Related papers: Quantum Walk Search on Complete Multipartite Graph…
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 treat a quantum walk model with in- and out- flows at every time step from the outside. We show that this quantum walk can find the marked vertex of the complete graph with a high probability in the stationary state. In exchange of the…
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…
Rydberg atoms provide a highly promising platform for quantum computation, leveraging their strong tunable interactions to encode and manipulate information in the electronic states of individual atoms. Key advantages of Rydberg atoms…
Lackadaisical quantum walk(LQW) has been an efficient technique in searching a target state from a database which is distributed on a two-dimensional lattice. We numerically study the quantum search algorithm based on the lackadaisical…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
In this work, we consider the application of continuous time quantum walking(CTQW) to the Maximum Clique(MC) Problem. Performing CTQW on graphs will generate distinct periodic probability amplitude for different vertices. We will show that…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
This paper studies the search for a single arc in a graph using the Szegedy walk. Arc search can be interpreted as finding a quantum particle not only in its position but also with a specific internal state. The quantum walk employed in…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
This work introduces a graph-phased Szegedy's quantum walk, which incorporates link phases and local arbitrary phase rotations (APR), unlocking new possibilities for quantum algorithm efficiency. We demonstrate how to adapt quantum circuits…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
We study spatial search with continuous-time quantum walks on real-world complex networks. We use smaller replicas of the Internet network obtained with a recent geometric renormalization method introduced by Garc\'ia-P\'erez et al., Nat.…
We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N^{2/3}) query quantum algorithm.…
Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a…
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…
Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a…
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk…
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…