Dinur-Lin-Vidick (DLV) code[1] 

Description

Member of a family of quantum locally testable codes constructed using cubical chain complexes, which are \(t\)-order extensions of the complexes underlying expander codes (\(t=1\)) and expander lifted-product codes (\(t=2\)).

For \(t=4\), assuming a conjecture about random linear maps, there exists a family with linear dimension and inverse poly-logarithmic relative distance and soundness. Applying weight reduction yields order \(\Omega(1/\text{polylog}n)\) soundness, distance, and dimension, but order \(\Theta(n)\) locality [2; Table 4]. Applying distance amplification and soundness amplification yields asymptotically constant soundness, order \(\Theta(n)\) distance, order \(\Theta(n)\) dimension, but poly-logarithmic locality [2; Table 4].

Parent

Cousin

  • Quantum locally testable code (QLTC) — DLV codes have linear dimension and inverse poly-logarithmic relative distance and soundness, assuming a conjecture about random linear maps [1]. Applying distance amplification and soundness amplification yields asymptotically constant soundness, order \(\Theta(n)\) distance, order \(\Theta(n)\) dimension, but poly-logarithmic locality [2; Table 4].

References

[1]
I. Dinur, T.-C. Lin, and T. Vidick, “Expansion of higher-dimensional cubical complexes with application to quantum locally testable codes”, (2024) arXiv:2402.07476
[2]
A. Wills, T.-C. Lin, and M.-H. Hsieh, “Tradeoff Constructions for Quantum Locally Testable Codes”, (2024) arXiv:2309.05541
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Zoo Code ID: dlv

Cite as:
“Dinur-Lin-Vidick (DLV) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/dlv
BibTeX:
@incollection{eczoo_dlv, title={Dinur-Lin-Vidick (DLV) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/dlv} }
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Cite as:

“Dinur-Lin-Vidick (DLV) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/dlv

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/qldpc/homological/dlv.yml.