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Hsieh-Halasz-Balents (HHB) code[1]

Description

A member of one of two fracton-code families, named HHB models A and B, defined on a cubic lattice with two qubits per site. Both are expected to be foliated type-I fracton codes [2; Eqs. (D42-D43)].

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
Qubit QLDPC codeStabilizer Hamiltonian-based QECC Quantum
Parents
Qubit QLDPC code
Fracton stabilizer codeLattice stabilizer Stabilizer Hamiltonian-based QECC Quantum
Both HHB models are expected to be foliated type-I fracton codes [2; Eqs. (D42-D43)].
Hsieh-Halasz-Balents (HHB) code

References

[1]
G. B. Halász, T. H. Hsieh, and L. Balents, “Fracton Topological Phases from Strongly Coupled Spin Chains”, Physical Review Letters 119, (2017) arXiv:1707.02308 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
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Zoo Code ID: hhb_fracton

Cite as:
“Hsieh-Halasz-Balents (HHB) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/hhb_fracton, arXiv:2606.11484
BibTeX:
@incollection{eczoo_hhb_fracton,
title={Hsieh-Halasz-Balents (HHB) code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/hhb_fracton}
}
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Permanent link:
https://errorcorrectionzoo.org/c/hhb_fracton

Cite as:

“Hsieh-Halasz-Balents (HHB) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/hhb_fracton, arXiv:2606.11484

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