Simulations of quantum walks on regular graphs

We have developed a simulator program in Python that can execute classical and quantum random walks on regular graphs. The user implements the oracle (a function that returns the adjacency list for a given vertex) and the quantum coin used in the simulation. The software simulates the walk and produces a Latex report file detailing the results. Running several simulations, we compared the behavior of classical and coined quantum walks on some regular graphs and demonstrated the periodicity in a few small special cases. We present such reports with some mathematical explanations.