Improved Single-Shot Decoding of Higher-Dimensional Hypergraph-Product Codes

Oscar Higgott, Nikolas P. Breuckmann

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)

Abstract

In this work, we study the single-shot performance of higher-dimensional hypergraph product codes decoded using belief propagation and ordered-statistics decoding [P. Panteleev and G. Kalachev, Quantum 5, 585 (2021)]. We find that decoding data-qubit and syndrome-measurement errors together in a single stage leads to single-shot thresholds that greatly exceed all previously observed single-shot thresholds for these codes. For the three-dimensional toric code and a phenomenological noise model, our results are consistent with a sustainable threshold of 7.1% for Z errors, compared to the threshold of 2.90% previously found using a two-stage decoder [Quintavalle et al., 2021]. For the four-dimensional (4D) toric code, for which both X and Z error correction is single shot, our results are consistent with a sustainable single-shot threshold of 4.3%, which is even higher than the threshold of 2.93% for the two-dimensional toric code for the same noise model but using L rounds of stabilizer measurement. We also explore the performance of balanced-product and 4D hypergraph-product codes, which we show lead to a reduction in qubit overhead compared the surface code for phenomenological error rates as high as 1%.

Original languageEnglish
Article number020332
JournalPRX Quantum
Volume4
Issue number2
DOIs
Publication statusPublished - Apr 2023

Bibliographical note

Funding Information:
O.H. acknowledges support from the Engineering and Physical Sciences Research Council (EPSRC) (Grant No. EP/L015242/1). N.P.B. acknowledges support through the EPSRC Prosperity Partnership in Quantum Software for Simulation and Modelling (Grant No. EP/S005021/1). We thank Dan Browne and Joschka Roffe for feedback on an earlier version of the manuscript.

Publisher Copyright:
© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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