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]. The original five-squares code is a 2D topological subsystem code with local two-qubit gauge generators; on a torus, it encodes two logical qubits [1].Decoding
For the original five-squares code, preprocessing maps decoding onto two copies of the toric code, after which one can use minimum-weight matching or renormalization-group decoding [1].Generalized five-squares codes can also be decoded via a mapping to two copies of the surface code [3].Code Capacity Threshold
For depolarizing noise, the original five-squares code has a threshold around \(1.5\%\) under the simple decoder and around \(2\%\) under the improved decoder [1].Cousin
- Toric code— For the original five-squares code, preprocessing maps decoding onto two copies of the toric code [1].
Primary Hierarchy
Parents
Generalized five-squares codes are special cases of Sarvepalli-Brown subsystem codes [3; Sec. II.B].
Generalized five-squares code
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