Clifford subgroup-orbit QSC[1]
Alternative Names: Sidelnikov QSC.
Description
A \(((2^r,2,2-\sqrt{2},8))\) QSC for \(r \geq 1\) constructed using the real Clifford subgroup-orbit code. Logical constellations are constructed by applying elements of an index-two subgroup of the real Clifford group, when taken as a subgroup of the orthogonal group [2] to \(2\) different vectors on the complex sphere. The code is known as the Witting code for \(r=2\) because its two logical constellations form vertices of Witting polytopes.Cousins
- Real-Clifford subgroup-orbit code— Clifford group-orbit QSCs are quantum counterparts of real Clifford subgroup-orbit codes.
- Witting polytope code— Logical constellations of the Clifford subgroup-orbit code for \(r=2\) form vertices of Witting polytopes.
- 24-cell code— Logical constellations of the Clifford subgroup-orbit code for \(r=1\) form vertices of 24-cells when mapped into the real sphere, while code constellations form vertices of a disphenoidal 288-cell.
- Disphenoidal 288-cell code— Logical constellations of the Clifford subgroup-orbit code for \(r=1\) form vertices of 24-cells when mapped into the real sphere, while code constellations form vertices of a disphenoidal 288-cell.
Member of code lists
Primary Hierarchy
References
- [1]
- S. P. Jain, J. T. Iosue, A. Barg, and V. V. Albert, “Quantum spherical codes”, Nature Physics 20, 1300 (2024) arXiv:2302.11593 DOI
- [2]
- G. Nebe, E. M. Rains, and N. J. A. Sloane, “The invariants of the Clifford groups”, (2000) arXiv:math/0001038
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Shubham P. Jain (2023-04-15)
Cite as:
“Clifford subgroup-orbit QSC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_sidelnikov, arXiv:2606.11484