Decoherence in Search Algorithms

Recently several quantum search algorithms based on quantum walks were proposed. Those algorithms differ from Grover's algorithm in many aspects. The goal is to find a marked vertex in a graph faster than classical algorithms. Since the implementation of those new algorithms in quantum computers or in other quantum devices is error-prone, it is important to analyze their robustness under decoherence. In this work we analyze the impact of decoherence on quantum search algorithms implemented on two-dimensional grids and on hypercubes.