Fracton code
Description
A code whose codewords make up the ground-state space of a fracton-phase Hamiltonian.
Parents
- Hamiltonian-based code — Codespace is the ground-state subspace of a geometrically local commuting-projector Hamiltonian admitting a fracton phase.
- Quantum low-density parity-check (QLDPC) code — Fracton codes admit geometrically local stabilizer generators on a cubic lattice.
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].
- 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].
References
- [1]
- M. Pretko, X. Chen, and Y. You, “Fracton phases of matter”, International Journal of Modern Physics A 35, 2030003 (2020) arXiv:2001.01722 DOI
- [2]
- D. Aasen et al., “Topological defect networks for fractons of all types”, Physical Review Research 2, (2020) arXiv:2002.05166 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
Page edit log
- Victor V. Albert (2022-01-05) — most recent
Cite as:
“Fracton code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/fracton