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We investigate the quantum walk on the line when decoherences are introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. Both mechanisms drive the system to a classical…

The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…

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…

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 consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order…

We introduce a model of a quantum walk on a graph in which a particle jumps between neighboring nodes and interacts with independent spins sitting on the edges. Entanglement propagates with the walker. We apply this model to the case of a…

Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior…

We investigate continuous-time quantum walks of two fermionic atoms loaded in one-dimensional optical lattices with on-site interaction and subjected to a Zeeman field. The quantum walks are accompanied by spin-flipping processes. We…

We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…

We discuss recent developments in the study of quantum wavefunctions and transport in classically ergodic systems. Surprisingly, short-time classical dynamics leaves permanent imprints on long-time and stationary quantum behavior, which are…

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.…

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…

We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…

The quantization of particle trajectories gives rise to remarkable features such as the coherent superposition of quantum channels and the quantum switch, which offer significant advantages in the communication of both classical and quantum…

Quantum walks have frequently envisioned the behavior of a quantum state traversing a classically defined, generally finite, graph structure. While this approach has already generated significant results, it imposes a strong assumption: all…

A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…

In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time series have led to state-of-the art…

In quantum computing, the quantum walk search algorithm is designed for locating fixed marked nodes within a graph. However, when multiple marked nodes exist, the conventional search algorithm lacks the capacity to simultaneously amplify…

Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…

A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…