Fracton code

Description

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

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.

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].
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].

[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

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