Related papers: Sensitivity of quantum walk to phase reversal and …
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…
Hypergraph has been selected as a powerful candidate for characterizing higher-order networks and has received increasing attention in recent years. In this article, we study random walks with resetting on hypergraph by utilizing spectral…
We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk…
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…
Quantum walks obey unitary dynamics: they form closed quantum systems. The system becomes open if the walk suffers from imperfections represented as missing links on the underlying basic graph structure, described by dynamical percolation.…
The join $X\vee Y$ of two graphs $X$ and $Y$ is the graph obtained by joining each vertex of $X$ to each vertex of $Y$. We explore the behaviour of a continuous quantum walk on a weighted join graph having the adjacency matrix or Laplacian…
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…
A fundamental problem on graph-structured data is that of quantifying similarity between graphs. Graph kernels are an established technique for such tasks; in particular, those based on random walks and return probabilities have proven to…
A randomly walking quantum particle searches in Grover's $\Theta(\sqrt{N})$ iterations for a marked vertex on the complete graph of $N$ vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a…
In this paper, we consider discrete time quantum walks on graphs with coin focusing on the decentralized model, where the coin operation is allowed to change with the vertex of the graph. When the coin operations can be modified at every…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm,…
The exponential speed-up of quantum walks on certain graphs, relative to classical particles diffusing on the same graph, is a striking observation. It has suggested the possibility of new fast quantum algorithms. We point out here that…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
The task of finding an element in an unstructured database is known as spatial search and can be expressed as a quantum walk evolution on a graph. In this article, we modify the usual search problem by adding an extra trapping vertex to the…
We construct a quantum searching model of a signed edge driven by a quantum walk. The time evolution operator of this quantum walk provides a weighted adjacency matrix induced by the assignment of sign to each edge. This sign can be…
Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an "initiator" graph with itself, have risen in popularity in network science due to their ability to generate complex networks with…