Doğrusal olmayan non-markovian gürültünün kuantum korelasyonların dinamiğine etkisi

The main aim of this thesis is to obtain exact analytical solutions for three different problems which have relevance in quantum computer and quantum information science research areas. The first problem deals with the dynamics of two interacting qubits which are driven by a periodical external field. Solution of this problem is important for the control of qubits in quantum computers. The problem is split into three parts; in the first step, we investigated the dynamics of a single qubit driven by a harmonic field and have shown that Magnus expansion can be used to derive recursion relations for the exact dynamics of the system. As the second step, we have used Bellomo method to obtain analytical probability amplitudes for two non-interacting qubits driven by an harmonic field. We have derived a set of third order ordinary differential equations for the dynamics of driven two interacting qubits that is the last part of the problem. The second problem deals with the fourth-order corrections to the master equation of a charged harmonic oscillator in a black-body radiation field by using Krylov averaging method. Quantum master equations which determine the dynamics of the density matrix of the system are, almost always, second-order in the interaction parameter and determining the validity range of such an approximation for the relevant system parameters is crucial for assessing the accuracy of the dynamics obtained by solving such an equation. We have shown that the third- and the fourth-order contributions are, mostly, opposite in sign and cancel each other for the charged harmonic oscillator + black-body field system. The third problem that we have studied is related to the dynamics of spin-boson model which has a wide-range of applications in physics, chemistry and biology. As the first part of this problem, we have considered the dynamics of spin-boson model with a structured spectral density which is used to describe the environment in both superconducting qubits and biological light harvesting systems. We were able to obtain exact analytical expressions for the environmental correlation functions and derived exact expressions for the population dynamics of such a system. As the second part of the study on the dynamics of the spin-boson model, we have considered the effect of dichotomous noise in qubit transition frequency on the population and coherence of a qubit in a thermal bath. At high and low temperature limits, we have obtained analytical expressions for the transition rates and decay of coherence by using a non-Markovian master equation approach in the polaron transformation formulation. An interesting result of the study is that the dichotomous noise plays a constructive role on the transition rate in case of low temperature, overdamped and both intermediate and strong coupling.