Related papers: Continuous-time quantum walks on the symmetric gro…

Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum walk algorithm can destroy any quantum mechanical speed-up due to Anderson localization. We…

Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts.…

This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…

Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…

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…

Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the…

This PhD thesis is dedicated to the study of the interplay between symmetries of quantum states and their self-similar properties. It consists of three connected threads of research: polynomial invariants for multiphoton states,…

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…

We investigate the genuinely quantum features of continuous-time quantum walks by combining a single-time and a multi-time quantifier of nonclassicality. On the one hand, we consider the quantum-classical dynamical distance…

In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it…

We study continuous time quantum walk on a random comb graph with infinite teeth. Due to localization effects along the spine, the walk cannot go to infinity in the spine direction, while it can escape to infinity along the teeth of the…

Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…

A continuous-time quantum walk is investigated on complex networks with the characteristic property of community structure, which is shared by most real-world networks. Motivated by the prospect of viable quantum networks, I focus on the…

Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.

Multi-photon quantum walks in integrated optics are an attractive controlled quantum system, that can mimic less readily accessible quantum systems and exhibit behavior that cannot in general be accurately replicated by classical light…

We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…

This paper gives the quantum walks determined by graph zeta functions. The result enables us to obtain the characteristic polynomial of the transition matrix of the quantum walk, and it determines the behavior of the quantum walk. We treat…

Discrete-time quantum walks are known to exhibit exotic topological states and phases. Physical realization of quantum walks in a noisy environment may destroy these phases. We investigate the behavior of topological states in quantum walks…

We study the random walk on a finite dihedral group $G$ driven by the uniform measure on $k$ independently and uniformly chosen elements. We show that the walk exhibits cutoff with high probability throughout nearly the entire regime $1 \ll…

The continuous limit of quantum walks (QWs) on the line is revisited through a recently developed method. In all cases but one, the limit coincides with the dynamics of a Dirac fermion coupled to an artificial electric and/or relativistic…