Scattering Quantum Random Walks on Square Grids and Randomly Generated Mazes

The Scattering Quantum Random Walk scheme has found success as a basis for search algorithms on highly symmetric graph structures. In this paper we examine its effectiveness at locating a specially marked vertex on square grid graphs, consisting of N$^2$ nodes. We simulate these quantum systems using classical computational methods, and find that the probability distributions that arise are very favorable for a hybrid quantum / classical algorithm. We then examine how this hybrid algorithm handles varying types of randomness in both location of the special vertex and later random obstacles placed throughout the geometry, showing that that the algorithm is resilient to both cases.