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].
Primary Hierarchy
Parents
Stellated surface code
Children
The triangular surface code is the \(s=3\) member of the stellated surface-code family [1; Appx. D].
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
Page edit log
- Victor V. Albert (2026-05-03) — most recent
Cite as:
“Stellated surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/stellated_surface