\(((9,2,3))\) Ruskai code[1]
Description
Nine-qubit PI code that protects against single-qubit errors as well as two-qubit errors arising from exchange processes.
In terms of Dicke states, the codewords are \begin{align} \begin{split} |0_{L}\rangle&\propto|D_{0}^{9}\rangle+\sqrt{3}|D_{6}^{9}\rangle\\ |1_{L}\rangle&\propto\sqrt{3}|D_{3}^{9}\rangle+|D_{9}^{9}\rangle~. \end{split} \tag*{(1)}\end{align}
Protection
Protects against all single-qubit errors as well as two-qubit errors arising from exchange processes.
Parents
- GNU PI code — The \(((9,2,3))\) Ruskai code is a GNU PI code [2].
- Small-distance block quantum code
Cousin
- \([[9,1,3]]\) Shor code — The \(((9,2,3))\) Ruskai code results from projecting the Shor code into the PI qubit subspace [1].
References
- [1]
- M. B. Ruskai, “Pauli Exchange Errors in Quantum Computation”, Physical Review Letters 85, 194 (2000) arXiv:quant-ph/9906114 DOI
- [2]
- Y. Ouyang, “Permutation-invariant quantum codes”, Physical Review A 90, (2014) arXiv:1302.3247 DOI
Page edit log
- Victor V. Albert (2024-02-07) — most recent
Cite as:
“\(((9,2,3))\) Ruskai code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/ruskai