Approximating optimal decoding of quantum LDPC codes with narrow frontiers

Anthony Leverrier; Rüdiger Urbanke

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arXiv · 2606.20513

Approximating optimal decoding of quantum LDPC codes with narrow frontiers

Anthony Leverrier·Rüdiger Urbanke

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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.

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Anthony Leverrier, Rüdiger Urbanke. 2026-06-18. Approximating optimal decoding of quantum LDPC codes with narrow frontiers. https://arxiv.org/abs/2606.20513

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