Related papers: Quantum Walk Inspired Neural Networks for Graph-St…

Though classical random walks have been studied for many years, research concerning their quantum analogues, quantum random walks, has only come about recently. Numerous simulations of both types of walks have been run and analyzed, and are…

We address routing of classical and quantum information over quantum network, and show how to exploit chirality to achieve nearly optimal and robust transport. In particular, we prove how continuous time chiral quantum walks over a minimal…

Molecular property prediction is of crucial importance in many disciplines such as drug discovery, molecular biology, or material and process design. The frequently employed quantitative structure-property/activity relationships…

Graph neural networks (GNN) represent an emerging line of deep learning models that operate on graph structures. It is becoming more and more popular due to its high accuracy achieved in many graph-related tasks. However, GNN is not as well…

Graphs serve as fundamental descriptors for systems composed of interacting elements, capturing a wide array of data types, from molecular interactions to social networks and knowledge graphs. In this paper, we present an exhaustive review…

Graph-structured data are pervasive across domains including social networks, biological networks, and knowledge graphs. Due to their non-Euclidean nature, such data pose significant challenges to conventional machine learning methods. This…

A central question in neuroscience is how self-organizing dynamic interactions in the brain emerge on their relatively static structural backbone. Due to the complexity of spatial and temporal dependencies between different brain areas,…

We develop a new quantum neural network layer designed to run efficiently on a quantum computer but that can be simulated on a classical computer when restricted in the way it entangles input states. We first ask how a classical neural…

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…

We develop a new framework that extends the quantum walk framework of Magniez, Nayak, Roland, and Santha, by utilizing the idea of quantum data structures to construct an efficient method of nesting quantum walks. Surprisingly, only…

Quantum random walks (QRWs) are random processes in which the resulting probability density of the "walker" state, whose movement is governed by a "coin" state, is described in a non-classical manner. Previously, Q-plates have been used to…

Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing…

Deep learning has been shown to be able to recognize data patterns better than humans in specific circumstances or contexts. In parallel, quantum computing has demonstrated to be able to output complex wave functions with a few number of…

The quantum convolutional neural network (QCNN) is a promising quantum machine learning (QML) model that is expected to achieve quantum advantages in classically intractable problems. However, the QCNN requires a large number of…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph…

Graph kernels used to be the dominant approach to feature engineering for structured data, which are superseded by modern GNNs as the former lacks learnability. Recently, a suite of Kernel Convolution Networks (KCNs) successfully…

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…

Quantum neural networks (QNNs) represent a pioneering intersection of quantum computing and deep learning. In this study, we unveil a fundamental convolution property inherent to QNNs, stemming from the natural parallelism of quantum gate…