Localized statistics decoding for quantum low-density parity-check codes

Timo Hillmann (), Lucas Berent (), Armanda O. Quintavalle, Jens Eisert, Robert Wille and Joschka Roffe ()
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Timo Hillmann: Chalmers University of Technology
Lucas Berent: Technical University of Munich
Armanda O. Quintavalle: Freie Universität Berlin
Jens Eisert: Freie Universität Berlin
Robert Wille: Technical University of Munich
Joschka Roffe: Freie Universität Berlin

Nature Communications, 2025, vol. 16, issue 1, 1-11

Abstract: Abstract 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.

Date: 2025
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DOI: 10.1038/s41467-025-63214-7

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