A Nonadditive Quantum Code

Abstract

Every good quantum error-correcting code discovered thus far, such as those known as ``stabilizer'' or ``additive'' codes, has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices. In this Letter we present the first example of a code that is better than any code of this type. It encodes six states in five qubits and can correct the erasure of any single qubit.