Related papers: Unifying quantum spatial search, state transfer an…
Recently, the work on quantum automorphism groups of graphs has seen renewed progress, which we expand in this paper. Quantum symmetry is a richer notion of symmetry than the classical symmetries of a graph. In general, it is non-trivial to…
Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…
Many applications require to learn, mine, analyze and visualize large-scale graphs. These graphs are often too large to be addressed efficiently using conventional graph processing technologies. Many applications have requirements to…
We develop a novel method for measuring the similarity between complete weighted graphs, which are probed by means of discrete-time quantum walks. Directly probing complete graphs using discrete-time quantum walks is intractable due to the…
We investigate quantum state transfer on a class of bipartite graphs, namely the butterfly graphs, within the framework of discrete-time quantum walks. These graphs facilitate the construction of scalable quantum networks that enable…
Dynamic programming is a cornerstone of graph-based optimization. While effective, it scales unfavorably with problem size. In this work, we present QuantGraph, a two-stage quantum-enhanced framework that casts local and global…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…
We introduce a novel quantum algorithm for similar subgraph identification in form of an NP-hard cardinality-constrained binary quadratic optimization problem. Given a weighted reference graph with Laplacian $\boldsymbol{B}$, our algorithm…
This work examines the time complexity of quantum search algorithms on combinatorial $t$-designs with multiple marked elements using the continuous-time quantum walk. Through a detailed exploration of $t$-designs and their incidence…
In this paper we show that all nodes can be found optimally for almost all random Erd\H{o}s-R\'enyi ${\mathcal G}(n,p)$ graphs using continuous-time quantum spatial search procedure. This works for both adjacency and Laplacian matrices,…
We study quantum algorithms for spatial search on finite dimensional grids. Patel et al. and Falk have proposed algorithms based on a quantum walk without a coin, with different operators applied at even and odd steps. Until now, such…
This paper discusses continuous-time quantum walks and asymptotic state transfer in graphs with an involution. By providing quantitative bounds on the eigenvectors of the Hamiltonian, it provides an approach to achieving high-fidelity state…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…
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…
We give a new formula for computing the isospectral reduction of a matrix (and graph) down to a submatrix (or subgraph). Using this, we generalize the notion of isospectral reductions. In addition, we give a procedure for constructing a…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of…
Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…