Author(s)

Jesús Lacalle¹, Luis Miguel Pozo-Coronado¹, André Luiz Fonseca de Oliveira², Rafael Martín-Cuevas³

¹Dep. de Matemática Aplicada a las TIC, ETS de Ingeniería de Sistemas Informáticos, Universidad Politécnica de Madrid, C/Alan Turing s/n, Madrid, Spain.
²Facultad de Ingeniería, Universidad ORT Uruguay, Montevideo, Uruguay.
³Programa de Doctorado en Ciencias y Tecnologías de la Computación para Smart Cities, ETS de Ingeniería de Sistemas Informáticos, Universidad Politécnica de Madrid, C/Alan Turing s/n, Madrid, Spain.

In this article, we study the ability of error-correcting quantum codes to increase the fidelity of quantum states throughout a quantum computation. We analyze arbitrary quantum codes that encode all qubits involved in the computation, and we study the evolution of n-qubit fidelity from the end of one application of the correcting circuit to the end of the next application. We assume that the correcting circuit does not introduce new errors, that it does not increase the execution time (i.e. its application takes zero seconds) and that quantum errors are isotropic. We show that the quantum code increases the fidelity of the states perturbed by quantum errors but that this improvement is not enough to justify the use of quantum codes. Namely, we prove that, taking into account that the time interval between the application of the two corrections is multiplied (at least) by the number of qubits n (due to the coding), the best option is not to use quantum codes, since the fidelity of the uncoded state over a time interval n times smaller is greater than that of the state resulting from the quantum code correction.

Quantum Error Correcting Codes, Isotropic Quantum Computing Errors, Quantum Computing Error Fidelity, Quantum Computing Error Variance

Lacalle, J. , Pozo-Coronado, L. , de Oliveira, A. and Martín-Cuevas, R. (2023) Quantum Codes Do Not Increase Fidelity against Isotropic Errors. Journal of Applied Mathematics and Physics, 11, 555-571. doi: 10.4236/jamp.2023.112034.