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
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Zoo Code ID: ampdamp_numopt

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
BibTeX:
@incollection{eczoo_ampdamp_numopt, title={Numerically optimized four-qubit AD code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/ampdamp_numopt} }
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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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/ampdamp_numopt.yml.