Related papers: Return probability of one-dimensional discrete-tim…
We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…
We consider the 2D alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or "hidden" extra dimension. If one starts from…
We provide an explanation of recent experimental results of Xue et al., where full revivals in a time-dependent quantum walk model with a periodically changing coin are found. Using methods originally developed for "electric" walks with a…
We study the problem of site recurrence of discrete time nearest neighbor open quantum random walks (OQWs) on the integer line, proving basic properties and some of its relations with the corresponding problem for unitary (coined) quantum…
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…
Quantum walk (QW) is the quantum analog of the random walk. QW is an integral part of the development of numerous quantum algorithms. Hence, an in-depth understanding of QW helps us to grasp the quantum algorithms. We revisit the…
We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-dependent quantum walk naturally appears in the asymptotic…
The class of random walks in one dimension, returning to the origin, restricted by the requirement that any site visited (different from the origin) is visited an even number of times, is analyzed in the present note. We call this class the…
Random walks, and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the first return time distribution of a 1D random walker, which is a heavy-tailed distribution with infinite…
The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…
The probability distributions of discrete-time quantum walks have been often investigated, and many interesting properties of them have been discovered. The probability that the walker can be find at a position is defined by diagonal…
In this paper we present closed-form expressions for the wave function that governs the evolution of the discrete-time quantum walk on a line when the coin operator is arbitrary. The formulas were derived assuming that the walker can either…
We study a one-dimensional random walk whose expected drift depends both on time and the position of a particle. We establish a non-trivial phase transition for the recurrence vs. transience of the walk, and show some interesting…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach to topology which is based on the…
We identify a key difference between quantum search by discrete- and continuous-time quantum walks: a discrete-time walk typically performs one walk step per oracle query, whereas a continuous-time walk can effectively perform multiple walk…
We apply results from Baryshnikov, Brady, Bressler and Pemantle (2008) to compute limiting probability profiles for various quantum random walks in one and two dimensions. Using analytic machinery we show some features of the limit…
We discuss the question of recurrence for persistent, or Newtonian, random walks in Z^2, i.e., random walks whose transition probabilities depend both on the walker's position and incoming direction. We use results by Toth and Schmidt-Conze…
We investigate the relation between transport properties and entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional discrete time quantum walks. We obtain closed-form expressions for the…