Quasi-cyclic QLDPC code[1,2] 

Description

A QLDPC code such that cyclic shifts of the subsystems by \(\ell\geq 1\) leave the codespace invariant. Such codes have circulant stabilizer generator matrices [1,2].

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References

[1]
M. Hagiwara and H. Imai, “Quantum Quasi-Cyclic LDPC Codes”, 2007 IEEE International Symposium on Information Theory 806 (2007) arXiv:quant-ph/0701020 DOI
[2]
K. Kasai, M. Hagiwara, H. Imai, and K. Sakaniwa, “Quantum Error Correction Beyond the Bounded Distance Decoding Limit”, IEEE Transactions on Information Theory 58, 1223 (2012) arXiv:1007.1778 DOI
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Zoo Code ID: quasi_cyclic_qldpc

Cite as:
“Quasi-cyclic QLDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quasi_cyclic_qldpc
BibTeX:
@incollection{eczoo_quasi_cyclic_qldpc, title={Quasi-cyclic QLDPC code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quasi_cyclic_qldpc} }
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Cite as:

“Quasi-cyclic QLDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quasi_cyclic_qldpc

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/properties/stabilizer/qldpc/quasi_cyclic_qldpc.yml.