Quantum codes do not fix qubit independent errors

• Main Authors: Lacalle, J, Pozo-Coronado, L. M, de Oliveira, A. L. Fonseca, Martín-Cuevas, R
• Format: Journal Article
• Language: English
• Published: 06.01.2021
• Subjects: Physics - Quantum Physics
• DOI: 10.48550/arxiv.2101.03971

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.