Quantum Random Walks on Cayley Graphs

We investigate the problem of quantum random walk on Cayley graphs. Quantum random walks are proved to be useful in different aspect of quantum computation. Our motivation is finding the current limitations of quantum random walks, and how these results can be applied to graphs with certain structures. For this purpose, we focus on Cayley graphs, the diagrammatic representation of groups. Aside from containing useful classes of graphs hypercubes, grids etc. one can use quantum random walks on Cayley graphs for random element generation and element finding which makes this class interesting for our study.