Icosahedral Fock-state code[1]
Description
A constant-excitation Fock-state code designed to realize the \(2I\) group of gates using Gaussian rotations. It is obtained from the corresponding icosahedral spin code via the simplex mapping between spin and constant-excitation Fock spaces [1].
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 codes 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 <mml:math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”inline”> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> <mml:mo stretchy=”false”>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy=”false”>)</mml:mo> </mml:math> : Spin, Bosonic, and Permutation-Invariant Codes from Convex Geometry”, PRX Quantum 7, (2026) arXiv:2509.20545 DOI
- [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 (2026-06-08) — most recent
- Victor V. Albert (2025-10-25)
Cite as:
“Icosahedral Fock-state code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/icosahedral_fock, arXiv:2606.11484