Evolutionary BP+OSD Decoding for Low-Latency Quantum Error Correction

TL;DR

An evolutionary belief propagation decoder for quantum error correction, which incorporates trainable weights into the BP algorithm and optimizes them via the differential evolution algorithm, which achieves better decoding performance and lower computational complexity than BP+OSD.

Abstract

We propose an evolutionary belief propagation (EBP) decoder for quantum error correction, which incorporates trainable weights into the BP algorithm and optimizes them via the differential evolution algorithm. This approach enables end-to-end optimization of the EBP combined with ordered statistics decoding (OSD). Experimental results on surface codes and quantum low-density parity-check codes show that EBP+OSD achieves better decoding performance and lower computational complexity than BP+OSD, particularly under strict low latency constraints (within 5 BP iterations).

Figures (4)

• Figure 1: (a) DE algorithm optimizing the weight set $\mathcal{W}$ inside the EBP decoder, where the optimization explicitly targets the overall EBP+OSD performance ${\rm LER}_{\rm +}$ rather than the standalone EBP performance. (b) Surface code with $d=3$ illustrating the weight-sharing technique, where edges of the same color share identical weights.
• Figure 2: Effect of the proposed sharing technique: (a) The number of weights is greatly reduced and remains constant across different $d$ in surface codes. (b) This reduction accelerates DE convergence and yields lower ${\rm LER}_{\rm +}$ for $d=7$.
• Figure 3: Performance comparison between BP+OSD and EBP+OSD for surface codes (left column) and QLDPC codes (right column) in terms of LER (upper row) and threshold (lower row).
• Figure 4: Comparison of decoding complexity between BP+OSD and EBP+OSD decoders: (a) EBP consistently reduces the average iteration count and ${\rm FFR}_{\rm Pre}$ for surface and QLDPC codes. (b) EBP+OSD achieves a 35–63% reduction in total complexity across all codes.