document: The goal of the glued trees (GT) algorithm for quantum search is the following: beginning from the left-most vertex of a given GT graph, traverse the graph and reach the right-most vertex, referred to as the target vertex. Childs et al. [1] use this algorithm to show quantum walk search to be fundamentally more effective than classical random walk search by presenting a class of graphs (the GT graphs) that force classical random walks to make exponentially many queries to an oracle encoding the structure of the graph, but that are traversable by quantum walks with a polynomial number of queries to such an oracle. In order to study the robustness of the algorithm to the detrimental effects of decoherence, we shall determine how effectively it achieves its goal when subjected to an increasing degree of phase damping noise. For this reason, we will focus on the probability that the walker is on the target vertex at the end of the walk. We thus consider GT graphs such as the one illustrated in Fig. 1(b), i.e. consisting of n layers before the gluing stage, and thus labelled as G′n.
extractive_keyphrases: classical random walks classical random walk search class of graphs glued trees gluing stage graph gt increasing degree of phase damping noise quantum search quantum walk search
abstractive_keyphrases: gt graph gt graphs