Fracton code


A code whose codewords make up the ground-state space of a fracton-phase Hamiltonian.



  • Haah cubic code — Haah cubic codes are the first examples of Type-II fracton phases [1].


  • Topological code — Fracton phases can be understood as topological defect networks, meaning that they can be described in the language of topological quantum field theory [2].
  • Groupoid toric code — Some groupiod toric code models admit fracton-like features such as extensive ground-state degeneracy and excitations with restricted mobility.
  • Translationally invariant stabilizer code — Translationally-invariant stabilizer codes can realize fracton orders. Conversely, fracton codes need not be translationally invariant, and can realize multiple phases on one lattice.
  • XZZX surface code — Subsystem symmetries play a role in finite-bias decoders for both codes [3].


M. Pretko, X. Chen, and Y. You, “Fracton phases of matter”, International Journal of Modern Physics A 35, 2030003 (2020) arXiv:2001.01722 DOI
D. Aasen et al., “Topological defect networks for fractons of all types”, Physical Review Research 2, (2020) arXiv:2002.05166 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
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Zoo Code ID: fracton

Cite as:
“Fracton code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_fracton, title={Fracton code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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Cite as:

“Fracton code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.