\([[8,3,2]]\) Surface code on a cube[1]
Alternative names: Landahl plucky code, Cubic surface code.
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.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
Parents
The surface code on a cube is a twist-defect surface code whose degree-three vertices can be interpreted as disclination twists [1].
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
\([[8,3,2]]\) Surface code on a cube
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
Page edit log
- Victor V. Albert (2025-08-13) — most recent
Cite as:
“\([[8,3,2]]\) Surface code on a cube”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/cubic_surface