Checkerboard model code[1] 


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].


Parallelized matching decoder [3].

Code Capacity Threshold

Independent \(X,Z\) noise: \(\sim 7.5\%\), higher than 3D surface code and color code [4].



  • X-cube model code — The checkerboard model is equivalent to two copies of the X-cube model via a local unitary [5].


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
H. Song et al., “Twisted fracton models in three dimensions”, Physical Review B 99, (2019) arXiv:1805.06899 DOI
B. J. Brown and D. J. Williamson, “Parallelized quantum error correction with fracton topological codes”, Physical Review Research 2, (2020) arXiv:1901.08061 DOI
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
W. Shirley, K. Slagle, and X. Chen, “Foliated fracton order in the checkerboard model”, Physical Review B 99, (2019) arXiv:1806.08633 DOI
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Zoo Code ID: checkerboard

Cite as:
“Checkerboard model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.
@incollection{eczoo_checkerboard, title={Checkerboard model code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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Cite as:

“Checkerboard model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.