Doubled color code[1] 

Description

Family of \([[2t^3+8t^2+6t-1,1,2t+1]]\) subsystem color codes (with \(t\geq 1\)), constructed using a generalization of the doubling transformation [2], that admit a Clifford + \(T\) transversal gate set using gauge fixing.

Transversal Gates

Doubled color codes are triply-even, so they yield a transversal \(T\) gate [1]. Using gauge fixing, the codes admit a Clifford + \(T\) transversal gate set.

Parent

Child

Cousin

  • Divisible code — Doubled color codes are constructed using a generalization of the doubling transformation [2] that combine doubly-even codes to make triply-even codes.

References

[1]
S. Bravyi and A. Cross, “Doubled Color Codes”, (2015) arXiv:1509.03239
[2]
K. Betsumiya and A. Munemasa, “On triply even binary codes”, Journal of the London Mathematical Society 86, 1 (2012) arXiv:1012.4134 DOI
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Zoo Code ID: doubled_color

Cite as:
“Doubled color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/doubled_color
BibTeX:
@incollection{eczoo_doubled_color,
  title={Doubled color code},
  booktitle={The Error Correction Zoo},
  year={2023},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/doubled_color}
}
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Permanent link:
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Cite as:

“Doubled color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/doubled_color

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/subsystem/topological/doubled_color.yml.