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Modular-qudit 3D surface code[1,2]

Description

A generalization of the 3D surface code to modular qudits. Qudits are placed on edges, \(Z\)-type stabilizer generators are placed on square plaquettes oriented in all three directions, and \(X\)-type stabilizers are placed on the six edges neighboring every vertex [1].

Primary Hierarchy

Parents
A quantum triple model for the group \(G=\mathbb{Z}_q\) is a modular-qudit 3D surface code.
The modular-qudit 3D surface code realizes 3D \(\mathbb{Z}_q\) gauge theory with bosonic charge and loop excitations (BcBl).
Modular-qudit 3D surface code
Children
The qudit 3D surface code reduces to the 3D surface code for \(q=2\). The 3D surface code realizes 3D \(\mathbb{Z}_2\) gauge theory with bosonic charge and loop excitations (BcBl). The welded surface code does not satisfy homogeneous topological order [3].

References

[1]
H. Moradi and X.-G. Wen, “Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations”, Physical Review B 91, (2015) arXiv:1404.4618 DOI
[2]
C. Lee, Y. Hu, G. Y. Cho, and H. Watanabe, “\(\mathbb{Z}_N\) generalizations of three-dimensional stabilizer codes”, (2025) arXiv:2504.09847
[3]
J. Haah, “A degeneracy bound for homogeneous topological order”, SciPost Physics 10, (2021) arXiv:2009.13551 DOI
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Zoo Code ID: qudit_3d_surface

Cite as:
“Modular-qudit 3D surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qudit_3d_surface
BibTeX:
@incollection{eczoo_qudit_3d_surface, title={Modular-qudit 3D surface code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qudit_3d_surface} }
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Permanent link:
https://errorcorrectionzoo.org/c/qudit_3d_surface

Cite as:

“Modular-qudit 3D surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qudit_3d_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/surface/higher_d/qudit_3d_surface.yml.