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Cited by 37Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyError Correcting Code Techniques

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

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Hillmann, Timo, Berent, Lucas, Quintavalle, Armanda O., Eisert, Jens, Wille, Robert, Roffe, Joschka·2025·Nature Communications
DOI 10.1038/s41467-025-63214-7PMC PMC12405505
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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.

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  • Enhancing BP with classical decoding techniques such as ordered statistics decoding (OSD) or localized statistics decoding (LSD) significantly improves performance.

    “Also, one can enhance BP with classical decoding techniques such as ordered statistics decoding (OSD) [197] or localized statistics decoding (LSD) [198]. These approaches significantly improve performance.”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [198]

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Metadata

Authors
Hillmann, T., Berent, L., Quintavalle, A. O., Eisert, J., Wille, R., & Roffe, J.
Affiliations
  • Chalmers University of Technology (SE)
  • Technical University of Munich (DE)
  • Freie Universität Berlin (DE)
  • Helmholtz-Zentrum Berlin für Materialien und Energie (DE)
  • Software Competence Center Hagenberg (Austria) (AT)
Corresponding author
  • Hillmann, Timo
  • Berent, Lucas
  • Roffe, Joschka
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2025-09-02
Volume
16
Issue
1
Pages
8214-8214
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-025-63214-7
PMC
PMC12405505
OpenAlex
W4413927467
Cited by
37
References
6
Citations by year
2026: 20 · 2025: 16
FWCI
11.73
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • PubMed Central (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • Refubium (Universitätsbibliothek der Freien Universität Berlin) (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • HZB Repository (Helmholtz-Zentrum Berlin für Materialien und Energie GmbH (HZB)) (submittedVersion, other-oa)
  • Edinburgh Research Explorer (University of Edinburgh) (submittedVersion, cc-by)
  • Chalmers Research (Chalmers University of Technology) (submittedVersion)
  • arXiv (Cornell University)
  • Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver (cc-by)
Funders
Chalmers Excellence Initiative Nano and the Knut and Alice Wallenberg Foundation through the Wallenberg Centre for Quantum Technology
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Computer Networks and Communications › Error Correcting Code Techniques
Keywords
quantum low-density parity-check codes, quantum error correction, parallel matrix factorization, fault-tolerant quantum computing, syndrome decoding, hardware implementation

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