CAMINHADAS QUANTICAS EM REDES ˆ UNIDIMENSIONAIS NAO-HOMOG ˜ ENEAS

Abstract

In this work we present an analysis of the evolution of the discrete quantum walks using the quantim walk scattering method, which occurs when a particle with a certain amount of energy E, collides with of delta-type potentials, with intensities that vary along the network profile. In parallel, we could also verify the equivalence between the quantum walk with coin and quantum walk models. In the quantum walk scattering method, which is based on an interferometric analogy, a scattering process occurs at each vertex of a onedimensional graph. In the literature, we have studies that show the behavior of the particle in a system whose intensity of the delta potentials are constant along a unidimensional graph, but in our proposal, we evaluated the behavior of the scattering quantum walk where the intensity of the same potential varies according to three mathematical functions: sine, cosine and modular arithmetic. With the scattering method, we also verified its equivalence to the coin quantum walk model, when reproducing results referring to works already published, where the configuration of the system is defined by the use of nonuniform quantum coins. As a result, we obtained the graphical representation of the spreading pattern for different network profiles, the probability graph and the standard deviation of the quantum walks being the cosine profile obtaining the highest standard deviation and verified its equivalence with the coin quantum walk model.