Related papers: Quantum walks on regular uniform hypergraphs
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 construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in…
Spatial search is an important problem in quantum computation, which aims to find a marked vertex on a graph. We propose a novel approach for designing deterministic quantum search algorithms on a variety of graphs via alternating quantum…
Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular…
When searching for a marked vertex in a graph, Szegedy's usual search operator is defined by using the transition probability matrix of the random walk with absorbing barriers at the marked vertices. Instead of using this operator, we…
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…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
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…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
This article presents a new quantum PageRank algorithm on graphs using discrete-time open quantum walks. Google's PageRank is a widely used algorithm for ranking the web pages on the World Wide Web in classical computation. From a broader…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
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 walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
Classical random walks on well-behaved graphs are rapidly mixing towards the uniform distribution. Moore and Russell showed that a continuous quantum walk on the hypercube is instantaneously uniform mixing. We show that the continuous-time…
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…
In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…
Coined Quantum Walks (QWs) are being used in many contexts with the goal of understanding quantum systems and building quantum algorithms for quantum computers. Alternative models such as Szegedy's and continuous-time QWs were proposed…
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…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…