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

doi:10.1088/1674-1056/ac11cf

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.

Keywords: tanner graph belief propagation decoder augmented model fourier transform

Received: 17 May 2021
Revised: 28 June 2021
Accepted manuscript online: 07 July 2021

PACS:	03.67.Ac	(Quantum algorithms, protocols, and simulations)
	03.67.Hk	(Quantum communication)
	03.67.Dd	(Quantum cryptography and communication security)

Fund: 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).

Corresponding Authors: Hong-Yang Ma
E-mail: hongyang_ma@aliyun.com

Cite this article:

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 2022 Chin. Phys. B 31 010304

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

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