Clifford subgroup-orbit QSC[1]
Description
A \(((2^r,2,2-\sqrt{2},8))\) QSC for \(r \geq 2\) 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.
Parent
Cousins
- Real-Clifford subgroup-orbit code — Clifford group-orbit QSCs are quantum analogues 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.
References
- [1]
- S. P. Jain et al., “Quantum spherical codes”, Nature Physics (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
- Shubham P. Jain (2023-04-15) — most recent
Cite as:
“Clifford subgroup-orbit QSC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/clifford_group