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 s...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Hillmann, Timo, Berent, Lucas, Quintavalle, Armanda O, Eisert, Jens, Wille, Robert, Roffe, Joschka
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.06.2024
Subjects
Algorithms
Decoders
Decoding
Error correcting codes
Fault tolerance
Parity
Quantum computing
Real time
Statistics
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422