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Anisotropic \(\mathbb{Z}_2\) Laplacian model code[1,2]

Description

A graph-based analogue of a Type-I fracton phase with lineon-like restricted mobility [1,2].

On generic sparse graphs, the Laplacian seed is not rank deficient enough to generate fracton order [3]. Instead, the model exhibits partially confined point-like excitations in a phase more akin to nonlocal topological order.

Cousins

  • Repetition code— The anisotropic \(\mathbb{Z}_2\) Laplacian model is the hypergraph product of a cyclic repetition code and a Laplacian code [3].
  • Laplacian code— The anisotropic \(\mathbb{Z}_2\) Laplacian model is the hypergraph product of a cyclic repetition code and a Laplacian code [3].

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 Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS codeQLDPC Qubit Generalized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum
Higher-dimensional homological product code
Hypergraph product (HGP) codeQLDPC CSS Generalized homological-product Lattice stabilizer Stabilizer Hamiltonian-based Qubit QECC Quantum
Parents
Hypergraph product (HGP) code
The anisotropic \(\mathbb{Z}_2\) Laplacian model is the hypergraph product of a cyclic repetition code and a Laplacian code [3].
Fracton stabilizer codeLattice stabilizer Stabilizer Hamiltonian-based QECC Quantum
The anisotropic \(\mathbb{Z}_2\) Laplacian model code is a graph-based analogue of a Type-I fracton phase with lineon-like restricted mobility.
Anisotropic \(\mathbb{Z}_2\) Laplacian model code

References

[1]
P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, “Gapped lineon and fracton models on graphs”, Physical Review B 107, (2023) arXiv:2210.03727 DOI
[2]
H. Ebisu and B. Han, “Anisotropic higher rank \(\mathbb{Z}_N\) topological phases on graphs”, SciPost Physics 14, (2023) arXiv:2209.07987 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
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Zoo Code ID: anisotropic_z2_laplacian

Cite as:
“Anisotropic \(\mathbb{Z}_2\) Laplacian model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/anisotropic_z2_laplacian
BibTeX:
@incollection{eczoo_anisotropic_z2_laplacian, title={Anisotropic \(\mathbb{Z}_2\) Laplacian model code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/anisotropic_z2_laplacian} }
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Permanent link:
https://errorcorrectionzoo.org/c/anisotropic_z2_laplacian

Cite as:

“Anisotropic \(\mathbb{Z}_2\) Laplacian model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/anisotropic_z2_laplacian

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fracton/anisotropic_z2_laplacian.yml.