\(SU(3)\) spin code[1]
Description
An extension of Clifford single-spin codes to the group \(SU(3)\), whose codespace is a projection onto a particular irrep of a subgroup of \(SU(3)\) of an underlying spin that houses some particular irrep of \(SU(3)\).Cousin
- \(((5,3,2))_3\) qutrit code— The \(((5,3,2))_3\) qutrit code can be interpreted as a \(SU(3)\) single-spin code via the simplex mapping [2; Prop. VI.2].
Member of code lists
Primary Hierarchy
Parents
\(SU(3)\) spin codes are group-representation codes with \(G\) being a subgroup of \(SU(3)\) [1].
\(SU(3)\) spin code
References
- [1]
- X. Herbert, J. Gross, and M. Newman, “Qutrit codes within representations of SU(3)”, (2023) arXiv:2312.00162
- [2]
- 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
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2023-12-07)
Cite as:
“\(SU(3)\) spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/su3_spin, arXiv:2606.11484