Proteção da informação quântica contra ocorrência de erros computacionais e de apagamentos.

Abstract

Computational errors and quantum erasures are the types of changes that may occur naturally due to the interaction between quantum systems and the environment. The aim of this thesis is to propose a code capable of performing the information protection against the occurrence of these types of changes. To do this,first we solve the problem of finding an explicit construction that performs efficiently the calculation of the error syndrome for the quantum graphs codes (QGC’s). This was achieved by means of an adjustment of the inverse quantum Fourier transform. With this, we present a detailed description of the decoding operation for non-degenerate QGC’s. After that, we introduce an improvement of the code given by Yanget al. [JETP Letters 79 (2004)] to characterize a scheme able to protect the information against the occurrence of multiple quantum erasures using Greenberger-Horne-Zeilinger (GHZ) states. The technique developed in this scheme allows to protectk-qubit (k≥3) information against the occurrence oft =k/2 quantum erasures. The proposed scheme makes use of(t+1) redundant blocks and has the restriction that each erasure must occur in different blocks. Aiming to fulfill the goals of this thesis, we propose a concatenation scheme in which the external code is a quantum error-correcting code and the internal code is quantum erasure-correcting code that does not perform measurements. If the requirements of this construction are met, the resulting concatenated code protects the information against the occurrence of computational errors and quantum erasures. Finally, we illustrate the results obtained in this work by means of an example in which one qbit of information is protected against the occurrence of two erasures and one computational error.