\(((5,3,2))_3\) qutrit code[1]
Description
Smallest qutrit block code realizing the \(\Sigma(360\phi)=3.A_6\) subgroup of \(SU(3)\) transversally. The next smallest code is \(((7,3,2))_3\).Transversal and Permutation-Based Gates
\(\Sigma(360\phi)=3.A_6\) group gates can be realized transversally.Cousin
- \(SU(3)\) spin 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].
Primary Hierarchy
Parents
The \(((5,3,2))_3\) qutrit code admits a transversal representation of the twisted \(1\)-group \(\Sigma(360\phi)=3.A_6\) [1].
\(((5,3,2))_3\) qutrit code
References
- [1]
- E. Kubischta and I. Teixeira, “Quantum Codes from Twisted Unitary t -Groups”, Physical Review Letters 133, (2024) arXiv:2402.01638 DOI
- [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 (2024-01-06)
Cite as:
“\(((5,3,2))_3\) qutrit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/su3_sigma360, arXiv:2606.11484