Description
A QLDPC code such that cyclic shifts of the subsystems by \(\ell\geq 1\) leave the codespace invariant. Stabilizer generator matrices of such codes can be put into block form, where each nonzero block is a circulant matrix [1,2].Cousins
- Quasi-cyclic LDPC (QC-LDPC) code— QC-QLDPC codes are quantum counterparts of QC-LDPC codes. QC-LDPC codes can be used to make qubit QLDPC codes using various non-CSS constructions [3]. There exist explicit constructions of both whose parity-check (stabilizer generator) matrices have column weight 2 and girth 12 [4].
- Galois-qudit BCH code— Some Galois-qudit BCH codes are QC-QLDPC [5; Ch. 16].
Member of code lists
Primary Hierarchy
Parents
Quasi-cyclic QLDPC (QC-QLDPC) code
Children
Lattice stabilizer codeBB Twist-defect color Twist-defect surface CDSC Kitaev surface Fracton stabilizer
Lattice stabilizer codes are QLDPC codes that are invariant under translations by a lattice unit cell.
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
- [3]
- P. Tan and J. Li, “Efficient Quantum Stabilizer Codes: LDPC and LDPC-Convolutional Constructions”, IEEE Transactions on Information Theory 56, 476 (2010) DOI
- [4]
- D. Komoto and K. Kasai, “Explicit Construction of Quantum Quasi-Cyclic Low-Density Parity-Check Codes with Column Weight 2 and Girth 12”, (2025) arXiv:2501.13444
- [5]
- S. A. Aly, “On Quantum and Classical Error Control Codes: Constructions and Applications”, (2008) arXiv:0812.5104
Page edit log
- Victor V. Albert (2024-08-01) — most recent
Cite as:
“Quasi-cyclic QLDPC (QC-QLDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quasi_cyclic_qldpc