Quantum walks exhibit different properties compared with classical random walks, most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as quantum-walk-replicating random walks, have been studied in the literature where the eventual properties of QWRW coincide with those of QWs. However, we consider that the unique attributes of QWRWs have not been fully utilized in the former studies to obtain deeper or new insights into QWs. In this paper, we (...) highlight the directivity of one-dimensional discrete quantum walks via QWRWs. By exploiting the fact that QWRW allows trajectories of individual walkers to be considered, we first discuss the determination of future directions of QWRWs, through which the effect of linear spreading and localization is manifested in another way. Furthermore, the transition probabilities of QWRWs can also be visualized and show a highly complex shape, representing QWs in a novel way. Moreover, we discuss the first return time to the origin between RWs and QWs, which is made possible via the notion of QWRWs. We observe that the first return time statistics of QWs are quite different from RWs, caused by both the linear spreading and localization properties of QWs. (shrink)

The laser chaos decision maker has been demonstrated to enable ultra-high-speed solutions of multiarmed bandit problems or decision-making in the GHz order. However, the underlying mechanisms are not well understood. In this paper, we analyze the chaotic dynamics inherent in experimentally observed laser chaos time series via surrogate data and further accelerate the decision-making performance via parameter optimization. We first evaluate the negative autocorrelation in a chaotic time series and its impact on decision-making detail. Then, we analyze the decision-making ability (...) using three different surrogate chaos time series to examine the underlying mechanism. We clarify that the negative autocorrelation of laser chaos improves decision-making and that the amplitude distribution of the original laser chaos time series is not optimal. Hence, we introduce a new parameter for adjusting the amplitude distribution of the laser chaos to enhance the decision-making performance. This study provides a new insight into exploiting the supremacy of chaotic dynamics in artificially constructed intelligent systems. (shrink)