Approximating optimal decoding of quantum LDPC codes with narrow frontiers

• URL: http://arxiv.org/abs/2606.20513v1
• Date: Thu, 18 Jun 2026 17:34:11 GMT
• Title: Approximating optimal decoding of quantum LDPC codes with narrow frontiers
• Abstract summary: We introduce the Frontier decoder, a dynamic-programming decoder for sparse quantum decoding problems.<n>In the code-capacity setting, the decoder reaches thresholds close to optimal for the surface code and the color code.<n>When the list size is constant, the decoder has linear complexity, suggesting the possibility of low-latency implementations.
• Score: 1.8907108368038215
• License: http://creativecommons.org/licenses/by/4.0/
• 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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