Related papers: Unifying quantum spatial search, state transfer an…
Quantum algorithms designed for realistic quantum many-body systems, such as chemistry and materials, usually require a large number of measurements of the Hamiltonian. Exploiting different ideas, such as {importance sampling,} observable…
How might one "reduce" a graph? That is, generate a smaller graph that preserves the global structure at the expense of discarding local details? There has been extensive work on both graph sparsification (removing edges) and graph…
I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…
This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph…
Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state transfer in continuous-time quantum walks, which is…
When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, additional marked vertices can make the search harder by…
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…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
Network centrality has important implications well beyond its role in physical and information transport analysis; as such, various quantum walk-based algorithms have been proposed for measuring network vertex centrality. In this work, we…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
We study the existence of state transfer with respect to the $q$-Laplacian matrix of a graph equipped with a non-trivial involution. We show that the occurrence of perfect state transfer between certain pair (or plus) states in such a graph…
In this paper, we study quantum walks on the extension of association schemes. Various state transfers can be achieved on these graphs, such as multiple state transfer among extreme points of a simplex, fractional revival on subsimplexes.…
We introduce uniformly vertex-transitive graphs as vertex-transitive graphs satisfying a stronger condition on their automorphism groups, motivated by a problem which arises from a Sinkhorn-type algorithm. We use the derangement graph…
We introduce the concept of group state transfer on graphs, summarize its relationship to other concepts in the theory of quantum walks, set up a basic theory, and discuss examples. Let $X$ be a graph with adjacency matrix $A$ and consider…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
We investigate the behavior of coherence in scattering quantum walk search on complete graph under the condition that the total number of vertices of the graph is greatly larger than the marked number of vertices we are searching, $N \gg…
We study the quantum query algorithms for simplex finding, a generalization of triangle finding to hypergraphs. This problem satisfies a rank-reduction property: a quantum query algorithm for finding simplices in rank-$r$ hypergraphs can be…
A discrete-time quantum walk is the quantum analogue of a Markov chain on a graph. Zhan [J. Algebraic Combin. 53(4):1187-1213, 2020] proposes a model of discrete-time quantum walk whose transition matrix is given by two reflections, using…
We study the sampling complexity of a probability distribution associated with an ensemble ofidentical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice.With uniform nearest-neighbor hopping we show that…
This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…