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Stellated surface code[1]

Description

A twist-defect surface-code family parameterized by a rotational symmetry order \(s\), with a central toric-code twist connected to the boundary by a domain wall. The \(s=3\) member is the triangular surface code [2].

In the plaquette construction of Ref. [1; Appx. D], qubits lie on vertices, each plaquette hosts one stabilizer, and plaquettes along the central domain wall act in mixed Pauli bases.

Rate

Stellated surface codes have \(c=2-\frac{2}{s}\) for odd \(s\) and \(c=2-\frac{4}{s}\) for even \(s\), both approaching \(2\) as \(s\) grows [1; Appx. D].

Cousin

  • Stellated color code— Stellated color codes are color-code analogues of stellated surface codes; the surface-code family has the same rotational parameter \(s\), but half the asymptotic \(c\)-value of the 4.8.8 stellated color-code family [1].

References

[1]
M. S. Kesselring, F. Pastawski, J. Eisert, and B. J. Brown, “The boundaries and twist defects of the color code and their applications to topological quantum computation”, Quantum 2, 101 (2018) arXiv:1806.02820 DOI
[2]
T. J. Yoder and I. H. Kim, “The surface code with a twist”, Quantum 1, 2 (2017) arXiv:1612.04795 DOI
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Zoo Code ID: stellated_surface

Cite as:
“Stellated surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/stellated_surface
BibTeX:
@incollection{eczoo_stellated_surface, title={Stellated surface code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stellated_surface} }
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Cite as:

“Stellated surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/stellated_surface

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