SymBreak: Mitigating Quantum Degeneracy Issues in QLDPC Code Decoders by Breaking Symmetry

TL;DR

SymBreak is a novel decoder for quantum LDPC codes that mitigates degeneracy issues, significantly improving decoding accuracy and speed over existing belief propagation methods, thus advancing practical quantum error correction.

Contribution

It introduces SymBreak, a decoder that adaptively modifies the decoding graph to address quantum degeneracy, enhancing belief propagation decoding performance for qLDPC codes.

Findings

Achieves 16.17x reduction in logical error rate over BP

Reduces decoding time by 81.03% compared to BP+OSD

Outperforms existing decoders across various qLDPC codes

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 $16.17\times$ reduction in logical error rate compared to BP and $3.23\times$ 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.