Related papers: Transport properties in directed Quantum Walks on …
We consider the definition of quantum walks on directed graphs. Call a directed graph reversible if, for each pair of vertices (i, j), if i is connected to j then there is a path from j to i. We show that reversibility is a necessary and…
We report an enhancement of the decay rate of the survival probability when non-local initial conditions in position space are considered in the Quantum Walk on the line. It is shown how this interference effect can be understood…
We study the distributions of the continuous-time quantum walk on a one-dimensional lattice. In particular we will consider walks on unbounded lattices, walks with one and two boundaries and Dirichlet boundary conditions, and walks with…
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…
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 derive analytical results for continuous-time quantum walks from a new class of initial states with tunable delocalization. The dynamics are governed by a Hamiltonian with complex hopping amplitudes. We provide closed-form equations for…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
We give the first example of faster transport with a quantum walk on an inherently directed graph, on the directed line with a variable number of self-loops at each vertex. These self-loops can be thought of as adding a number of small…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by…
This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the `normalized' position of the walk. When the position is in the…
Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…
We study an extended dynamical system on the non-negative real line with piecewise linear non-uniformly expanding local dynamics. With a uniformly distributed initial state, the distribution of successive states coincides with that of a…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
Coherent transport of excitations along chains of coupled quantum systems represents an interesting problem with a number of applications ranging from quantum optics to solar cell technology. A convenient tool for studying such processes…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
Let $(G,\mu)$ be a uniformly elliptic random conductance graph on $\mathbb{Z}^d$ with a Poisson point process of particles at time $t=0$ that perform independent simple random walks. We show that inside a cube $Q_K$ of side length $K$, if…
We study the state transfer through quantum walks placed on a bounded one-dimensional path. We first consider continuous-time quantum walks from a Gaussian state. We find such a state when superposing centered on the starting and antipodal…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…