Optimizing the spatial spread of a quantum walk

Locating sources of complex quantum networks

“…Farhi [5] first proposed the concept of the continuous quantum walk and investigated its efficiency on decision tree problems. In recent years, continuous quantum walk has been widely used in areas such as simulating the operation mechanism of quantum systems [6] and quantum message transfer process [6,7], developing general quantum computing models [3], and defining the centrality of network nodes [8,9]. In addition, the relationship between quantum network topology and quantum message propagation mechanism has been explored, including the effect of network structure on the ability of nodes to transmit quantum message [10], on the efficiency of quantum message propagation [11,12], on the probability of quantum message distribution on nodes [9,13], and the relationship between quantum network mediostructure and quantum message transmission [14], etc.…”

Studies on the generalized elephant quantum walk

“…It is worthwhile also to mention that for some algorithmic applications it is desired to control the propagation of the walker while also controlling the way in which the quantum coin participates in the full state. 72,79 The generalized elephant quantum walk can be interesting for this purpose since, with the q-exponential distribution, we can control its propagation and the participation of the coin as we can see in Fig. 23 through the Inverse Participation Ratio, IPR = ( x (P t (x)) 2 ) −1 .…”