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Qutrit-Pauli group-representation 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.

Cousin

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Primary Hierarchy

Quantum Domain
Bosonic Kingdom
Bosonic codeQECC Quantum
Parents
Bosonic code
Group-representation codeQECC Quantum
The qutrit-Pauli group-representation code is a group-representation code with \(G\) being the single-qutrit Pauli group.
Qutrit-Pauli group-representation code

References

[1]
Y. Wang, Y. Xu, and Z.-W. Liu, “Encoded quantum gates by geometric rotation on tessellations”, (2024) arXiv:2410.18713
[2]
H. S. M. Coxeter. Regular polytopes. Courier Corporation, 1973.
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Zoo Code ID: qutrit_pauli_gkp_subcode

Cite as:
“Qutrit-Pauli group-representation code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qutrit_pauli_gkp_subcode
BibTeX:
@incollection{eczoo_qutrit_pauli_gkp_subcode, title={Qutrit-Pauli group-representation code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qutrit_pauli_gkp_subcode} }
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Permanent link:
https://errorcorrectionzoo.org/c/qutrit_pauli_gkp_subcode

Cite as:

“Qutrit-Pauli group-representation code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qutrit_pauli_gkp_subcode

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/uncategorized/qutrit_pauli_gkp_subcode.yml.