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.