Related papers: The tessellation problem of quantum walks

We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e. classical time-dependent fluctuations affecting the tunneling amplitudes of…

In this paper, we propose QWalkVec, a quantum walk-based node embedding method. A quantum walk is a quantum version of a random walk that demonstrates a faster propagation than a random walk on a graph. We focus on the fact that the effect…

Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant…

It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by solving instances of the HSP. A common feature of the…

A randomly walking quantum particle evolving by Schr\"odinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time $\Theta(N^{3/4})$. In this paper, we give a weighted version of this graph that…

Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation…

Up to now, relatively few exponential quantum speed-ups have been achieved. Out of them, the welded tree problem (Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman'2003) is one of the unusual examples, as the exponential speed-up is…

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…

We propose a novel heuristic quantum algorithm for the Minimum Vertex Cover (MVC) problem based on continuous-time quantum walks (CTQWs). In this framework, the coherent propagation of a quantum walker over a graph encodes its structural…

Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…

We study a 2-D disordered time-discrete quantum walk based on 1-D `generalized elephant quantum walk' where an entangling coin operator is assumed and which paves the way to a new set of properties. We show that considering a given disorder…

Graph classification is a fundamental but challenging issue for numerous real-world applications. Despite recent great progress in image/video classification, convolutional neural networks (CNNs) cannot yet cater to graphs well because of…

Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…

Graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. The increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on…

Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…

We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…

We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate…

A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…

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…