\([[14,3,3]]\) Rhombic dodecahedron surface code[1] 

Also known as Landahl jaunty code.

Description

A \([[14,3,3]]\) twist-defect surface code whose qubits lie on the vertices of a rhombic dodecahedron. Its non-CSS nature is due to twist defects [2] stemming from the geometry of the polytope.

Parents

Cousins

  • Polytope code — The rhombic dodecahedron surface code arranges qubits and stabilizer generators on polytopes.
  • Dodecahedron code — The qubits of the \([[14,3,3]]\) rhombic dodecahedron surface code lie on the vertices of the small stellated dodecahedron.

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: rhombic_dodecahedron_surface

Cite as:
“\([[14,3,3]]\) Rhombic dodecahedron surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/rhombic_dodecahedron_surface
BibTeX:
@incollection{eczoo_rhombic_dodecahedron_surface, title={\([[14,3,3]]\) Rhombic dodecahedron surface code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/rhombic_dodecahedron_surface} }
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Permanent link:
https://errorcorrectionzoo.org/c/rhombic_dodecahedron_surface

Cite as:

“\([[14,3,3]]\) Rhombic dodecahedron surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/rhombic_dodecahedron_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/surface/non-css/rhombic_dodecahedron_surface.yml.