Non-binary unitary error bases and quantum codes

摘要

Error operator bases for systems of any dimension are defined and natural generalizations of the bit-flip/ sign-change error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of Abelian groups. As a consequence, quantum codes can be constructed form linear codes over (ital Z)(sub (ital n)) for any (ital n). The generalization of the punctured code construction leads to many codes which permit transversal (i.e. fault tolerant) implementations of certain operations compatible with the error basis.