Scalable networks for discrete quantum random walks

Abstract

Recently, quantum random walks (QRWs) have been thoroughly studied in order to develop new quantum algorithms. In this paper we propose scalable quantum networks for discrete QRWs on circles, lines, and also in higher dimensions. In our method the information about the position of the walker is stored in a quantum register and the network consists of only one-qubit rotation and ${(\text{controlled})}^{n}\text{\ensuremath{-}}\mathrm{NOT}$ gates, therefore it is purely computational and independent of the physical implementation. As an example, we describe the experimental realization in an ion-trap system.