Spatial search by continuous-time quantum walks on complex networks is focused on using a quantum walk in continuous time in order to find a single or multiple marked vertices within the complex network. The specific formalism used here is to consider a coupling constant that shifts the state of the quantum walker from the initial state to the target state, which is the marked vertex. The thesis begins with establishing the mathematical framework of network theory, quantum walks and numerical methods that will be used in the remainder of the thesis. Then spatial search by continuous-time quantum walk is studied on regular and semi-regular graphs, where most analytical results can be found. This will get us acquainted with spatial search by quantum walk. The complex networks studied are Barabasi-Albert graphs and the Internet network on the level of autonomous systems. Different renormalized and pruned versions of the Internet network are studied. The parameters of the quantum walk that are focused on are the optimal values for the coupling constant, success probability, time and search time.
Spatial search is the problem of finding a marked vertex in a graph. A continuous-time quantum walk in the single-excitation subspace of an n spin system solves the problem of spatial search by finding the marked vertex in O(n) time. Here, we investigate a natural extension of the spatial search problem, marking multiple vertices of a graph, which are still marked with local fields. We prove that a continuous-time quantum walk in the k-excitation subspace of n spins can determine the binary string of k marked vertices with an asymptotic fidelity in time O(n), despite the size of the state space growing as O(nk). Numerically, we show that this algorithm can be implemented with interactions that decay as 1/rα, where r is the distance between spins, and an α that is readily available in current ion trap systems.