Numerically optimized four-qubit AD code[1]
Description
Four-qubit code that can (approximately) correct a single AD error with higher entanglement fidelity than the \([[4,1,2]]\) subcodes of the \([[4,2,2]]\) code. The code was obtained by a biconvex optimization of the entanglement fidelity.
The admits a codeword basis of \begin{align} \begin{split} |\overline{0}\rangle&=\sqrt{1-\frac{1}{2(1-\gamma)^{2}}}|0000\rangle+\frac{1}{\sqrt{2}(1-\gamma)}|1111\rangle\\|\overline{1}\rangle&=\frac{1}{2}(|0011\rangle+|0101\rangle-|1010\rangle+|1100\rangle)\end{split} \tag*{(1)}\end{align} for AD error rate \(\gamma\).
Encoding
Analytical encoding channel [1].
Decoding
Analytical recovery channel [1].
Parents
Cousin
- \([[4,2,2]]\) Four-qubit code — The numerically optimized four-qubit AD code that can correct a single AD error with higher entanglement fidelity than the \([[4,1,2]]\) Leung-Nielsen-Chuang-Yamamoto code subcode of the \([[4,2,2]]\) code.
References
- [1]
- X. Mao, Q. Xu, and L. Jiang, “Optimized four-qubit quantum error correcting code for amplitude damping channel”, (2024) arXiv:2411.12952
Page edit log
- Victor V. Albert (2024-11-21) — most recent
Cite as:
“Numerically optimized four-qubit AD code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/ampdamp_numopt