Classical fractal liquid code[1,2] 

Description

Member of a family of \([L^D,O(L^{D-1}),O(L^{D-\epsilon})]_p\) linear codes on \(D\)-dimensional square lattices of side length \(L\) and for some prime \(p\) and \(\epsilon > 0\) that is based on \(p\)-ary generalizations of the Sierpinski triangle.

Protection

Parameters of some code families saturate the classical version of the BPT bound [1].

Parents

Child

Cousins

  • Hamiltonian-based code — Classical fractal liquid codewords form the ground-state space of a class of spin-glass models with three-body interactions.
  • Sierpinsky fractal spin-liquid (SFSL) code — Both the classical fractal liquid code and the Sierpinsky fractal spin-liquid code utilize the Sierpinski triangle in their constructions. The latter code admits an excitation-moving operator shaped like a Sierpinski triangle [3; Fig. 2].

References

[1]
B. Yoshida, “Information storage capacity of discrete spin systems”, Annals of Physics 338, 134 (2013) arXiv:1111.3275 DOI
[2]
B. Yoshida, “Exotic topological order in fractal spin liquids”, Physical Review B 88, (2013) arXiv:1302.6248 DOI
[3]
A. Dua et al., “Sorting topological stabilizer models in three dimensions”, Physical Review B 100, (2019) arXiv:1908.08049 DOI
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Zoo Code ID: classical_fractal_liquid

Cite as:
“Classical fractal liquid code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/classical_fractal_liquid
BibTeX:
@incollection{eczoo_classical_fractal_liquid, title={Classical fractal liquid code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/classical_fractal_liquid} }
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Cite as:

“Classical fractal liquid code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/classical_fractal_liquid

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/quantum_inspired/classical_fractal_liquid.yml.