Generalized five-squares code[13] 

Description

Member of a family of subsystem codes that are generalizations [2,3] of a code defined on a three-valent hypergraph associated with the five-squares lattice [1].

Decoding

Decoding of five-squares codes leads to a mapping of these codes to two copies of the surface code [1,3].

Code Capacity Threshold

Original five-squares code has a threshold of at least \(2\%\) against depolarizing noise [1].

Parents

Cousin

  • Kitaev surface code — Decoding of five-squares codes leads to a mapping of these codes to two copies of the surface code [1,3].

References

[1]
M. Suchara, S. Bravyi, and B. Terhal, “Constructions and noise threshold of topological subsystem codes”, Journal of Physics A: Mathematical and Theoretical 44, 155301 (2011) arXiv:1012.0425 DOI
[2]
P. Sarvepalli and K. R. Brown, “Topological subsystem codes from graphs and hypergraphs”, Physical Review A 86, (2012) arXiv:1207.0479 DOI
[3]
V. V. Gayatri and P. K. Sarvepalli, “Decoding Algorithms for Hypergraph Subsystem Codes and Generalized Subsystem Surface Codes”, (2018) arXiv:1805.12542
Page edit log

Your contribution is welcome!

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

edit on this site

Zoo Code ID: five_squares

Cite as:
“Generalized five-squares code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/five_squares
BibTeX:
@incollection{eczoo_five_squares, title={Generalized five-squares code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/five_squares} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/five_squares

Cite as:

“Generalized five-squares code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/five_squares

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/subsystem/topological/five_squares.yml.