\([[8,3,2]]\) Surface code on a cube[1]
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.
A stabilizer tableau for the code is given by [3; ID 6851] \begin{align} \begin{array}{cccccccc} I & Y & Y & I & Z & I & Z & I \\ X & I & Z & Z & X & I & I & I \\ I & X & I & X & Y & Y & I & I \\ I & Z & I & I & I & Z & X & Z \\ Z & I & I & Y & I & X & I & Y \end{array}~. \tag*{(1)}\end{align}
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.
Primary Hierarchy
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
- [3]
- Qiskit Community, “Qiskit QEC framework”, URL
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2025-08-13)
- Andrew J. Landahl (2025-08-13)
- Jim Harrington (2025-08-13)
Cite as:
“\([[8,3,2]]\) Surface code on a cube”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/cubic_surface, arXiv:2606.11484