Related papers: Multiparticle quantum walks for distinguishing har…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
Berry and Wang [Phys. Rev. A {\bf 83}, 042317 (2011)] show numerically that a discrete-time quantum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we…
We investigate the quantum dynamics of particles on graphs ("quantum random walks"), with the aim of developing quantum algorithms for determining if two graphs are isomorphic (related to each other by a relabeling of vertices). We focus on…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…
Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of…
We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
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…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…
We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
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…
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…
We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure…