Decoding correlated errors in quantum LDPC codes

We introduce a decoding framework for correlated errors in quantum LDPC codes under circuit-level noise. Our approach is a graph augmentation and rewiring for inference (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. 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 (on par with XYZ-Relay-BP) through ensemble decoding, where 24 randomized normalized min-sum decoders run in parallel on the transformed graph. For the distance 12 Bivariate Bicycle code the logical error rate of (6.70 ± 1.93) × 10−9 is achieved at a 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. Quantum low-density parity-check codes are promising but still miss feasible and reliable general decoding methods. Here, the authors present a decoding graph transformation which results into an accurate, fast, hardware-friendly decoding method for quantum LDPC codes that handles realistic correlated noise while maintaining very low logical error rates.