Related papers: A graph with fractional revival

The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…

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…

We investigate state transfer on a hypercube by means of a quantum walk where the sender and the receiver vertices are marked by a weighted loops. First, we analyze search for a single marked vertex, which can be used for state transfer…

Any graph which is not vertex transitive has a proper induced subgraph which is unique due to its structure or the way of its connection to the rest of the graph. We have called such subgraph as an anchor. Using an anchor which, in fact, is…

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…

We prove that in any recurrent reversible random rooted graph, two independent simple random walks started at the same vertex collide infinitely often almost surely. This applies to the Uniform Infinite Planar Triangulation and…

It is a celebrated fact that a simple random walk on an infinite $k$-ary tree for $k \geq 2$ returns to the initial vertex at most finitely many times during infinitely many transitions; it is called transient. This work points out the fact…

We explore the possibility of using quantum walks on graphs to find structural anomalies, such as extra edges or loops, on a graph. We focus our attention on star graphs, whose edges are like spokes coming out of a central hub. If there are…

Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…

The continuous-time quantum walk is a particle evolving by Schr\"odinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems,…

We consider recurrence versus transience for models of random walks on domains of $\mathbb{Z}^d$, in which monotone interaction enforces domain growth as a result of visits by the walk (or probes it sent), to the neighborhood of domain…

The revival structure of Stark wave packets is considered. These wave packets have energies depending on two quantum numbers and are characterized by two sets of classical periods and revival times. The additional time scales result in…

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude…

Quantum walks of interacting particles may display non-trivial features due to the interplay between the statistical nature and the many-body interactions associated to them. We analyze the quantum walk of interacting defects on top of an…

We consider an analogue of the well-known Riemann Hypothesis based on quantum walks on graphs with the help of the Konno-Sato theorem. Furthermore, we give some examples for complete, cycle, and star graphs.

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…

Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…

We study a simple random walk on Z^2 with constraints on the axis. Motivation comes from physics when particles (a gas for example, see [Dal88]) are submitted to a local field. In our case we assume that the particle evolves freely in the…

Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…

In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolation-like emergence of a macroscopic observable component in graphs in which the state of a fraction of…