\(((8,1,3))\) Plenio-Vedral-Knight CE code[1]
Description
An eight-qubit single error-correcting code that is the first CE code. Each logical state is a superposition of computational basis states with four excitations.
Admits codewords of the form \begin{align} \begin{split} |\overline{0}\rangle&=(|00001111\rangle+|11101000\rangle−|10010110\rangle−|01110001\rangle\\&+|11010100\rangle+|00110011\rangle+|01001101\rangle+|10101010\rangle)/\sqrt{8}\\ |\overline{1}\rangle&=X^{\otimes8}|\overline{0}\rangle~. \end{split} \tag*{(1)}\end{align}
Primary Hierarchy
Parents
\(((8,1,3))\) Plenio-Vedral-Knight CE code
References
- [1]
- M. B. Plenio, V. Vedral, and P. L. Knight, “Quantum error correction in the presence of spontaneous emission”, Physical Review A 55, 67 (1997) arXiv:quant-ph/9603022 DOI
Page edit log
- Victor V. Albert (2024-02-13) — most recent
Cite as:
“\(((8,1,3))\) Plenio-Vedral-Knight CE code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qubit_8_1_3