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Sierpinsky fractal spin-liquid (SFSL) code[1,2]

Description

A fractal type-I fracton CSS code defined on a cubic lattice [3; Eq. (D22)]. The code admits an excitation-moving operator shaped like a Sierpinski triangle [3; Fig. 2].

Cousins

  • Newman-Moore code— The Sierpinsky fractal spin-liquid code is a hypergraph product of the repetition code and the Newman-Moore code [4,5].
  • Repetition code— The Sierpinsky fractal spin-liquid code is a hypergraph product of the repetition code and the Newman-Moore code [4,5].

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Qubit Hamiltonian-based QECC Quantum
Parents
Qubit CSS code
Fracton stabilizer codeLattice stabilizer QLDPC Stabilizer Hamiltonian-based QECC Quantum
The Sierpinsky fractal spin-liquid code is a fractal type-I fracton code [3].
Hypergraph product (HGP) codeGeneralized homological-product Lattice stabilizer QLDPC CSS Stabilizer Qubit Hamiltonian-based QECC Quantum
The Sierpinsky fractal spin-liquid code is a hypergraph product of the repetition code and the Newman-Moore code [4,5].
Sierpinsky fractal spin-liquid (SFSL) code

References

[1]
C. Castelnovo and C. Chamon, “Topological quantum glassiness”, Philosophical Magazine 92, 304 (2012) arXiv:1108.2051 DOI
[2]
B. Yoshida, “Exotic topological order in fractal spin liquids”, Physical Review B 88, (2013) arXiv:1302.6248 DOI
[3]
A. Dua, I. H. Kim, M. Cheng, and D. J. Williamson, “Sorting topological stabilizer models in three dimensions”, Physical Review B 100, (2019) arXiv:1908.08049 DOI
[4]
Y. Tan, B. Roberts, N. Tantivasadakarn, B. Yoshida, and N. Y. Yao, “Fracton models from product codes”, (2024) arXiv:2312.08462
[5]
T. Rakovszky and V. Khemani, “The Physics of (good) LDPC Codes II. Product constructions”, (2024) arXiv:2402.16831
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Zoo Code ID: sierpinsky_fractal_liquid

Cite as:
“Sierpinsky fractal spin-liquid (SFSL) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/sierpinsky_fractal_liquid
BibTeX:
@incollection{eczoo_sierpinsky_fractal_liquid, title={Sierpinsky fractal spin-liquid (SFSL) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/sierpinsky_fractal_liquid} }
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Permanent link:
https://errorcorrectionzoo.org/c/sierpinsky_fractal_liquid

Cite as:

“Sierpinsky fractal spin-liquid (SFSL) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/sierpinsky_fractal_liquid

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fracton/sierpinsky_fractal_liquid.yml.