Combining hard and soft decoders for hypergraph product codes

Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF). This decoder displays sub-optimal performance in practice and requires very large error correcting codes to be effective. In this work,...

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Main Authors: Antoine Grospellier, Lucien Grouès, Anirudh Krishna, Anthony Leverrier
Format: Article
Language:English
Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2021-04-01
Series:Quantum
Online Access:https://quantum-journal.org/papers/q-2021-04-15-432/pdf/
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author Antoine Grospellier
Lucien Grouès
Anirudh Krishna
Anthony Leverrier
author_facet Antoine Grospellier
Lucien Grouès
Anirudh Krishna
Anthony Leverrier
author_sort Antoine Grospellier
collection DOAJ
description Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF). This decoder displays sub-optimal performance in practice and requires very large error correcting codes to be effective. In this work, we present new hybrid decoders that combine the belief propagation (BP) algorithm with the SSF decoder. We present the results of numerical simulations when codes are subject to independent bit-flip and phase-flip errors. We provide evidence that the threshold of these codes is roughly 7.5% assuming an ideal syndrome extraction, and remains close to 3% in the presence of syndrome noise. This result subsumes and significantly improves upon an earlier work by Grospellier and Krishna (arXiv:1810.03681). The low-complexity high-performance of these heuristic decoders suggests that decoding should not be a substantial difficulty when moving from zero-rate surface codes to constant-rate LDPC codes and gives a further hint that such codes are well-worth investigating in the context of building large universal quantum computers.
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spelling doaj.art-61c4f75003e74a70a7bcc1e68ed96c762022-12-21T22:05:03ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2021-04-01543210.22331/q-2021-04-15-43210.22331/q-2021-04-15-432Combining hard and soft decoders for hypergraph product codesAntoine GrospellierLucien GrouèsAnirudh KrishnaAnthony LeverrierHypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF). This decoder displays sub-optimal performance in practice and requires very large error correcting codes to be effective. In this work, we present new hybrid decoders that combine the belief propagation (BP) algorithm with the SSF decoder. We present the results of numerical simulations when codes are subject to independent bit-flip and phase-flip errors. We provide evidence that the threshold of these codes is roughly 7.5% assuming an ideal syndrome extraction, and remains close to 3% in the presence of syndrome noise. This result subsumes and significantly improves upon an earlier work by Grospellier and Krishna (arXiv:1810.03681). The low-complexity high-performance of these heuristic decoders suggests that decoding should not be a substantial difficulty when moving from zero-rate surface codes to constant-rate LDPC codes and gives a further hint that such codes are well-worth investigating in the context of building large universal quantum computers.https://quantum-journal.org/papers/q-2021-04-15-432/pdf/
spellingShingle Antoine Grospellier
Lucien Grouès
Anirudh Krishna
Anthony Leverrier
Combining hard and soft decoders for hypergraph product codes
Quantum
title Combining hard and soft decoders for hypergraph product codes
title_full Combining hard and soft decoders for hypergraph product codes
title_fullStr Combining hard and soft decoders for hypergraph product codes
title_full_unstemmed Combining hard and soft decoders for hypergraph product codes
title_short Combining hard and soft decoders for hypergraph product codes
title_sort combining hard and soft decoders for hypergraph product codes
url https://quantum-journal.org/papers/q-2021-04-15-432/pdf/
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