Decoding Correlated Errors in Quantum LDPC Codes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912981871230976 |
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| author | Maan, Arshpreet Singh Herrero, Francisco-Garcia Paler, Alexandru Savin, Valentin |
| author_facet | Maan, Arshpreet Singh Herrero, Francisco-Garcia Paler, Alexandru Savin, Valentin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14060 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decoding Correlated Errors in Quantum LDPC Codes Maan, Arshpreet Singh Herrero, Francisco-Garcia Paler, Alexandru Savin, Valentin Quantum Physics 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. |
| title | Decoding Correlated Errors in Quantum LDPC Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.14060 |