Related papers: Quantum walks on regular uniform hypergraphs

Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…

For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…

Various quantum-walk based algorithms have been proposed to analyse and rank the centrality of graph vertices. However, issues arise when working with directed graphs --- the resulting non-Hermitian Hamiltonian leads to non-unitary…

We develop a general theory for a quantum-walk search on a star graph. A star graph has N edges each of which is attached to a central vertex. A graph G is attached to one of these edges, and we would like to find out to which edge it is…

The quantization of the PageRank algorithm is a promising tool for a future quantum internet. Here we present a modification of the quantum PageRank introducing arbitrary phase rotations (APR) in the underlying Szegedy's quantum walk. We…

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 give a short overview over recent developments on quantum graphs and outline the connection between general quantum graphs and so-called quantum random walks.

We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…

Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic…

We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…

We present a theoretical framework for the analysis of amplitude transfer in Quantum Variational Algorithms (QVAs) for combinatorial optimisation with mixing unitaries defined by vertex-transitive graphs, based on their continuous-time…

In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…

Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…

The development of Graph Neural Networks (GNNs) has led to great progress in machine learning on graph-structured data. These networks operate via diffusing information across the graph nodes while capturing the structure of the graph.…

High-fidelity quantum state transfer is critical for quantum communication and scalable quantum computation. Current quantum state transfer algorithms on the complete bipartite graph, which are based on discrete-time quantum walk search…

Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…

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…

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for $N$-fold star power graph, which are invariant under the 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 initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time…