Related papers: Continuous-time quantum walks on dynamical percola…
We address memory effects and diffusive properties of a continuous-time quantum walk on a one-dimensional percolation lattice affected by spatially correlated random telegraph noise. In particular, by introducing spatially correlated…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
We address quantum spatial search on graphs and its implementation by continuous-time quantum walks in the presence of dynamical noise. In particular, we focus on search on the complete graph and on the star graph of order $N$, proving that…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
We address the dynamics of continuous-time quantum walks on one-dimensional disordered lattices inducing dynamical noise in the system. Noise is described as time-dependent fluctuations of the tunneling amplitudes between adjacent sites,…
We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…
In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of problem to a subspace that can be considerably smaller than the original one. Along the lines of…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
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…
Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are…
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,…
We present a generalized definition of discrete-time quantum walks convenient for capturing a rather broad spectrum of walker's behavior on arbitrary graphs. It includes and covers both: the geometry of possible walker's positions with…
Decoherence phenomenon has been widely studied in different types of quantum walks. In this work we show how to model decoherence inspired by percolation on staggered quantum walks. Two models of unitary noise are described: breaking…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides 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…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…