Related papers: Success criteria for quantum search on graphs
We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by…
Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and…
We consider the problem of searching for a node on a labelled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of…
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.…
We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{U_1,\ldots,U_n\}$ is universal. We provide the compact form criteria leading to a simple algorithm that allows deciding universality of any given set of…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graphs that can be summarized as follows: instead of finding…
General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to…
Recently, graph based nearest neighbor search gets more and more popular on large-scale retrieval tasks. The attractiveness of this type of approaches lies in its superior performance over most of the known nearest neighbor search…
From a quantum information perspective, verifying quantum coherence in a quantum experiment typically requires adjusting measurement settings or changing inputs. A paradigmatic example is that of a double-slit experiment, where observing…
Graph search, the process of visiting vertices in a graph in a specific order, has demonstrated magical powers in many important algorithms. But a systematic study was only initiated by Corneil et al.~a decade ago, and only by then we…
To execute quantum circuits on a quantum processor, they must be modified to meet the physical constraints of the quantum device. This process, called quantum circuit mapping, results in a gate/circuit depth overhead that depends on both…
The query complexity of graph properties is well-studied when queries are on edges. We investigate the same when queries are on nodes. In this setting a graph $G = (V, E)$ on $n$ vertices and a property $\mathcal{P}$ are given. A black-box…
In this work, for the given adjacency matrix of a graph, we present an algorithm which checks the connectivity of a graph and computes all of its connected components. Also, it is mathematically proved that the algorithm presents all the…
Quantum walks are roughly analogous to classical random walks, and like classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs it is useful to find the…
In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that…