00878nas a2200097   4500000000100000008004100001100002500042245005200067520063800119022002300757       2014                            d1 aPrzemysław Sadowski00aEfficient quantum search on Apollonian networks3 aIn this work we study a realisation of the quantum search algorithm on Apollonian network. We show that such networks are sufficient for search tasks due to the small-world and scale-free properties. In particular we present a strategy that allows to design efficient measurement rules regardless of the localization of the marked node. We derive the optimal measurement step for the repeatable search approach and we estimate the complexity of the introduced algorithm. We show that it is possible to obtain quadratic speed-up observed in the Grover's algorithm quadratically reducing the complexity of the network at the same time.  aquant-ph:1406.0339