\((5,1,2)\)-convolutional code[1]
Description
Quantum convolutional code with the stabilizer generators \begin{align} \begin{array}{cccccccc} X & Z & I & I & I & I & I & \cdots\\ Z & X & X & Z & I & I & I & \cdots\\ I & Z & X & X & Z & I & I & \cdots\\ I & I & Z & X & X & Z & I & \cdots\\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots \end{array} \tag*{(1)}\end{align}
Parent
Cousin
- Five-qubit perfect code — The \((5,1,2)\)-convolutional code is an infinite-qubit version of the five-qubit perfect code, with the former's lattice-translation symmetry being the extension of the latter's cyclic permutation symmetry.
References
- [1]
- H. Ollivier and J.-P. Tillich, “Description of a Quantum Convolutional Code”, Physical Review Letters 91, (2003) arXiv:quant-ph/0304189 DOI
Page edit log
- Victor V. Albert (2023-01-04) — most recent
Cite as:
“\((5,1,2)\)-convolutional code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/stab_5_1_2_convolutional