Icosahedral Fock-state code[1]
Description
A constant-excitation Fock-state code designed to realize the \(2I\) group of gates using Gaussian rotations.
The code has unnormalized logical states \begin{align} \begin{split} |0_{L}\rangle&\propto\sqrt{3}|07\rangle+\sqrt{7}|52\rangle\\ |1_{L}\rangle&\propto\sqrt{7}|25\rangle-\sqrt{3}|70\rangle\,. \end{split} \tag*{(1)}\end{align}
Cousins
- Icosahedral spin code— The icosahedral spin code maps to the icosahedral Fock-state code via the simplex mapping [1].
- \(((7,2,3))\) Pollatsek-Ruskai code— The \(((7,2,3))\) Pollatsek-Ruskai code maps to the icosahedral Fock-state code via the simplex mapping [1].
Primary Hierarchy
Parents
Icosahedral Fock-state codess are group-representation codes with the \(G = 2I\) subgroup of Gaussian rotations [2].
Icosahedral Fock-state code
References
- [1]
- 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
- [2]
- J. A. Gross, “Designing Codes around Interactions: The Case of a Spin”, Physical Review Letters 127, (2021) arXiv:2005.10910 DOI
Page edit log
- Victor V. Albert (2025-10-25) — most recent
Cite as:
“Icosahedral Fock-state code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/icosahedral_fock