相关论文: Quantum walks as a probe of structural anomalies i…

The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…

Quantum walks have emerged as a transformative paradigm in quantum information processing and can be applied to various graph problems. This study explores discrete-time quantum walks on simplicial complexes, a higher-order generalization…

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…

In this paper, we show reduction methods for search algorithms on graphs using quantum walks. By using a graph partitioning method called equitable partition for the the given graph, we determine "effective subspace" for the search…

Random walks simulate the randomness of objects, and are key instruments in various fields such as computer science, biology and physics. The counter part of classical random walks in quantum mechanics are the quantum walks. Quantum walk…

Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…

We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…

In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that…

Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…

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…

In a network, the vertices with similar characteristics construct communities. The vertices in a community are well-connected. Detecting the communities in a network is a challenging and important problem in the theory of complex networks.…

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…

It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of…

Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…

Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct…

Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks…

We analyze the solution of the coined quantum walk on a line. First, we derive the full solution, for arbitrary unitary transformations, by using a new approach based on the four "walk fields" which we show determine the dynamics. The…

We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…

In this dissertation we demonstrate that the continuous-time quantum walk models remain powerful for nontrivial graph structures. We consider two aspects of this problem. First, it is known that the standard Continuous-Time Quantum Walk…