Quasi-cyclic quantum code[1]
Description
A block code on \(n\) subsystems such that cyclic shifts of the subsystems by \(\ell\geq 1\) leave the codespace invariant.
Parent
Children
- Cyclic quantum code
- Translationally invariant stabilizer code — Translationally-invariant stabilizer codes are invariant under translations by a unit cell.
- Generalized bicycle (GB) code — An index-\(m\) quasi-cyclic (QC) code of length \(n=m\ell\) is usually defined as a linear-code invariant under the \(m\)-step shift permutation \(T_{n}^{m}\).
Cousin
References
- [1]
- M. Hagiwara and H. Imai, “Quantum Quasi-Cyclic LDPC Codes”, 2007 IEEE International Symposium on Information Theory (2007) arXiv:quant-ph/0701020 DOI
Page edit log
- Victor V. Albert (2022-10-19) — most recent
Cite as:
“Quasi-cyclic quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_quasi_cyclic