Fracton code 


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




  • 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 with defects [2,3].
  • 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 [4].


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
Z. Song et al., “Topological Defect Network Representations of Fracton Stabilizer Codes”, PRX Quantum 4, (2023) arXiv:2112.14717 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
Page edit log

Your contribution is welcome!

on (edit & pull request)

edit on this site

Zoo Code ID: fracton

Cite as:
“Fracton code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
  title={Fracton code},
  booktitle={The Error Correction Zoo},
  editor={Albert, Victor V. and Faist, Philippe},
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:

Cite as:

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