Related papers: QSearchNet: A Quantum Walk Search Framework for Li…
We study the dynamical localization of discrete time evolution of topological split-step quantum random walk (QRW) on a single-site defect starting from a uniform distribution. Using analytical and numerical calculations, we determine the…
Quantum walks have been shown to be fruitful tools in analysing the dynamic properties of quantum systems. This article proposes to use quantum walks as an approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…
We provide first evidence that under certain conditions, 1/2-spin fermions may naturally behave like a Grover search, looking for topological defects in a material. The theoretical framework is that of discrete-time quantum walks (QW), i.e.…
Graph Neural Networks (GNN) and Transformer-based architectures have achieved remarkable progress in graph learning, yet they still struggle to capture both global structural dependencies and model the dynamic information propagation. In…
A quantum walk on a lattice is a paradigm of a quantum search in a database. The database qubit strings are the lattice sites, qubit rotations are tunneling events, and the target site is tagged by an energy shift. For quantum walks on a…
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…
This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic…
In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse…
Fast computational algorithms are in constant demand, and their development has been driven by advances such as quantum speedup and classical acceleration. This paper intends to study search algorithms based on quantum walks in quantum…
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…
Quantum graph neural networks offer a powerful paradigm for learning on graph-structured data, yet their explainability is complicated by measurement-induced stochasticity and the combinatorial nature of graph structure. In this paper, we…
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…
A randomly walking quantum particle evolving by Schr\"odinger's equation searches on $d$-dimensional cubic lattices in $O(\sqrt{N})$ time when $d \ge 5$, and with progressively slower runtime as $d$ decreases. This suggests that graph…
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…
Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…
We address the quantum search of a target node on a cycle graph by means of a quantum walk assisted by continuous measurement and feedback. Unlike previous spatial search approaches, where the oracle is described as a projector on the…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
Graph data, with its structurally variable nature, represents complex real-world phenomena like chemical compounds, protein structures, and social networks. Traditional Graph Neural Networks (GNNs) primarily utilize the message-passing…