[Jump to code hierarchy]

Classical topological code[1–3]

Description

Classical code defined on a two-dimensional lattice and derived from a geometrically local stabilizer code, such as the surface code or color code.

Cousin

Member of code lists

Primary Hierarchy

Classical Domain
Binary Kingdom
Binary codeECC
Binary group-orbit codeECC
Linear binary codeLinear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC
Parents
Linear binary code
Quantum-inspired classical block codeECC
Classical topological code
Children
Plaquette Ising code
The 2D plaquette Ising model can be constructed by coupling layers of 1D \(\mathbb{Z}_2\) lattice gauge theory [4]. A field-theoretic description of the 2D plaquette Ising model can be obtained by coupling layers of 1D gauge theory [5].

References

[1]
H. Bombin and M. A. Martin-Delgado, “Homological error correction: Classical and quantum codes”, Journal of Mathematical Physics 48, (2007) arXiv:quant-ph/0605094 DOI
[2]
M.-S. Vaezi, G. Ortiz, and Z. Nussinov, “Robust topological degeneracy of classical theories”, Physical Review B 93, (2016) arXiv:1511.07867 DOI
[3]
D. Chandra, Z. Babar, H. V. Nguyen, D. Alanis, P. Botsinis, S. X. Ng, and L. Hanzo, “Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective”, IEEE Access 6, 13729 (2018) DOI
[4]
B. Rayhaun and D. Williamson, “Higher-form subsystem symmetry breaking: Subdimensional criticality and fracton phase transitions”, SciPost Physics 15, (2023) arXiv:2112.12735 DOI
[5]
P. Gorantla, A. Prem, N. Tantivasadakarn, and D. J. Williamson, “String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to \(p\)-String Condensation”, (2025) arXiv:2505.13604
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: topological_classical

Cite as:
“Classical topological code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/topological_classical
BibTeX:
@incollection{eczoo_topological_classical, title={Classical topological code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/topological_classical} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/topological_classical

Cite as:

“Classical topological code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/topological_classical

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/quantum_inspired/topological_classical.yml.