Qutrit-Pauli tessellation code[1]
Description
Euclidean-plane tessellation code whose projection is onto a copy of an irreducible representation of the single-qutrit Pauli group, realized by the \(\{3,3,3\}\) tessellation [1]. The code is a subcode of a two-mode GKP code and has GKP-like stabilizers. Logical \(X\), \(Z\), and \((ZX)^{-1}\) are implemented by \(2\pi/3\) rotations around tessellation vertices, while only a GKP-like logical \(Z\) is available via real-space displacement.Protection
The code corrects translation errors of Euclidean norm less than \(\sqrt{3}/2\). It also corrects momentum errors in any direction with \(|\vec{k}| < 2\pi/9\) [1].Cousins
- Gottesman-Kitaev-Preskill (GKP) code— The qutrit-Pauli tessellation code is a subcode of a two-mode GKP code with GKP-like stabilizers [1].
- Hyperbolic tessellation code— The qutrit-Pauli tessellation code is the Euclidean \(\{3,3,3\}\) member of the same curvature-dependent tessellation-code framework [1].
Member of code lists
Primary Hierarchy
Parents
The qutrit-Pauli tessellation code is a group-representation code with \(G\) being the single-qutrit Pauli group.
Qutrit-Pauli tessellation code
References
- [1]
- Y. Wang, Y. Xu, and Z.-W. Liu, “Tessellation Codes: Encoded Quantum Gates by Geometric Rotation”, Physical Review Letters 135, (2025) arXiv:2410.18713 DOI
Page edit log
- Victor V. Albert (2026-04-22) — most recent
- Victor V. Albert (2023-11-28)
Cite as:
“Qutrit-Pauli tessellation code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/qutrit_pauli_gkp_subcode