Minimising surface-code failures using a color-code decoder

Asmae Benhemou; Kaavya Sahay; Lingling Lao; Benjamin J. Brown

doi:10.22331/q-2025-02-17-1632

Minimising surface-code failures using a color-code decoder

Asmae Benhemou¹, Kaavya Sahay², Lingling Lao¹, and Benjamin J. Brown³

¹Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
²Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
³Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark

Published:	2025-02-17, volume 9, page 1632
Editor:	Felix Huber
Eprint:	arXiv:2306.16476v3
Doi:	https://doi.org/10.22331/q-2025-02-17-1632
Citation:	Quantum 9, 1632 (2025).

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Abstract

The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced by the depolarising noise model. The decoder is obtained by mapping the syndrome of the surface code onto that of the color code, thereby allowing us to adopt more sophisticated color-code decoding algorithms. Analytical arguments and exhaustive testing show that the resulting decoder can find a least-weight correction for all weight $d/2$ depolarising errors for even code distance $d$. This improves the logical error rate by an exponential factor $O(2^{d/2})$ compared with decoders that treat bit-flip and dephasing errors separately. We demonstrate this improvement with analytical arguments and supporting numerical simulations at low error rates. Of independent interest, we also demonstrate an exponential improvement in logical error rate for our decoder used to correct independent and identically distributed bit-flip errors affecting the color code compared with more conventional color-code decoding algorithms.

► BibTeX data

@article{Benhemou2025minimisingsurface,
  doi = {10.22331/q-2025-02-17-1632},
  url = {https://doi.org/10.22331/q-2025-02-17-1632},
  title = {Minimising surface-code failures using a color-code decoder},
  author = {Benhemou, Asmae and Sahay, Kaavya and Lao, Lingling and Brown, Benjamin J.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1632},
  month = feb,
  year = {2025}
}

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[3] Moritz Lange, Pontus Havström, Basudha Srivastava, Isak Bengtsson, Valdemar Bergentall, Karl Hammar, Olivia Heuts, Evert van Nieuwenburg, and Mats Granath, "Data-driven decoding of quantum error correcting codes using graph neural networks", Physical Review Research 7 2, 023181 (2025).

[4] Victor V. Albert and Philippe Faist, "Handbook of Error-Correcting Codes", arXiv:2606.11484, (2026).

[5] Cody Jones, "Improved accuracy for decoding surface codes with matching synthesis", arXiv:2408.12135, (2024).

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