Algoritmos baseados em cadeias de Markov quânticas

• Autor(a) principal: Santos, Raqueline Azevedo Medeiros
• Data de Publicação: 2014
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/175
• topic: Computadores quânticos; Quantum computers; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

Quantum Markov chains or quantum walks have been playing an important role in the development of efficient quantum algorithms. Therefore, studying its properties, analyzing its behavior in different topologies, and seeing the impact of decoherence on these walks and its algorithms is fundamental to the development of the area. In this context, we contribute through the analysis of the following issues. For Szegedy's quantum walk, we analytically study its behavior in the cycle; we describe how to calculate the limit distribution by providing examples for the two-dimensional grid, cycle and complete graph; we study a model of decoherence inspired by percolation, where we define the decoherent quantum hitting time and we establish a intensity range of decoherence where the decoherent quantum hitting time is quadratically smaller than the classic; the detection algorithm has a quadratic gain for the same range, under the action of decoherence. For the coined quantum walk, we present simulations of the algorithm for evaluating boolean formulas, also considering a faulty oracle model.