Non-additive Quantum Codes

Most quantum error-correcting codes (QECCs) that are designed to correct local errors are stabilizer codes which correspond to additive classical codes. Because of this correspondence, stabilizer codes are also referred to as additive codes, while non-stabilizer codes are called non-additive codes. Here we describe a framework that does not only allow a joint description of these codes, but which also enables the construction of new non-additive codes improving the parameters when compared to the best known stabilizer codes. These codes are based on the classical non-linear Goethals and Preparata codes which themselves are better than any classical linear code.