Localized statistics decoding 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.
Authors
- Robert Wille (ORCID: https://orcid.org/0000-0002-4993-7860)
- Lucas Berent (ORCID: https://orcid.org/0000-0002-2973-1689)
- Joschka Roffe (ORCID: https://orcid.org/0000-0001-9202-1156)
- Jens Eisert (ORCID: https://orcid.org/0000-0003-3033-1292)
- Timo Hillmann (ORCID: https://orcid.org/0000-0002-1476-0647)
- Armanda O. Quintavalle
Institutions
- Helmholtz-Zentrum Berlin für Materialien und Energie (DE)
- Software Competence Center Hagenberg (Austria) (AT)
- Technical University of Munich (DE)
- Chalmers University of Technology (SE)
- Freie Universität Berlin (DE)
- University of Edinburgh (GB)
Publication Details
- Journal
- Nature Communications
- Published
- 2025-09-02
- DOI
- https://doi.org/10.1038/s41467-025-63214-7
- Citations
- 19
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- article
- Field-Weighted Citation Impact
- 47.14
Funders
- UK Research and Innovation
- European Commission
- Deutsche Forschungsgemeinschaft
- Bundesministerium für Bildung und Forschung
- Knut och Alice Wallenbergs Stiftelse
- Bundesministerium für Digitalisierung und Wirtschaftsstandort
- Simons Institute for the Theory of Computing, University of California Berkeley
- Engineering and Physical Sciences Research Council
- Wallenberg Centre for Molecular and Translational Medicine
- Wallenberg Center for Quantum Technology, Chalmers University of Technology