Abstract
Classical Random walks and their behaviour have become a major part of applications in science. Although unitary quantum random walks were introduced as the quantum analog of classical random walks, interaction with an external environment was not taken into consideration in these walks. Open quantum random walk models were then later developed in order to take into account and incorporate external factors such as heat, that occurred, where the behaviour of these open quantum random walks was later studied. However, a crucial part of these walks was left out, the case where no movement took place. We review recent work which extends the existing open quantum walk models to include the case of self-jumping. Our task is to investigate and compare the similarities and differences in behaviour of the classical, unitary and open quantum random walks. In particular, we investigate the long-time behaviour of the open quantum random walk model and derive a central limit theorem making use of existing research.
M.Sc. (Applied Mathematics)