Fracton code

Description

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

Parents

Child

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

Cousins

  • 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].
  • 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].

Zoo code information

Internal code ID: fracton

Your contribution is welcome!

on github.com (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. https://errorcorrectionzoo.org/c/fracton
BibTeX:
@incollection{eczoo_fracton, title={Fracton code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/fracton} }
Permanent link:
https://errorcorrectionzoo.org/c/fracton

References

[1]
M. Pretko, X. Chen, and Y. You, “Fracton phases of matter”, International Journal of Modern Physics A 35, 2030003 (2020). DOI; 2001.01722
[2]
D. Aasen et al., “Topological defect networks for fractons of all types”, Physical Review Research 2, (2020). DOI; 2002.05166
[3]
B. J. Brown and D. J. Williamson, “Parallelized quantum error correction with fracton topological codes”, Physical Review Research 2, (2020). DOI; 1901.08061

Cite as:

“Fracton code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/fracton

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/properties/fracton.yml.