Quantum Random Walks with Perturbing Potential Barriers

Sammanfattning: With a recent interest in quantum computers, the properties of quantum mechanicalcounterparts to classical algorithms have been studied in the hope of providing efficientalgorithms for quantum computers. Because of the success of classical random walks inproviding good algorithms on classical computers, attention has been turned to quantumrandom walks, since they may similarly be used to construct efficient probabilisticalgorithms on quantum computers. In this thesis we examine properties of the quantumwalk on the line, in particular the standard deviation and the shape of the probabilitydistribution, and the effect of potentials perturbing the walk. We model these potentialsas rectangular barriers between the walker’s positions and introduce a probability of thewalker failing to perform the step procedure, similar to that of Wong in Ref. [14]. We findthat a potential localized around the starting position leads to an increased standard deviationand makes the walk increasingly ballistic. We also find that uniformly distributedrandom potentials have the general effect of localizing the distribution, similar to that ofAnderson localization.