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\([[8,3,2]]\) Surface code on a cube[1]

Alternative names: Landahl plucky code, Cubic surface code.

Description

An \([[8,3,2]]\) twist-defect surface code whose qubits lie on the vertices of a cube. It is obtained by three-coloring the faces of a cube and placing \(X\), \(Y\), and \(Z\) stabilizer generators on each pair of faces of the same color. Its non-CSS nature is due to twist defects [2] stemming from the geometry of the polytope.

Cousin

  • Hypercube code— The surface code on a cube, whose qubits lie on the vertices of a cube, is obtained by three-coloring the faces of a cube and placing \(X\), \(Y\), and \(Z\) stabilizer generators on each pair of faces of the same color.

References

[1]
A. J. Landahl, “The surface code on the rhombic dodecahedron”, (2020) arXiv:2010.06628
[2]
H. Bombin, “Topological Order with a Twist: Ising Anyons from an Abelian Model”, Physical Review Letters 105, (2010) arXiv:1004.1838 DOI
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Zoo Code ID: cubic_surface

Cite as:
\([[8,3,2]]\) Surface code on a cube”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/cubic_surface
BibTeX:
@incollection{eczoo_cubic_surface, title={\([[8,3,2]]\) Surface code on a cube}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/cubic_surface} }
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Permanent link:
https://errorcorrectionzoo.org/c/cubic_surface

Cite as:

\([[8,3,2]]\) Surface code on a cube”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/cubic_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/8/cubic_surface.yml.