Related papers: The underlying digraph of a coined quantum random …
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence…
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function…
Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear…
In this work we seek to generalize the connection between traversable wormholes and quantum channels. We do this via a connection between traversable wormholes and graph geometries on which we can perform quantum random walks for signal…
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.…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
It is shown that the path of a simple random walk on any graph, consisting of all vertices visited and edges crossed by the walk, is almost surely a recurrent subgraph.
The signature of a path is an essential object in the theory of rough paths. The signature representation of the data stream can recover standard statistics, e.g. the moments of the data stream. The classification of random walks indicates…
We introduce a minimal set of physically motivated postulates that the Hamiltonian H of a continuous-time quantum walk should satisfy in order to properly represent the quantum counterpart of the classical random walk on a given graph. We…
Quantum walks are quantum counterparts of Markov chains. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications.
We show that quantum walks interpolate between a coherent `wave walk' and a random walk depending on how strongly the walker's coin state is measured; i.e., the quantum walk exhibits the quintessentially quantum property of complementarity,…
Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on…
In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For these graphs, we compute the limiting distribution of the walk…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…