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Lift-connected surface (LCS) code[1]

Description

Member of one of several families of lifted-product codes that consist of sparsely interconnected stacks of surface codes.

Protection

Code distance is linear with \(n\) up to some maximum number of qubits.

Code Capacity Threshold

\(6.7\%\) and \(7.7\%\) under bit-flip noise and BP+OSD decoding for two families of LCS codes.

Threshold

\(2.9\%\) and \(3.2\%\) under phenomenological noise and BP+OSD decoding for two families of LCS codes.

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
Parents
Generalized homological-product qubit CSS code
Lifted-product (LP) codeGeneralized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum
Lift-connected surface (LCS) code
Children
Kitaev surface code
LCS codes consist of sparsely interconnected stacks of surface codes.

References

[1]
J. Old, M. Rispler, and M. Müller, “Lift-connected surface codes”, Quantum Science and Technology 9, 045012 (2024) arXiv:2401.02911 DOI
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Zoo Code ID: lcs

Cite as:
“Lift-connected surface (LCS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/lcs, arXiv:2606.11484
BibTeX:
@incollection{eczoo_lcs,
title={Lift-connected surface (LCS) 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/lcs}
}
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Permanent link:
https://errorcorrectionzoo.org/c/lcs

Cite as:

“Lift-connected surface (LCS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/lcs, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/qldpc/balanced_product/lp/lcs.yml.