Colour Codes Reach Surface Code Performance using Vibe Decoding
ORAL · Invited
Abstract
Two-dimensional quantum colour codes offer significant promise for quantum error correction, providing planar connectivity and low-overhead logical gates. Despite these advantages, their practical deployment has been limited by the complexity of decoding relative to surface codes.
In this work, we introduce vibe decoding, the first polynomial-time decoding method to bring colour-code performance on par with the surface code. Our approach combines an ensemble of belief-propagation decoders—each using a distinct serial message-passing schedule—with post-processing based on localised statistics decoding (LSD). We refer to this combined protocol as VibeLSD.
Our numerical simulations demonstrate that VibeLSD outperforms all existing practical polynomial-time colour-code decoders across a range of syndrome extraction schemes, noise models, and error rates. Our quantum memory simulations indicate that colour codes decoded with VibeLSD require qubit overhead comparable to, and in some cases lower than, that of the surface code.
Applied to experimental device data from Google Quantum AI [Lacroix et al.], VibeLSD decoding yields a threshold for distance-3 to distance-5 instances. Its strong performance on device data, together with the inherently parallel nature of localised statistics decoding, makes vibe decoding a promising candidate for implementation on specialised hardware and real-time decoding.
Our results position the colour code as a practical architecture for near-term quantum hardware, enabling improved compilation efficiency for both Clifford and non-Clifford gates without additional qubit overhead relative to the surface code.
References
[Lacroix et al.] Scaling and logic in the colour code on a superconducting quantum processor. Nature volume 645, pages 614–619 (2025)
In this work, we introduce vibe decoding, the first polynomial-time decoding method to bring colour-code performance on par with the surface code. Our approach combines an ensemble of belief-propagation decoders—each using a distinct serial message-passing schedule—with post-processing based on localised statistics decoding (LSD). We refer to this combined protocol as VibeLSD.
Our numerical simulations demonstrate that VibeLSD outperforms all existing practical polynomial-time colour-code decoders across a range of syndrome extraction schemes, noise models, and error rates. Our quantum memory simulations indicate that colour codes decoded with VibeLSD require qubit overhead comparable to, and in some cases lower than, that of the surface code.
Applied to experimental device data from Google Quantum AI [Lacroix et al.], VibeLSD decoding yields a threshold for distance-3 to distance-5 instances. Its strong performance on device data, together with the inherently parallel nature of localised statistics decoding, makes vibe decoding a promising candidate for implementation on specialised hardware and real-time decoding.
Our results position the colour code as a practical architecture for near-term quantum hardware, enabling improved compilation efficiency for both Clifford and non-Clifford gates without additional qubit overhead relative to the surface code.
References
[Lacroix et al.] Scaling and logic in the colour code on a superconducting quantum processor. Nature volume 645, pages 614–619 (2025)
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Publication: Stergios Koutsioumpas, Tamas Noszko, Hasan Sayginel, Mark Webster, Joschka Roffe. "Colour Codes Reach Surface Code Performance using Vibe Decoding". Preprint arXiv:2508.15743. Uploaded: 2025-08-21. arXiv: 2508.15743. doi: 10.48550/arXiv.2508.15743.
Presenters
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Joschka Roffe
- University of Edinburgh