Ball color code[1] 

Description

A color code defined on a \(D\)-dimensional colex. This family includes hyperoctahedron color codes (color codes defined on balls constructed from hyperoctahedra) and 3D ball color codes (color codes defined on duals of certain Archimedean solids).

Protection

The hyperoctahedron code family has parameters \([[2^D,D,2]]\) [1; Exam. 3]. 3D ball codes on duals of the truncated octahedron, truncated cuboctahedron, and truncated icosidodecahedron have parameters \([[24,11,2]]\), \([[48,23,2]]\), and \([[120,59,2]]\), respectively [1; Exam. 4].

Magic

The 3D ball codes on duals of the truncated octahedron, truncated cuboctahedron, and truncated icosidodecahedron have \(\gamma\) close to one.

Transversal Gates

The 3D ball codes on duals of the truncated octahedron, truncated cuboctahedron, and truncated icosidodecahedron have transveral \(CCZ\) gates.

Parents

Children

Cousins

  • Polytope code — Polytopes dual to the truncated octahedron, truncated cuboctahedron, and truncated icosidodecahedron are used to construct 3D ball color codes.
  • Biorthogonal spherical code — Orthoplexes are used to construct hyperoctahedron color codes.

References

[1]
M. Vasmer and A. Kubica, “Morphing Quantum Codes”, PRX Quantum 3, (2022) arXiv:2112.01446 DOI
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Zoo Code ID: ball_color

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

Cite as:

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

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