2021/01/06 by J. Lacalle, Lacalle, J., L. M. Pozo-Coronado +5
Physics and Astronomy · #81P68 #F.0 #FOS: Physical sciences #Quantum Physics (quant-ph) #acm:81P68 #msc:81P68 #quant-ph
paper · pdf · doi:10.48550/arxiv.2101.03971
arxiv created 2021/04/13 · arxiv updated 2021/04/14
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.