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Four Color Cube (FCC) fracton model code[1]

Description

A fracton code obtained from four coupled X-cube models using p-membrane condensation. A modular-qudit generalization has been proposed [2].

Rate

The logical space on a cubic lattice of length \(L\) with periodic boundary conditions is \(32L - 24\) qubits.

Cousin

  • X-cube model code— The FCC fracton model code is obtained from four coupled X-cube models using p-membrane condensation. [1].

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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
Parents
Qubit CSS code
Qubit QLDPC codeStabilizer Hamiltonian-based Qubit QECC Quantum
Fracton stabilizer codeLattice stabilizer Stabilizer Hamiltonian-based QECC Quantum
Four Color Cube (FCC) fracton model code

References

[1]
H. Ma, E. Lake, X. Chen, and M. Hermele, “Fracton topological order via coupled layers”, Physical Review B 95, (2017) arXiv:1701.00747 DOI
[2]
E. Wickenden, M. Qi, A. Dua, and M. Hermele, “Planon-modular fracton orders”, Physical Review B 112, (2025) arXiv:2412.14320 DOI
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Your contribution is welcome!

on github.com (edit & pull request)

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Zoo Code ID: fcc_fracton

Cite as:
“Four Color Cube (FCC) fracton model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/fcc_fracton, arXiv:2606.11484
BibTeX:
@incollection{eczoo_fcc_fracton,
title={Four Color Cube (FCC) fracton model 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/fcc_fracton}
}
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Permanent link:
https://errorcorrectionzoo.org/c/fcc_fracton

Cite as:

“Four Color Cube (FCC) fracton model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/fcc_fracton, arXiv:2606.11484

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