Fibonacci fractal spin-liquid code

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Fibonacci fractal spin-liquid code [1]

Alternative Names: Fibonacci prism model code.

Description

A fractal type-I fracton CSS code defined on a cubic lattice [2; Eq. (D23)].

Cousins

Fibonacci code— The Fibonacci fractal spin-liquid code is a hypergraph product of the repetition code and the Fibonacci code [1], and can be formulated directly as a BP code [3].
Repetition code— The Fibonacci fractal spin-liquid code is a hypergraph product of the repetition code and the Fibonacci code [1], and can be formulated directly as a BP code [3].
Balanced product (BP) code— The Fibonacci fractal spin-liquid code is a hypergraph product of the repetition code and the Fibonacci code [1], and can be formulated directly as a BP code [3].
Bosonization code— Bosonization can be used to realize a Fibonacci fractal spin-liquid code with an emergent fermion from a Majorana stabilizer code [4]. This code is shown to be distinct from the original code [5].

Member of code lists

Primary Hierarchy

Quantum Domain

Qubit Kingdom

Qubit codeQECC Quantum

Union stabilizer (USt) codeQECC Quantum

Qubit stabilizer codeQubit Stabilizer Hamiltonian-based QECC Quantum

Coherent-parity-check (CPC) code

Qubit CSS codeCSS Stabilizer Hamiltonian-based QECC Quantum

Generalized homological-product qubit CSS codeQLDPC Qubit CSS Generalized homological-product Stabilizer Hamiltonian-based QECC Quantum

Higher-dimensional homological product code

Homological product codeQLDPC Qubit CSS Generalized homological-product Stabilizer Hamiltonian-based QECC Quantum

Hypergraph product (HGP) codeGeneralized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum

Parents

Hypergraph product (HGP) code

The Fibonacci fractal spin-liquid code is a hypergraph product of the repetition code and the Fibonacci code [1], and can be formulated directly as a BP code [3].

Fracton stabilizer codeLattice stabilizer Stabilizer Hamiltonian-based QECC Quantum

The Fibonacci fractal spin-liquid code is a fractal type-I fracton code [2].

Fibonacci fractal spin-liquid code

References

[1]
B. Yoshida, “Exotic topological order in fractal spin liquids”, Physical Review B 88, (2013) arXiv:1302.6248 DOI
[2]
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
[3]
Y. Tan, B. Roberts, N. Tantivasadakarn, B. Yoshida, and N. Y. Yao, “Fracton models from product codes”, Physical Review Research 7, (2025) arXiv:2312.08462 DOI
[4]
N. Tantivasadakarn, “Jordan-Wigner dualities for translation-invariant Hamiltonians in any dimension: Emergent fermions in fracton topological order”, Physical Review Research 2, (2020) arXiv:2002.11345 DOI
[5]
H. Song, N. Tantivasadakarn, W. Shirley, and M. Hermele, “Fracton Self-Statistics”, Physical Review Letters 132, (2024) arXiv:2304.00028 DOI

Page edit log

Victor V. Albert (2026-06-08) — most recent
Victor V. Albert (2023-04-12)

Cite as:

“Fibonacci fractal spin-liquid code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/fibonacci_fractal_liquid, arXiv:2606.11484

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