  In this paper, we analyze the potential for new types of searches using the
formalism of scattering random walks on Quantum Computers. Given a particular
type of graph consisting of nodes and connections, a "Tree Maze", we would like
to find a selected final node as quickly as possible, faster than any classical
search algorithm. We show that this can be done using a quantum random walk,
both exactly through numerical calculations as well as analytically using
eigenvectors and eigenvalues of the quantum system.
