Icosahedral spin code[1]
Description
A single-spin code designed to realize a \(2I\) group of gates using \(SU(2)\) rotations.
The code has unnormalized logical states \begin{align} \begin{split} |0_{L}\rangle&\propto\sqrt{3}|_{7/2}^{7/2}\rangle+\sqrt{7}|_{-3/2}^{7/2}\rangle\\ |1_{L}\rangle&\propto\sqrt{7}|_{3/2}^{7/2}\rangle-\sqrt{3}|_{-7/2}^{7/2}\rangle\,. \end{split} \tag*{(1)}\end{align}
Cousins
- Icosahedral Fock-state code— The icosahedral spin code maps to the icosahedral Fock-state code via the simplex mapping [2].
- \(((7,2,3))\) Pollatsek-Ruskai code— The \(((7,2,3))\) Pollatsek-Ruskai code maps to the icosahedral spin code via the Dicke state mapping [3].
Member of code lists
Primary Hierarchy
Parents
Icosahedral spin code
References
- [1]
- J. A. Gross, “Designing Codes around Interactions: The Case of a Spin”, Physical Review Letters 127, (2021) arXiv:2005.10910 DOI
- [2]
- A. Aydin, V. V. Albert, and A. Barg, “Quantum error correction beyond \(SU(2)\): spin, bosonic, and permutation-invariant codes from convex geometry”, (2025) arXiv:2509.20545
- [3]
- E. Kubischta and I. Teixeira, “Family of Quantum Codes with Exotic Transversal Gates”, Physical Review Letters 131, (2023) arXiv:2305.07023 DOI
Page edit log
- Victor V. Albert (2025-10-25) — most recent
Cite as:
“Icosahedral spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/icosahedral_spin