  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.
