Lossless expander balanced-product code[1,2] 

Description

QLDPC code constructed by taking the balanced product of lossless expander graphs. Using one part of a quantum-code chain complex constructed with one-sided loss expanders [3] yields a \(c^3\)-LTC [1]. Using two-sided expanders, which are only conjectured to exist, yields an asymptotically good QLDPC code family [2].

Rate

Asymptotically good QLDPC codes [2], assuming the existence of two-sided lossless expanders.

Parents

Cousins

  • Locally testable code (LTC) — Using one part of a quantum-code chain complex constructed with one-sided loss expanders yields a \(c^3\)-LTC [1].
  • Good QLDPC code — Taking a balanced product of two-sided expanders, which are only conjectured to exist, yields an asymptotically good QLDPC code family [2].

References

[1]
T.-C. Lin and M.-H. Hsieh, “\(c^3\)-Locally Testable Codes from Lossless Expanders”, (2022) arXiv:2201.11369
[2]
T.-C. Lin and M.-H. Hsieh, “Good quantum LDPC codes with linear time decoder from lossless expanders”, (2022) arXiv:2203.03581
[3]
M. Capalbo et al., “Randomness conductors and constant-degree lossless expanders”, Proceedings of the thiry-fourth annual ACM symposium on Theory of computing (2002) DOI
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Zoo Code ID: lossless_expander

Cite as:
“Lossless expander balanced-product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/lossless_expander
BibTeX:
@incollection{eczoo_lossless_expander, title={Lossless expander balanced-product code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/lossless_expander} }
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Cite as:

“Lossless expander balanced-product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/lossless_expander

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