\(((n,1,2))\) Bravyi-Lee-Li-Yoshida PI code[1] 

Description

PI distance-two code on \(n\geq4\) qubits whose degree of entanglement vanishes asymptotically with \(n\) [1; Appx. D].

In terms of Dicke states, the codewords are \begin{align} \begin{split} |0_{L}\rangle&=\sqrt{1-\frac{2}{n}}|D_{0}^{n}\rangle+\sqrt{\frac{2}{n}}|D_{n}^{n}\rangle\\ |1_{L}\rangle&=|D_{2}^{n}\rangle~. \end{split} \tag*{(1)}\end{align}

Parents

Child

Cousin

  • Concatenated quantum code — The Bravyi-Lee-Li-Yoshida PI code can be concatenated to yield codes that have higher distance and that admit codewords with vanishing entanglement [1; Appx. D].

References

[1]
S. Bravyi et al., “How much entanglement is needed for quantum error correction?”, (2024) arXiv:2405.01332
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Zoo Code ID: unentangled_permutation_invariant

Cite as:
\(((n,1,2))\) Bravyi-Lee-Li-Yoshida PI code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/unentangled_permutation_invariant
BibTeX:
@incollection{eczoo_unentangled_permutation_invariant, title={\(((n,1,2))\) Bravyi-Lee-Li-Yoshida PI code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/unentangled_permutation_invariant} }
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https://errorcorrectionzoo.org/c/unentangled_permutation_invariant

Cite as:

\(((n,1,2))\) Bravyi-Lee-Li-Yoshida PI code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/unentangled_permutation_invariant

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/permutation_invariant/unentangled_permutation_invariant.yml.