Keyi Yin, Xiang Fang, Jixuan Ruan, Hezi Zhang, Dean Tullsen, Andrew Sornborger, Chenxu Liu, Ang Li, Travis Humble, Yufei Ding (Dec 05 2024).
Abstract: Quantum error correction (QEC) is critical for scalable and reliable quantum computing, but existing solutions, such as surface codes, incur significant qubit overhead. Quantum low-density parity check (qLDPC) codes have recently emerged as a promising alternative, requiring fewer qubits. However, the lack of efficient decoders remains a major barrier to their practical implementation. In this work, we introduce SymBreak, a novel decoder for qLDPC codes that adaptively modifies the decoding graph to improve the performance of state-of-the-art belief propagation (BP) decoders. Our key contribution is identifying quantum degeneracy as a root cause of the convergence issues often encountered in BP decoding of quantum LDPC codes. We propose a solution that mitigates this issue at the decoding graph level, achieving both fast and accurate decoding. Our results demonstrate that SymBreak outperforms BP and BP+OSD-a more complex variant of BP-with a
16.17× reduction in logical error rate compared to BP and
3.23× compared to BP+OSD across various qLDPC code families. With only an
18.97% time overhead compared to BP, SymBreak provides significantly faster decoding times than BP+OSD, representing a major advancement in efficient and accurate decoding for qLDPC-based QEC architectures.
