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
- Sarvepalli-Brown subsystem code — Generalized five-squares codes are special cases of Sarvepalli-Brown subsystem codes [3; Sec. II.B].
- Lattice subsystem code
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
- Victor V. Albert (2024-01-23) — most recent
Cite as:
“Generalized five-squares code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/five_squares