Efficient color code decoders in $d\geq 2$ dimensions from toric code decoders

Aleksander Kubica; Nicolas Delfosse

doi:10.22331/q-2023-02-21-929

Efficient color code decoders in $d\geq 2$ dimensions from toric code decoders

Aleksander Kubica^1,2 and Nicolas Delfosse³

¹Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
²Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada
³Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA

Published:	2023-02-21, volume 7, page 929
Eprint:	arXiv:1905.07393v3
Doi:	https://doi.org/10.22331/q-2023-02-21-929
Citation:	Quantum 7, 929 (2023).

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Abstract

We introduce an efficient decoder of the color code in $d\geq 2$ dimensions, the Restriction Decoder, which uses any $d$-dimensional toric code decoder combined with a local lifting procedure to find a recovery operation. We prove that the Restriction Decoder successfully corrects errors in the color code if and only if the corresponding toric code decoding succeeds. We also numerically estimate the Restriction Decoder threshold for the color code in two and three dimensions against the bit-flip and phase-flip noise with perfect syndrome extraction. We report that the 2D color code threshold $p_{\textrm{2D}} \approx 10.2\%$ on the square-octagon lattice is on a par with the toric code threshold on the square lattice.

Featured image: The Restriction Decoder combines a toric code decoder with a local lifting procedure in oder to find a recovery operator for the color code.

Conference Talk: Error correction with the color code

► BibTeX data

@article{Kubica2023efficientcolorcode,
  doi = {10.22331/q-2023-02-21-929},
  url = {https://doi.org/10.22331/q-2023-02-21-929},
  title = {Efficient color code decoders in {$d\geq 2$} dimensions from toric code decoders},
  author = {Kubica, Aleksander and Delfosse, Nicolas},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {929},
  month = feb,
  year = {2023}
}

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