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

Fuente: arXiv
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Main Authors: Hillmann, Timo, Berent, Lucas, Quintavalle, Armanda O., Eisert, Jens, Wille, Robert, Roffe, Joschka
Format: Preprint
Published: 2024
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author Hillmann, Timo
Berent, Lucas
Quintavalle, Armanda O.
Eisert, Jens
Wille, Robert
Roffe, Joschka
author_facet Hillmann, Timo
Berent, Lucas
Quintavalle, Armanda O.
Eisert, Jens
Wille, Robert
Roffe, Joschka
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_18655
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Localized statistics decoding for quantum low-density parity-check codes
Hillmann, Timo
Berent, Lucas
Quintavalle, Armanda O.
Eisert, Jens
Wille, Robert
Roffe, Joschka
Quantum Physics
Information Theory
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.
title Localized statistics decoding for quantum low-density parity-check codes
topic Quantum Physics
Information Theory
url https://arxiv.org/abs/2406.18655