Nonadditive Quantum Error-Correcting Code
Sixia Yu, Qing Chen, Ching–Yi Lai, C. H. Oh · Physical Review Letters · 2008
We report the first nonadditive quantum error-correcting code, namely, a ((9, 12, 3)) code which is a 12-dimensional subspace within a 9-qubit Hilbert space, that outperforms the optimal stabilizer code of the same length by encoding more levels while correcting arbitrary single-qubit errors. Taking advantage of the graph states, we construct explicitly a complete encoding-decoding circuit for the proposed nonadditive error-correcting code.