\(((3,2,2))_3\) Three-qutrit single-deletion code[1]
Description
Three-qutrit PI code that is the smallest qutrit PI code to correct one deletion error.
The code admits the following logical codewords: \begin{align} |\overline{0}\rangle &\propto|000\rangle+|111\rangle+|222\rangle\tag*{(1)}\\ |\overline{1}\rangle &\propto|012\rangle+|021\rangle+|102\rangle+|120\rangle+|201\rangle+|210\rangle~. \tag*{(2)}\end{align}
Protection
The smallest qutrit PI code to correct one deletion error.Cousins
- \(((4,2,2))\) Four-qubit single-deletion code— The four-qubit (three-qutrit) single-deletion code is the smallest PI qubit (qutrit) code to correct one deletion error.
- Wasilewski-Banaszek code— The three-qutrit single-deletion code maps to the Wasilewski-Banaszek code via the simplex mapping [1].
- \([[3,1,2]]_3\) Three-qutrit code— Projecting the three-qutrit code into the PI qutrit subspace yields the three-qutrit single-deletion code [1].
Primary Hierarchy
Parents
\(((3,2,2))_3\) Three-qutrit single-deletion 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
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2025-10-24)
Cite as:
“\(((3,2,2))_3\) Three-qutrit single-deletion code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/three_qutrit_permutation_invariant, arXiv:2606.11484