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arXiv · 2101.03971

Quantum codes do not fix qubit independent errors

J. Lacalle·L. M. Pozo-Coronado·A. L. Fonseca de Oliveira·R. Martín-Cuevas
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Abstract

In this work we prove that the 5-qubit quantum error correcting code does not fix qubit independent errors, even assuming that the correction circuit does not introduce new errors. We say that a quantum code does not fix a quantum computing error if its application does not reduce the variance of the error. We also prove for qubit independent errors that if the correction circuit of the 5-qubit quantum code detects an error, the corrected state has central symmetry and, as a consequence, its variance is maximum. We have been able to obtain these results thanks to the high symmetry of the 5-qubit quantum code and we believe that the necessary calculations for less symmetric codes are extremely complicated but that, despite this, the results obtained for the 5-qubit quantum code reveal a general behavior pattern of quantum error correcting codes against qubit independent errors.

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J. Lacalle, L. M. Pozo-Coronado, A. L. Fonseca de Oliveira, R. Martín-Cuevas. 2021-01-06. Quantum codes do not fix qubit independent errors. https://arxiv.org/abs/2101.03971

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