Correlações quânticas e o modelo DQC1

Abstract

Quantum computation may represent a progress of great value for the solution of some problems whose efficient solution is not known or that cannot be efficiently solved at all. In order to continuously develop this unconventional form of computing a number of problems are being assessed by the science community such as the identification of a property that may be the source of a computational gain, or the development of new quantum algorithms, protocols and computational models, besides the technical development towards the production of systems capable of implement such computations. Considering that, the studies presented in this thesis have as main subjects quantum correlations — a property that is pointed out as a likely source of computational gain for quantum computation — and the Deterministic Quantum Computation with One Quantum Bit (DQC1) model. The quantum correlations generated between two non-interacting quantum dots inside an optical nanocavity in the presence of decoherence channels are studied by means of numerical calculations, and the results show that these channels, although in general reduce the potential for quantum correlations generation, have a minor constructive role. Furthermore, the experimental implementation of a classicality witness in this system is proposed. The presence of these correlations in the realization of the Deutsch-Jozsa algorithm by the DQC1 model is assessed, noting that it may be generated and consumed in the process. A way to implement quantum computation by the DQC1 model on a optical system, where the state of a set of qbits is encoded on the transverse degrees of freedom of light and the polarization is taken as the control qbit is also proposed. Following this scheme some ways to implement the Deutsch-Jozsa, factoring and average fidelity decay estimation algorithms are presented, with the former being effectively experimentally tested along with the evaluation of the normalized trace of a unitary matrix.