Pauli tesselation QSC[1]
Description
Two-mode non-uniform QSC whose projection is onto a copy of an irreducible representation of the single-qubit Pauli group, the symmetry group of the \(\{2,2,4\}\) tesselation of the sphere. Each codeword is a quantum superposition of vertices of a tetrahedron with \(\pm 1\) coefficients.Gates
The single-qubit Pauli group can be realized via Gaussian rotations.Cousins
- Simplex spherical code— Each codeword of the Pauli tesselation QSC is a quantum superposition of vertices of a tetrahedron with \(\pm 1\) coefficients.
- 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.
- Bosonic quantum Fourier code— The bosonic quantum Fourier code and the Pauli group-representation QSC are both group-representation codes with \(G\) being the single-qubit Pauli group.
- Qutrit-Pauli 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.
Member of code lists
Primary Hierarchy
Parents
The Pauli tesselation QSC has non-uniform \(\pm 1\) coefficients.
The Pauli tesselation QSC is a group-representation code with \(G\) being the single-qubit Pauli group.
Pauli tesselation QSC
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 (2024-12-29) — most recent
Cite as:
“Pauli tesselation QSC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/pauli_qsc