Teoria quântica da computação

This undergraduate thesis aims formally define aspects of Quantum Turing Machine using as a basis quantum finite automata. We introduce the basic concepts of quantum mechanics and quantum computing through principles such as superposition, entanglement of quantum states, quantum bits and algorithms. We demonstrate the Bell's teleportation theorem, enunciated in the form of Deutsch-Jozsa definition for quantum algorithms. The way as the overall text were written omits formal aspects of quantum mechanics, encouraging computer scientists to understand the framework of quantum computation. We conclude our thesis by listing the Quantum Turing Machine's main limitations regarding the well-known Classical Turing Machines

Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations

Teoria quântica da computação

This undergraduate thesis aims formally define aspects of Quantum Turing Machine using as a basis quantum finite automata. We introduce the basic concepts of quantum mechanics and quantum computing through principles such as superposition, entanglement of quantum states, quantum bits and algorithms. We demonstrate the Bell's teleportation theorem, enunciated in the form of Deutsch-Jozsa definition for quantum algorithms. The way as the overall text were written omits formal aspects of quantum mechanics, encouraging computer scientists to understand the framework of quantum computation. We conclude our thesis by listing the Quantum Turing Machine's main limitations regarding the well-known Classical Turing Machines

Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations