Standard deviation of a staggered quantum walk on a line of diamonds - Silva, Cauê Francisco Teixeira da (2018)
The discovery of the quantum mechanics changed the physics world. Newton’s laws of motion cannot be applied to very small physical systems. The quantum mechanics has many applications, one of them is the quantum computation, which was discovered in the 80’s and has steadily grown from that time to nowadays. One powerful tool of quantum computation is the quantum walk, which is the quantum version of random walk. In this work, we study some quantum walk models. The coined model was the first one to be proposed, this model has a quadratic larger position standard deviation compared to the one of the random walk. The second model is the staggered quantum walk, which was proposed recently. This model makes a partition of the vertices of the graph into cliques, and a partition is called tessellation, establishing a new problem of graph theory, related to the problem of graph coloring. We study 2-tessellable graphs and prove a new theorem in graph theory. An expression of the standard deviation of a staggered quantum walk on the line-of-diamond graph is obtained using a special basis, which is derived from the staggered Fourier transform.