Related papers: A limit theorem for a splitting distribution of a …

A discrete time quantum walk is considered in which the step lengths are chosen to be either $1$ or $2$ with the additional feature that the walker is persistent with a probability $p$. This implies that with probability $p$, the walker…

We attempt to analyze a one-dimensional space-inhomogeneous quantum walk (QW) with one defect at the origin, which has two different quantum coins in positive and negative parts. We call the QW "the two-phase QW", which we treated…

We study the evolution of initially extended distributions in the coined quantum walk on the line by analyzing the dispersion relation of the process and its associated wave equations. This allows us, in particular, to devise an initially…

We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.

Quantum random walk finds application in efficient quantum algorithms as well as in quantum network theory. Here we study the mixing time of a discrete quantum walk over a square lattice in presence percolation and decoherence. We consider…

We generalize the discrete quantum walk on the line using a time dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time…

We introduce and analyze a one-dimensional quantum walk with two time-independent rotations on the coin. We study the influence on the property of quantum walk due to the second rotation on the coin. Based on the asymptotic solution in the…

We present a new scheme for a discrete-time quantum walk on two- and three-dimensional lattices using a two-state particle. We use different Pauli basis as translational eigestates for different axis and show that the coin operation, which…

We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…

Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…

Split-step quantum walks are models of supersymmetric quantum walk, and thus their Witten indices can be defined. We prove that the Witten index of a split-step quantum walk coincides with the difference between the winding numbers of…

We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…

Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been…

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…

Quantum Key Distribution (QKD) is an emerging cryptographic method designed for secure key sharing. Its security is theoretically guaranteed by fundamental principles of quantum mechanics, making it a leading candidate for future…

This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The…

The asymptotic behavior of the quantum walk on the line is investigated focusing on the probability distribution of chirality independently of position. The long-time limit of this distribution is shown to exist and to depend on the initial…

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…

We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the…

We consider a two-state quantum walk on a line where after the first step an absorbing sink is placed at the origin. The probability of finding the walker at position $j$, conditioned on that it has not returned to the origin, is…