Simple Quantum Error Correcting Codes
Abstract
Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe C2 ⊂eq C1, where C1 and C2 are classical codes, is used to obtain codes for up to 16 information qubits with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing C1 to have reduced distance, and introducing sign changes among the code words in a systematic manner. This systematic approach leads to single-error correcting codes for 3, 4 and 5 information qubits with block lengths of 8, 10 and 11 qubits respectively.
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