\(((n,1,2))\) 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
- PI qubit code
- Movassagh-Ouyang Hamiltonian code — The \(((n,1,2))\) PI code is a Movassagh-Ouyang Hamiltonian code constructed from a binary code consisting of all codewords of weight 0, 2, or \(n\) [1; Appx. D].
- Small-distance block quantum code
Child
- Four-qubit single-deletion code — The Bravyi-Lee-Li-Yoshida code reduces to the four-qubit single-deletion code for \(n=4\).
Cousin
- Concatenated qubit 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
Page edit log
- Victor V. Albert (2024-02-07) — most recent
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