-12-03 发布日期:2021-12-28
通讯作者: Hong-Yang Ma E-mail:hongyang_ma@aliyun.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132 and 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and the Higher Education Science and Technology Program of Shandong Province, China (Grant No. J18KZ012).

Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

Dan-Dan Yan(颜丹丹), Xing-Kui Fan(范兴奎), Zhen-Yu Chen(陈祯羽), and Hong-Yang Ma(马鸿洋)^†

School of Sciences, Qingdao University of Technology, Qingdao 266033, China

Received:2021-05-17 Revised:2021-06-28 Accepted:2021-07-07 Online:2021-12-03 Published:2021-12-28
Contact: Hong-Yang Ma E-mail:hongyang_ma@aliyun.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132 and 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and the Higher Education Science and Technology Program of Shandong Province, China (Grant No. J18KZ012).

摘要/Abstract

摘要： Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication. However, the existing decoders are generally incapable of checking node duplication of belief propagation (BP) on quantum low-density parity check (QLDPC) codes. Based on the probability theory in the machine learning, mathematical statistics and topological structure, a GF(4) (the Galois field is abbreviated as GF) augmented model BP decoder with Tanner graph is designed. The problem of repeated check nodes can be solved by this decoder. In simulation, when the random perturbation strength p=0.0115-0.0116 and number of attempts N=60-70, the highest decoding efficiency of the augmented model BP decoder is obtained, and the low-loss frame error rate (FER) decreases to 7.1975×10^-5. Hence, we design a novel augmented model decoder to compare the relationship between GF(2) and GF(4) for quantum code [[450,200]] on the depolarization channel. It can be verified that the proposed decoder provides the widely application range, and the decoding performance is better in QLDPC codes.

关键词: tanner graph, belief propagation decoder, augmented model, fourier transform

Abstract: Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication. However, the existing decoders are generally incapable of checking node duplication of belief propagation (BP) on quantum low-density parity check (QLDPC) codes. Based on the probability theory in the machine learning, mathematical statistics and topological structure, a GF(4) (the Galois field is abbreviated as GF) augmented model BP decoder with Tanner graph is designed. The problem of repeated check nodes can be solved by this decoder. In simulation, when the random perturbation strength p=0.0115-0.0116 and number of attempts N=60-70, the highest decoding efficiency of the augmented model BP decoder is obtained, and the low-loss frame error rate (FER) decreases to 7.1975×10^-5. Hence, we design a novel augmented model decoder to compare the relationship between GF(2) and GF(4) for quantum code [[450,200]] on the depolarization channel. It can be verified that the proposed decoder provides the widely application range, and the decoding performance is better in QLDPC codes.

Key words: tanner graph, belief propagation decoder, augmented model, fourier transform

中图分类号: (Quantum algorithms, protocols, and simulations)

03.67.Ac

03.67.Hk (Quantum communication) 03.67.Dd (Quantum cryptography and communication security)

Dan-Dan Yan(颜丹丹), Xing-Kui Fan(范兴奎), Zhen-Yu Chen(陈祯羽), and Hong-Yang Ma(马鸿洋). Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes[J]. 中国物理B, 2022, 31(1): 10304-010304.

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Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

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