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)


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
Issue number2
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 ""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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