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Quantum Error Correction and Orthogonal Geometry

A. R. Calderbank·E. M Rains·P. W. Shor·N. J. A. Sloane
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Abstract

A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.

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A. R. Calderbank, E. M Rains, P. W. Shor, N. J. A. Sloane. 1996-07-02. Quantum Error Correction and Orthogonal Geometry. https://doi.org/10.1103/physrevlett.78.405

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