Description
A fractal type-I fracton CSS code defined on a cubic lattice [3; Eq. (D22)]. The code admits an excitation-moving operator shaped like a Sierpinski triangle [3; Fig. 2].
Parents
- Qubit CSS code
- Fracton stabilizer code — The Sierpinsky fractal spin-liquid code is a fractal type-I fracton code [3].
- Hypergraph product (HGP) code — The Sierpinsky fractal spin-liquid code is the hypergraph product of the repetition code and the Newman-Moore code [4,5].
Cousin
- Newman-Moore code — The Sierpinsky fractal spin-liquid code is the hypergraph product of the repetition code and the Newman-Moore code [4,5].
References
- [1]
- C. Castelnovo and C. Chamon, “Topological quantum glassiness”, Philosophical Magazine 92, 304 (2012) arXiv:1108.2051 DOI
- [2]
- B. Yoshida, “Exotic topological order in fractal spin liquids”, Physical Review B 88, (2013) arXiv:1302.6248 DOI
- [3]
- A. Dua et al., “Sorting topological stabilizer models in three dimensions”, Physical Review B 100, (2019) arXiv:1908.08049 DOI
- [4]
- Y. Tan et al., “Fracton models from product codes”, (2024) arXiv:2312.08462
- [5]
- T. Rakovszky and V. Khemani, “The Physics of (good) LDPC Codes II. Product constructions”, (2024) arXiv:2402.16831
Page edit log
- Nathanan Tantivasadakarn (2024-06-27) — most recent
- Victor V. Albert (2023-04-12)
Cite as:
“Sierpinsky fractal spin-liquid (SFSL) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/sierpinsky_fractal_liquid