Parrondo's game of quantum search based on quantum walk

Abstract

The Parrondo game, devised by Parrondo, means that winning strategy is constructed a combination of losing strategy. This situation is called the Parrondo paradox. The Parrondo game based on quantum walk and the search algorithm via quantum walk have been widely studied, respectively. This paper newly presents a Parrondo game of quantum search based on quantum walk by combining both models. Moreover we confirm that Parrondo's paradox exists for our model on the one- and two-dimensional torus by numerical simulations. Afterwards we show the range in which the paradox occurs is symmetric about the origin on the $d$-dimensional torus $(d \geq 1)$ with even vertices and one marked vertex.