Two infinite families of nonadditive quantum error-correcting codes
arXiv:0901.1935
Abstract
We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear programming bound. All these nonadditive codes can be characterized by a stabilizer-like structure and thus their encoding circuits can be designed in a straightforward manner.
4 pages with 1 figure and 1 table