Approximating optimal decoding of quantum LDPC codes with narrow frontiers

2026-06-18

AI Summary

This work addresses the challenge of efficiently achieving near-optimal decoding for sparse quantum error-correcting codes under high noise levels by introducing the Frontier decoder. The proposed method pioneers the integration of pruned dynamic programming into quantum LDPC code decoding, combining ordered inference, residual syndrome merging, and a frontier-scoring mechanism to retain only the highest-scoring narrow frontiers that approximate the posterior probability over logical cosets. Under the code-capacity noise model, the decoder achieves performance close to the optimal thresholds of surface and color codes. In circuit-level noise simulations, it maintains an average list size below 100 for the [[144,12,12]] code at a physical error rate of 0.001 and exhibits potential for linear-time complexity, thereby significantly approaching fundamental theoretical limits.

Abstract

We introduce the Frontier decoder, a pruned dynamic-programming decoder for sparse quantum decoding problems. Frontier processes error variables in a chosen order, merges prefixes with the same residual syndrome and logical label, and approximates logical-coset posterior masses by retaining only a narrow scored frontier. Without pruning, the recursion is exact ordered inference with exponential complexity. In the code-capacity setting, the decoder reaches thresholds close to optimal for the surface code and the color code. In the circuit-level noise model, it achieves state-of-the-art performance with a very small average retained list size: less than 100 for the gross code $[[144,12,12]]$ at a physical error rate of $0.001$. When the list size is constant, the decoder has linear complexity, suggesting the possibility of low-latency implementations.

Problem

• quantum LDPC codes
• decoding
• error correction
• complexity
• threshold

Innovation

• quantum LDPC codes
• Frontier decoder
• pruned dynamic programming
• linear complexity
• approximate optimal decoding