Localized statistics decoding: A parallel decoding algorithm for quantum low-density parity-check codes
<|reference_start|>Localized statistics decoding: A parallel decoding algorithm for quantum low-density parity-check codes: Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to their implementation. In this work, we introduce localized statistics decoding, a reliability-guided inversion decoder that is highly parallelizable and applicable to arbitrary quantum low-density parity-check codes. Our approach employs a parallel matrix factorization strategy, which we call on-the-fly elimination, to identify, validate, and solve local decoding regions on the decoding graph. Through numerical simulations, we show that localized statistics decoding matches the performance of state-of-the-art decoders while reducing the runtime complexity for operation in the sub-threshold regime. Importantly, our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments.<|reference_end|>
@article{hillmann2024localized,
    title={Localized statistics decoding: A parallel decoding algorithm for quantum
  low-density parity-check codes},
    author={Timo Hillmann, Lucas Berent, Armanda O. Quintavalle, Jens Eisert,
  Robert Wille, Joschka Roffe},
    journal={arXiv preprint arXiv:2406.18655},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.18655},
    primaryClass={quant-ph cs.IT math.IT}
}