Parrondo’s game of quantum search based on quantum walk

The Parrondo game is a game where a combination of losing strategies becomes a winning strategy. This phenomenon is called the Parrondo paradox. The Parrondo game based on quantum walk and the search algorithm via quantum walk has been widely studied, respectively. This paper presents a Parrondo game for quantum search based on quantum walk for the first time. Moreover, we confirm that Parrondo’s paradox exists for our model on the one- and two-dimensional tori by numerical simulations. Afterward, we show the range in which the paradox occurs is symmetric about the origin on the d-dimensional torus \((d \ge 1)\) $(d\ge 1)$ with even vertices and one marked vertex.