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Abstract: We formulate a framework for discrete-time quantum walks, motivated by classical random walks with memory. We present a specific representation of the classical walk with memory 2 on which t...
Abstract: A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.
We study the quantum walk search algorithm of Shenvi, Kempe and Whaley [PRA 67 052307 (2003)] on data structures of one to two spatial dimensions, on which the algorithm is thought to be less efficie...
We consider crossovers with respect to the weak convergence theorems from a discrete-time quan- tum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time ...
We consider a discrete-time quantum walk Wt, at time t on a graph with joined half lines J, which is composed of  half lines with the same origin. Our analysis is based on a reduction of the walk o...
In this paper, we firstly establish the discrete time and finite state reflected backward stochastic difference equations(DF-RBSDEs for short); then we explore the corresponding basic properties and t...
We show that certain types of quantum walks can be modeled as waves that propagate in a medium with phase and group velocities that are explicitly calculable. Since the group and phase velocities indi...

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