Checkerboard model code[1]
Description
A foliated type-I fracton code defined on a cubic lattice that admits weight-eight \(X\)- and \(Z\)-type stabilizer generators on the eight vertices of each cube in the lattice.
Variants include the twisted checkerboard model [2].
Decoding
Parallelized matching decoder [3].
Code Capacity Threshold
Independent \(X,Z\) noise: \(\sim 7.5\%\), higher than 3D surface code and color code [4].
Parents
- Qubit CSS code
- Fracton stabilizer code — The checkerboard model is equivalent to two copies of the X-cube model via a local constant-depth unitary [5]. Hence, it is a foliated type-I fracton code.
Cousins
- X-cube model code — The checkerboard model is equivalent to two copies of the X-cube model via a local constant-depth unitary [5].
- Fracton Floquet code — The ISG of the X-cube Floquet code can be that of the X-cube model code or the checkerboard model code.
References
- [1]
- S. Vijay, J. Haah, and L. Fu, “A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations”, Physical Review B 92, (2015) arXiv:1505.02576 DOI
- [2]
- H. Song et al., “Twisted fracton models in three dimensions”, Physical Review B 99, (2019) arXiv:1805.06899 DOI
- [3]
- B. J. Brown and D. J. Williamson, “Parallelized quantum error correction with fracton topological codes”, Physical Review Research 2, (2020) arXiv:1901.08061 DOI
- [4]
- H. Song et al., “Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry”, Physical Review Letters 129, (2022) arXiv:2112.05122 DOI
- [5]
- W. Shirley, K. Slagle, and X. Chen, “Foliated fracton order in the checkerboard model”, Physical Review B 99, (2019) arXiv:1806.08633 DOI
Page edit log
- Victor V. Albert (2024-01-30) — most recent
Cite as:
“Checkerboard model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/checkerboard