Two Infinite Families of Nonadditive Quantum Error-Correcting Codes

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.