Decoding Correlated Errors in Quantum LDPC Codes

• URL: http://arxiv.org/abs/2510.14060v1
• Date: Wed, 15 Oct 2025 19:59:05 GMT
• Title: Decoding Correlated Errors in Quantum LDPC Codes
• Authors: Arshpreet Singh Maan, Francisco-Garcia Herrero, Alexandru Paler, Valentin Savin,
• Abstract summary: We introduce a decoding framework for correlated errors in quantum LDPC codes under circuit-level noise.<n>The core of our approach is a graph augmentation and rewiring for interference (GARI) method, which modifies the correlated detector error model.<n>Preliminary FPGA implementation results show that such high accuracy can be achieved in real time, with a per-round average decoding latency of 273 ns and sub-microsecond latency in 99.99% of the decoding instances.
• Score: 41.04211723135311
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a decoding framework for correlated errors in quantum LDPC codes under circuit-level noise. The core of our approach is a graph augmentation and rewiring for interference (GARI) method, which modifies the correlated detector error model by eliminating 4-cycles involving Y-type errors, while preserving the equivalence of the decoding problem. We test our approach on the bivariate bicycle codes of distances 6, 10, and 12. A normalized min-sum decoder with a hybrid serial-layered schedule is applied on the transformed graph, achieving high accuracy with low latency. Performance is further enhanced through ensemble decoding, where 24 randomized normalized min-sum decoders run in parallel on the transformed graph, yielding the highest reported accuracy (on par with XYZ-Relay-BP) with unprecedented speed for the tested codes under uniform depolarizing circuit level noise. For the distance 12 (gross) code, our approach yields a logical error rate of $(6.70 \pm 1.93) \times 10^{-9}$ at a practical physical error rate of $10^{-3}$. Furthermore, preliminary FPGA implementation results show that such high accuracy can be achieved in real time, with a per-round average decoding latency of 273 ns and sub-microsecond latency in 99.99% of the decoding instances.

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