We introduce a geometric framework for continuous-time quantum walks on graphs by embedding each vertex into a Euclidean space through its time-dependent quantum probability distribution. This construction induces a rich geometry in which quantum tra...
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 systems. In...
We generalize the Schrödinger equation on graphs to include long-range interactions (LRI) by means of the Mellin-transformed d-path Laplacian operators. We find analytical expressions for the transition and return probabilities of a quantum part...
Quantum graphs are ideally suited to studying the spectral statistics of chaotic systems. Depending on the boundary conditions at the vertices, there are Neumann and Dirichlet graphs. The latter ones correspond to totally disassembled graphs with a s...
A Cayley graph
Cayley and nilpotent graphs arise from the interaction between graph theory and algebra and are used to visualize the structures of some algebraic objects as groups and commutative rings. On the other hand, Green and Schroll introduced Brauer graph a...
This paper focuses on modeling a disorder ensemble of quantum dots (QDs) as a special kind of Random Geometric Graphs (RGG) with weighted links. We compute any link weight as the overlap integral (or electron probability amplitude) between the QDs (=...
Quantum codes are crucial building blocks of quantum computers. With a self-dual quantum code is attached, canonically, a unique stabilised quantum state. Improving on a previous publication, we show how to determine the coefficients on the basis of...
This paper describes a practical approach to the quantum theory using the simulation and processing technology available today. The proposed project allows us to create an exploration graph so that for an initial starting configuration of the qubits,...
We consider the problem of measuring the similarity between two graphs using continuous-time quantum walks and comparing their time-evolution by means of the quantum Jensen-Shannon divergence. Contrary to previous works that focused solely on undirec...
This follow-up scientific case study builds on prior research to explore the computational challenges of applying quantum algorithms to financial asset management, focusing specifically on solving the graph-cut problem for investment recommendation....
Quantum secure multi-party summation (QSMS) is a fundamental problem in quantum secure multi-party computation (QSMC), wherein multiple parties compute the sum of their data without revealing them. This paper proposes a novel QSMS protocol based on g...
Inspired by classical graph neural networks, we discuss a novel quantum graph neural network (QGNN) model to predict the chemical and physical properties of molecules and materials. QGNNs were investigated to predict the energy gap between the highes...
Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations that are aimed at allowing us a better understanding of the physics involved in the process from...
Graph isomorphism is to determine whether two graphs have the same topological structure. It plays a significant role in areas of image matching, biochemistry, and information retrieval. Quantum walk, as a novel quantum computation model, has been em...
We bring together in one place some of the main results and applications from our recent work on quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time to investiga...
We present a simple protocol for certifying graph states in quantum networks using stabiliser measurements. The certification statements can easily be applied to different protocols using graph states. We see, for example, how it can be used for meas...
Quantum optimization algorithms are some of the most promising algorithms expected to show a quantum advantage. When solving quadratic unconstrained binary optimization problems, quantum optimization algorithms usually provide an approximate solution...
Quantum kernels hold significant promise for achieving computational advantages in quantum machine learning (QML), yet their effectiveness critically depends on the design of expressive and hardware-compatible feature maps, a challenge that is partic...
The isomorphism problem involves judging whether two graphs are topologically the same and producing structure-preserving isomorphism mapping. It is widely used in various areas. Diverse algorithms have been proposed to solve this problem in polynomi...
Quantum search algorithms provide a way to speed up combinatorial search, and have found several applications in modern quantum technology. In particular, spatial search on graphs, based on continuous-time quantum walks (CTQW), represents a promising...
In the era of data-driven education, educational social networks generate large volumes of high-dimensional and complex-structured data through learner interactions, collaborative activities, and resource-sharing behaviors, posing significant challen...
It is shown that it is possible to adapt the quantum graph model of graphene to some types of nonequilateral graphynes considered in the literature; we also discuss the corresponding nanotubes. The proposed models are, in fact, effective models and a...
Narrative extraction algorithms construct storylines by finding coherent paths through document collections. The Narrative Trails algorithm frames this as maximum-capacity path optimization, where path quality depends on a coherence function measurin...
Charging-station selection must combine reachability, uncertain completion time and operational preferences. We study a station selection rule that combines an upper-quantile score with probabilities obtained from a continuous time quantum walk. We b...
This is a noticeably short biography and introductory paper on multiplier Hopf algebras. It delves into questions regarding the significance of this abstract construction and the motivation behind its creation. It also concerns quantum linear groups,...
The pathological mechanism of autism spectrum disorder (ASD) exhibits dual heterogeneity: abnormal local energy metabolism and brain-wide high-order topological failure. To synergistically characterize these complex signals captured by advanced neuro...
Creative insight is a core phenomenon of human cognition, often characterized by the sudden emergence of novel and contextually appropriate ideas. Classical models based on symbolic search or associative networks struggle to capture the non-linear, c...
Accurate brain tumor segmentation from multimodal magnetic resonance imaging (MRI) remains challenging because of dissimilar tumor appearance and irregular spatial structure. This study proposes FKAN-GSAGE-LVQC, a hybrid segmentation framework integr...
Quantum walks are a powerful framework for simulating complex quantum systems and designing quantum algorithms, particularly for spatial search on graphs, where the goal is to find a marked vertex efficiently. In this work, we present efficient quant...
Ramsey analysis is applied to the problem of the relativistic and quantum synchronization of clocks. Various protocols of synchronization are addressed. Einstein and Eddington special relativity synchronization procedures are considered, and quantum...
The proliferation of digital infrastructures and the Internet of Things (IoT) has led to a rapid increase in interconnected devices, exposing modern systems to increasingly sophisticated cyber threats. Intrusion detection in such environments remains...
This study proposes a novel hybrid prediction model (QGCN-LSTM) that combines Quantum Graph Convolutional Networks (QGCN) with classical Long Short-Term Memory (LSTM). The model takes space-time data as input and employs a hierarchical graph-based qu...
Graph neural networks (GNNs) have achieved great success in graph classification, with graph pooling methods being widely adopted for related tasks. Existing approaches typically rely on node ranking or clustering to coarsen graphs, but often fail to...
The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend...
Quantum computers, due to their superposition and entanglement properties, provide significant advantages in solving certain problems compared with classical computers. Therefore, it is crucial to identify issues that can be efficiently solved by noi...
Background: Metamorphic malware is among the most persistent adversarial challenges in cybersecurity: it rewrites its own instruction stream on every propagation, preserving functional semantics while presenting a syntactically distinct binary that d...
This study explores the application of quantum computing in asset management, focusing on the use of the Quantum Approximate Optimization Algorithm (QAOA) to solve specific classes of financial asset recommendation problems. While quantum computing h...
Quantum memories are a critical component of entanglement-based quantum networks, enabling the storage and synchronisation of quantum states across dynamic links. However, current quantum memories have significantly lower capacity than the rate at wh...
We consider the interactions of traveling localized wave solutions with a vertex in a star graph domain that describes multiple Josephson junctions with a common/branch point (i.e., tricrystal junctions). The system is modeled by the sine-Gordon equa...
Sparse count data, such as patent document–keyword matrices, often contain excessive zeros and overdispersion, making conventional distance-based clustering methods less suitable. This study proposes a zero-inflated likelihood-based graph neura...
Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in
Feynman diagrams represent one of the most powerful and fascinating tools developed in theoretical physics in the last century. Introduced within the framework of quantum electrodynamics as a suitable method for computing the amplitude of a physical...
We address the problem of routing quantum and classical information from one sender to many possible receivers in a network. By employing the formalism of quantum walks, we describe the dynamics on a discrete structure based on a complete graph, wher...
We discuss a connection between the generalized Euler characteristic
We show that there is a relationship between the generalized Euler characteristic
Recent publications have introduced the concept of quantum-like (QL) bits, along with their associated QL states and QL gate operations, which emerge from the dynamics of complex, synchronized networks. The present work extends these ideas to multi-l...
Keeping track of air quality is paramount to issue preemptive measures to mitigate adversarial effects on the population. This study introduces a new quantum–classical approach, combining a graph-based deep learning structure with a quantum neu...
A graph-theoretical approach to the analysis of motion and rest in many-body systems is developed. Point bodies are represented as vertices of a complete bi-colored graph, termed the motion–rest graph (MRG). Two vertices are connected by a rust...
A general quantum thermodynamics network is composed of thermal devices connected to environments through quantum wires. The coupling between the devices and the wires may introduce additional decay channels which modify the system performance with r...
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