Cubic honeycomb color code[1] 

Description

3D color code defined on a four-colorable bitruncated cubic honeycomb uniform tiling.

Transversal Gates

A code family on a truncated cube with particular boundary conditions admits a transversal control-\(S\) gate via physical \(T\) and \(T^{\dagger}\) gates [2].

Parent

Cousin

References

[1]
H. Bombin and M. A. Martin-Delgado, “Exact topological quantum order inD=3and beyond: Branyons and brane-net condensates”, Physical Review B 75, (2007) arXiv:cond-mat/0607736 DOI
[2]
B. J. Brown, “Color code with a logical control-\(S\) gate using transversal \(T\) rotations”, (2024) arXiv:2411.15035
[3]
M. Davydova, N. Tantivasadakarn, S. Balasubramanian, and D. Aasen, “Quantum computation from dynamic automorphism codes”, Quantum 8, 1448 (2024) arXiv:2307.10353 DOI
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Zoo Code ID: cubic_honeycomb_color

Cite as:
“Cubic honeycomb color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/cubic_honeycomb_color
BibTeX:
@incollection{eczoo_cubic_honeycomb_color, title={Cubic honeycomb color code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/cubic_honeycomb_color} }
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Permanent link:
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Cite as:

“Cubic honeycomb color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/cubic_honeycomb_color

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/color/3d_color/cubic_honeycomb_color.yml.