3D lattice stabilizer code 

Description

Lattice stabilizer code in three spatial dimensions. Qubit codes are conjectured to admit either fracton phases or abelian topological phases that are equivalent to multiple copies of the 3D surface code and/or the 3D fermionic surface code [1].

Parent

Children

Cousins

  • Abelian topological code — Qubit 3D stabilizer codes are conjectured to admit either fracton phases or abelian topological phases that are equivalent to multiple copies of the 3D surface code and/or the 3D fermionic surface code [1].
  • Self-correcting quantum code — 3D translationally-invariant qubit stabilizer code families with constant \(k\) support logical string operators and thus cannot be self-correcting [2]. For non-constant \(k\), such families can support at most a logarithmic energy barrier [3].

References

[1]
A. Dua et al., “Sorting topological stabilizer models in three dimensions”, Physical Review B 100, (2019) arXiv:1908.08049 DOI
[2]
B. Yoshida, “Feasibility of self-correcting quantum memory and thermal stability of topological order”, Annals of Physics 326, 2566 (2011) arXiv:1103.1885 DOI
[3]
J. Haah, “Local stabilizer codes in three dimensions without string logical operators”, Physical Review A 83, (2011) arXiv:1101.1962 DOI
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Zoo Code ID: 3d_stabilizer

Cite as:
“3D lattice stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/3d_stabilizer
BibTeX:
@incollection{eczoo_3d_stabilizer, title={3D lattice stabilizer code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/3d_stabilizer} }
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Cite as:

“3D lattice stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/3d_stabilizer

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/properties/stabilizer/topological_stabilizer/3d_stabilizer.yml.