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A nonadditive quantum code

Eric M. Rains·R. H. Hardin·Peter W. Shor·N. J. A. Sloane
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Abstract

Up to now every good quantum error-correcting code discovered has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices; such codes are known as stabilizer or additive codes. 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.

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Eric M. Rains, R. H. Hardin, Peter W. Shor, N. J. A. Sloane. 1997-05-09. A nonadditive quantum code. https://doi.org/10.1103/physrevlett.79.953

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