Qutrit-Pauli tesselation code[1]
Description
A subcode of a two-mode GKP code whose projection is onto a copy of an irreducible representation of the single-qutrit Pauli group, the symmetry group of the \(\{3,3,3\}\) tesselation of real space [2; pg. 136]. The code admits the corresponding gates via displacements and phase-space rotations.Cousins
- Gottesman-Kitaev-Preskill (GKP) code— The qutrit-Pauli tesselation code is a subcode of a two-mode GKP code [1].
- Hyperbolic tesselation code— Tesselation codes are constructed using symmetry groups of tesselations of real, spherical, and hyperbolic spaces [1]. Examples include the qutrit-Pauli tesselation code, Pauli tesselation QSC, and hyperbolic tesselation code, respectively.
- Pauli tesselation QSC— Tesselation codes are constructed using symmetry groups of tesselations of real, spherical, and hyperbolic spaces [1]. Examples include the qutrit-Pauli tesselation code, Pauli tesselation QSC, and hyperbolic tesselation code, respectively.
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Primary Hierarchy
Parents
The qutrit-Pauli tesselation code is a group-representation code with \(G\) being the single-qutrit Pauli group.
Qutrit-Pauli tesselation 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
- [2]
- H. S. M. Coxeter. Regular polytopes. Courier Corporation, 1973.
Page edit log
- Victor V. Albert (2023-11-28) — most recent
Cite as:
“Qutrit-Pauli tesselation code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qutrit_pauli_gkp_subcode