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Search Results (193)

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Keywords = quantum classification

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24 pages, 4267 KiB  
Article
RA-XTNet: A Novel CNN Model to Predict Rheumatoid Arthritis from Hand Radiographs and Thermal Images: A Comparison with CNN Transformer and Quantum Computing
by Ahalya R. Kesavapillai, Shabnam M. Aslam, Snekhalatha Umapathy and Fadiyah Almutairi
Diagnostics 2024, 14(17), 1911; https://doi.org/10.3390/diagnostics14171911 - 30 Aug 2024
Viewed by 481
Abstract
The aim and objective of the research are to develop an automated diagnosis system for the prediction of rheumatoid arthritis (RA) based on artificial intelligence (AI) and quantum computing for hand radiographs and thermal images. The hand radiographs and thermal images were segmented [...] Read more.
The aim and objective of the research are to develop an automated diagnosis system for the prediction of rheumatoid arthritis (RA) based on artificial intelligence (AI) and quantum computing for hand radiographs and thermal images. The hand radiographs and thermal images were segmented using a UNet++ model and color-based k-means clustering technique, respectively. The attributes from the segmented regions were generated using the Speeded-Up Robust Features (SURF) feature extractor and classification was performed using k-star and Hoeffding classifiers. For the ground truth and the predicted test image, the study utilizing UNet++ segmentation achieved a pixel-wise accuracy of 98.75%, an intersection over union (IoU) of 0.87, and a dice coefficient of 0.86, indicating a high level of similarity. The custom RA-X-ray thermal imaging (XTNet) surpassed all the models for the detection of RA with a classification accuracy of 90% and 93% for X-ray and thermal imaging modalities, respectively. Furthermore, the study employed quantum support vector machine (QSVM) as a quantum computing approach which yielded an accuracy of 93.75% and 87.5% for the detection of RA from hand X-ray and thermal images. In addition, vision transformer (ViT) was employed to classify RA which obtained an accuracy of 80% for hand X-rays and 90% for thermal images. Thus, depending on the performance measures, the RA-XTNet model can be used as an effective automated diagnostic method to diagnose RA accurately and rapidly in hand radiographs and thermal images. Full article
(This article belongs to the Section Machine Learning and Artificial Intelligence in Diagnostics)
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20 pages, 5693 KiB  
Article
H-QNN: A Hybrid Quantum–Classical Neural Network for Improved Binary Image Classification
by Muhammad Asfand Hafeez, Arslan Munir and Hayat Ullah
AI 2024, 5(3), 1462-1481; https://doi.org/10.3390/ai5030070 - 19 Aug 2024
Viewed by 850
Abstract
Image classification is an important application for deep learning. With the advent of quantum technology, quantum neural networks (QNNs) have become the focus of research. Traditional deep learning-based image classification involves using a convolutional neural network (CNN) to extract features from the image [...] Read more.
Image classification is an important application for deep learning. With the advent of quantum technology, quantum neural networks (QNNs) have become the focus of research. Traditional deep learning-based image classification involves using a convolutional neural network (CNN) to extract features from the image and a multi-layer perceptron (MLP) network to create the decision boundaries. However, quantum circuits with parameters can extract rich features from images and also create complex decision boundaries. This paper proposes a hybrid QNN (H-QNN) model designed for binary image classification that capitalizes on the strengths of quantum computing and classical neural networks. Our H-QNN model uses a compact, two-qubit quantum circuit integrated with a classical convolutional architecture, making it highly efficient for computation on noisy intermediate-scale quantum (NISQ) devices that are currently leading the way in practical quantum computing applications. Our H-QNN model significantly enhances classification accuracy, achieving a 90.1% accuracy rate on binary image datasets. In addition, we have extensively evaluated baseline CNN and our proposed H-QNN models for image retrieval tasks. The obtained quantitative results exhibit the generalization of our H-QNN for downstream image retrieval tasks. Furthermore, our model addresses the issue of overfitting for small datasets, making it a valuable tool for practical applications. Full article
(This article belongs to the Special Issue Advances in Quantum Computing and Quantum Machine Learning)
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20 pages, 3931 KiB  
Article
Novel Hybrid Quantum Architecture-Based Lung Cancer Detection Using Chest Radiograph and Computerized Tomography Images
by Jason Elroy Martis, Sannidhan M S, Balasubramani R, A. M. Mutawa and M. Murugappan
Bioengineering 2024, 11(8), 799; https://doi.org/10.3390/bioengineering11080799 - 7 Aug 2024
Viewed by 1068
Abstract
Lung cancer, the second most common type of cancer worldwide, presents significant health challenges. Detecting this disease early is essential for improving patient outcomes and simplifying treatment. In this study, we propose a hybrid framework that combines deep learning (DL) with quantum computing [...] Read more.
Lung cancer, the second most common type of cancer worldwide, presents significant health challenges. Detecting this disease early is essential for improving patient outcomes and simplifying treatment. In this study, we propose a hybrid framework that combines deep learning (DL) with quantum computing to enhance the accuracy of lung cancer detection using chest radiographs (CXR) and computerized tomography (CT) images. Our system utilizes pre-trained models for feature extraction and quantum circuits for classification, achieving state-of-the-art performance in various metrics. Not only does our system achieve an overall accuracy of 92.12%, it also excels in other crucial performance measures, such as sensitivity (94%), specificity (90%), F1-score (93%), and precision (92%). These results demonstrate that our hybrid approach can more accurately identify lung cancer signatures compared to traditional methods. Moreover, the incorporation of quantum computing enhances processing speed and scalability, making our system a promising tool for early lung cancer screening and diagnosis. By leveraging the strengths of quantum computing, our approach surpasses traditional methods in terms of speed, accuracy, and efficiency. This study highlights the potential of hybrid computational technologies to transform early cancer detection, paving the way for wider clinical applications and improved patient care outcomes. Full article
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11 pages, 488 KiB  
Article
A Deep Learning Approach to Investigating Clandestine Laboratories Using a GC-QEPAS Sensor
by Giorgio Felizzato, Nicola Liberatore, Sandro Mengali, Roberto Viola, Vittorio Moriggia and Francesco Saverio Romolo
Chemosensors 2024, 12(8), 152; https://doi.org/10.3390/chemosensors12080152 - 5 Aug 2024
Viewed by 661
Abstract
Illicit drug production in clandestine laboratories involves the use of large quantities of different chemicals that can be obtained for legitimate purposes. The identification of these chemicals, including reagents, catalyzers and solvents, is crucial for forensic investigations. From a legal point of view, [...] Read more.
Illicit drug production in clandestine laboratories involves the use of large quantities of different chemicals that can be obtained for legitimate purposes. The identification of these chemicals, including reagents, catalyzers and solvents, is crucial for forensic investigations. From a legal point of view, a drug precursor is a material that is specific and critical to the production of a finished chemical and that constitutes a significant portion of the final molecular structure of the drug. In this study, a gas chromatography quartz-enhanced photoacoustic spectroscopy (GC-QEPAS) sensor—in conjunction with a deep learning model—was evaluated for its effectiveness in the detection and identification of interesting compounds for the production of amphetamine, methamphetamine, 3,4-methylenedioxymethamphetamine (MDMA), phenylcyclohexyl piperidine (PCP), and cocaine. The GC-QEPAS sensor includes a gas sampler, a fast GC for separation, and a QEPAS detector, which excites molecules exiting the GC column using a quantum cascade laser to provide the infra-red (IR) spectrum. The on-site capability of the GC-QEPAS system offers significant advantages over the current instruments employed in this field, including rapid analysis, which is crucial in field operations. This allows law enforcement to quickly identify specimens of interest on site. The system’s performance was validated by taking into account the limit of detection, repeatability, and within-laboratory reproducibility. The results showed excellent repeatability and reproducibility for both the GC and QEPAS modules. The deep learning model, a multilayer perceptron neural network, was trained using IR spectra and retention times, achieving very high classification accuracy in the testing conditions. This study demonstrated the efficacy of the GC-QEPAS sensor combined with a deep learning model for the reliable identification of drug precursors, providing a robust tool for law enforcement during criminal investigations in clandestine laboratories. Full article
(This article belongs to the Special Issue Chemical Sensing and Analytical Methods for Forensic Applications)
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17 pages, 2863 KiB  
Article
QCL Infrared Spectroscopy Combined with Machine Learning as a Useful Tool for Classifying Acetaminophen Tablets by Brand
by José A. Martínez-Trespalacios, Daniel E. Polo-Herrera, Tamara Y. Félix-Massa, Samuel P. Hernandez-Rivera, Joaquín Hernandez-Fernandez, Fredy Colpas-Castillo and John R. Castro-Suarez
Molecules 2024, 29(15), 3562; https://doi.org/10.3390/molecules29153562 - 28 Jul 2024
Viewed by 897
Abstract
The development of new methods of identification of active pharmaceutical ingredients (API) is a subject of paramount importance for research centers, the pharmaceutical industry, and law enforcement agencies. Here, a system for identifying and classifying pharmaceutical tablets containing acetaminophen (AAP) by brand has [...] Read more.
The development of new methods of identification of active pharmaceutical ingredients (API) is a subject of paramount importance for research centers, the pharmaceutical industry, and law enforcement agencies. Here, a system for identifying and classifying pharmaceutical tablets containing acetaminophen (AAP) by brand has been developed. In total, 15 tablets of 11 brands for a total of 165 samples were analyzed. Mid-infrared vibrational spectroscopy with multivariate analysis was employed. Quantum cascade lasers (QCLs) were used as mid-infrared sources. IR spectra in the spectral range 980–1600 cm−1 were recorded. Five different classification methods were used. First, a spectral search through correlation indices. Second, machine learning algorithms such as principal component analysis (PCA), support vector classification (SVC), decision tree classifier (DTC), and artificial neural network (ANN) were employed to classify tablets by brands. SNV and first derivative were used as preprocessing to improve the spectral information. Precision, recall, specificity, F1-score, and accuracy were used as criteria to evaluate the best SVC, DEE, and ANN classification models obtained. The IR spectra of the tablets show characteristic vibrational signals of AAP and other APIs present. Spectral classification by spectral search and PCA showed limitations in differentiating between brands, particularly for tablets containing AAP as the only API. Machine learning models, specifically SVC, achieved high accuracy in classifying AAP tablets according to their brand, even for brands containing only AAP. Full article
(This article belongs to the Special Issue Molecular Spectroscopy in Applied Chemistry)
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12 pages, 1877 KiB  
Article
Breast Cancer Detection with Quanvolutional Neural Networks
by Nadine Matondo-Mvula and Khaled Elleithy
Entropy 2024, 26(8), 630; https://doi.org/10.3390/e26080630 - 26 Jul 2024
Viewed by 710
Abstract
Quantum machine learning holds the potential to revolutionize cancer treatment and diagnostic imaging by uncovering complex patterns beyond the reach of classical methods. This study explores the effectiveness of quantum convolutional layers in classifying ultrasound breast images for cancer detection. By encoding classical [...] Read more.
Quantum machine learning holds the potential to revolutionize cancer treatment and diagnostic imaging by uncovering complex patterns beyond the reach of classical methods. This study explores the effectiveness of quantum convolutional layers in classifying ultrasound breast images for cancer detection. By encoding classical data into quantum states through angle embedding and employing a robustly entangled 9-qubit circuit design with an SU(4) gate, we developed a Quantum Convolutional Neural Network (QCNN) and compared it to a classical CNN of similar architecture. Our QCNN model, leveraging two quantum circuits as convolutional layers, achieved an impressive peak training accuracy of 76.66% and a validation accuracy of 87.17% at a learning rate of 1 × 10−2. In contrast, the classical CNN model attained a training accuracy of 77.52% and a validation accuracy of 83.33%. These compelling results highlight the potential of quantum circuits to serve as effective convolutional layers for feature extraction in image classification, especially with small datasets. Full article
(This article belongs to the Special Issue The Future of Quantum Machine Learning and Quantum AI)
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12 pages, 257 KiB  
Article
Quantum Injectivity of Frames in Quaternionic Hilbert Spaces
by Zhenheng Xu, Guoqing Hong, Zuhua Guo and Jianxia Zhang
Mathematics 2024, 12(14), 2174; https://doi.org/10.3390/math12142174 - 11 Jul 2024
Viewed by 436
Abstract
A quantum injective frame is a frame capable of differentiating states based on their respective frame measurements, whereas the quantum-detection problem associated with frames endeavors to delineate all such frames. In the present paper, the concept of injective frames in infinite dimensional quaternionic [...] Read more.
A quantum injective frame is a frame capable of differentiating states based on their respective frame measurements, whereas the quantum-detection problem associated with frames endeavors to delineate all such frames. In the present paper, the concept of injective frames in infinite dimensional quaternionic Hilbert spaces is introduced. Further, some properties of injective frames such as the invariance of injective frames under invertible operators are discussed and several solutions to the frame quantum-detection problem are given. Finally, by employing operator theory and frames theory in quaternionic Hilbert spaces, some characterizations and classifications of frames for solving the injectivity problem are given. Full article
(This article belongs to the Section Algebra, Geometry and Topology)
21 pages, 2914 KiB  
Article
Multimodal Quanvolutional and Convolutional Neural Networks for Multi-Class Image Classification
by Yuri Gordienko, Yevhenii Trochun and Sergii Stirenko
Big Data Cogn. Comput. 2024, 8(7), 75; https://doi.org/10.3390/bdcc8070075 - 8 Jul 2024
Viewed by 1000
Abstract
By utilizing hybrid quantum–classical neural networks (HNNs), this research aims to enhance the efficiency of image classification tasks. HNNs allow us to utilize quantum computing to solve machine learning problems, which can be highly power-efficient and provide significant computation speedup compared to classical [...] Read more.
By utilizing hybrid quantum–classical neural networks (HNNs), this research aims to enhance the efficiency of image classification tasks. HNNs allow us to utilize quantum computing to solve machine learning problems, which can be highly power-efficient and provide significant computation speedup compared to classical operations. This is particularly relevant in sustainable applications where reducing computational resources and energy consumption is crucial. This study explores the feasibility of a novel architecture by leveraging quantum devices as the first layer of the neural network, which proved to be useful for scaling HNNs’ training process. Understanding the role of quanvolutional operations and how they interact with classical neural networks can lead to optimized model architectures that are more efficient and effective for image classification tasks. This research investigates the performance of HNNs across different datasets, including CIFAR100 and Satellite Images of Hurricane Damage by evaluating the performance of HNNs on these datasets in comparison with the performance of reference classical models. By evaluating the scalability of HNNs on diverse datasets, the study provides insights into their applicability across various real-world scenarios, which is essential for building sustainable machine learning solutions that can adapt to different environments. Leveraging transfer learning techniques with pre-trained models such as ResNet, EfficientNet, and VGG16 demonstrates the potential for HNNs to benefit from existing knowledge in classical neural networks. This approach can significantly reduce the computational cost of training HNNs from scratch while still achieving competitive performance. The feasibility study conducted in this research assesses the practicality and viability of deploying HNNs for real-world image classification tasks. By comparing the performance of HNNs with classical reference models like ResNet, EfficientNet, and VGG-16, this study provides evidence of the potential advantages of HNNs in certain scenarios. Overall, the findings of this research contribute to advancing sustainable applications of machine learning by proposing novel techniques, optimizing model architectures, and demonstrating the feasibility of adopting HNNs for real-world image classification problems. These insights can inform the development of more efficient and environmentally friendly machine learning solutions. Full article
(This article belongs to the Special Issue Machine Learning and AI Technology for Sustainable Development)
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25 pages, 728 KiB  
Article
Quantum K-Nearest Neighbors: Utilizing QRAM and SWAP-Test Techniques for Enhanced Performance
by Alberto Maldonado-Romo, J. Yaljá Montiel-Pérez, Victor Onofre, Javier Maldonado-Romo  and Juan Humberto Sossa-Azuela 
Mathematics 2024, 12(12), 1872; https://doi.org/10.3390/math12121872 - 16 Jun 2024
Viewed by 740
Abstract
This work introduces a quantum K-Nearest Neighbor (K-NN) classifier algorithm. The algorithm utilizes angle encoding through a Quantum Random Access Memory (QRAM) using n number of qubit addresses with O(log(n)) space complexity. It incorporates Grover’s algorithm and [...] Read more.
This work introduces a quantum K-Nearest Neighbor (K-NN) classifier algorithm. The algorithm utilizes angle encoding through a Quantum Random Access Memory (QRAM) using n number of qubit addresses with O(log(n)) space complexity. It incorporates Grover’s algorithm and the quantum SWAP-Test to identify similar states and determine the nearest neighbors with high probability, achieving Om search complexity, where m is the qubit address. We implement a simulation of the algorithm using IBM’s Qiskit with GPU support, applying it to the Iris and MNIST datasets with two different angle encodings. The experiments employ multiple QRAM cell sizes (8, 16, 32, 64, 128) and perform ten trials per size. According to the performance, accuracy values in the Iris dataset range from 89.3 ± 5.78% to 94.0 ± 1.56%. The MNIST dataset’s mean binary accuracy values range from 79.45 ± 18.84% to 94.00 ± 2.11% for classes 0 and 1. Additionally, a comparison of the results of this proposed approach with different state-of-the-art versions of QK-NN and the classical K-NN using Scikit-learn. This method achieves a 96.4 ± 2.22% accuracy in the Iris dataset. Finally, this proposal contributes an experimental result to the state of the art for the MNIST dataset, achieving an accuracy of 96.55 ± 2.00%. This work presents a new implementation proposal for QK-NN and conducts multiple experiments that yield more robust results than previous implementations. Although our average performance approaches still need to surpass the classic results, an experimental increase in the size of QRAM or the amount of data to encode is not achieved due to limitations. However, our results show promising improvement when considering working with more feature numbers and accommodating more data in the QRAM. Full article
(This article belongs to the Special Issue Quantum Computing and Networking)
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38 pages, 6602 KiB  
Article
Leveraging Data Locality in Quantum Convolutional Classifiers
by Mingyoung Jeng, Alvir Nobel, Vinayak Jha, David Levy, Dylan Kneidel, Manu Chaudhary, Ishraq Islam, Audrey Facer, Manish Singh, Evan Baumgartner, Eade Vanderhoof, Abina Arshad and Esam El-Araby
Entropy 2024, 26(6), 461; https://doi.org/10.3390/e26060461 - 28 May 2024
Viewed by 596
Abstract
Quantum computing (QC) has opened the door to advancements in machine learning (ML) tasks that are currently implemented in the classical domain. Convolutional neural networks (CNNs) are classical ML architectures that exploit data locality and possess a simpler structure than a fully connected [...] Read more.
Quantum computing (QC) has opened the door to advancements in machine learning (ML) tasks that are currently implemented in the classical domain. Convolutional neural networks (CNNs) are classical ML architectures that exploit data locality and possess a simpler structure than a fully connected multi-layer perceptrons (MLPs) without compromising the accuracy of classification. However, the concept of preserving data locality is usually overlooked in the existing quantum counterparts of CNNs, particularly for extracting multifeatures in multidimensional data. In this paper, we present an multidimensional quantum convolutional classifier (MQCC) that performs multidimensional and multifeature quantum convolution with average and Euclidean pooling, thus adapting the CNN structure to a variational quantum algorithm (VQA). The experimental work was conducted using multidimensional data to validate the correctness and demonstrate the scalability of the proposed method utilizing both noisy and noise-free quantum simulations. We evaluated the MQCC model with reference to reported work on state-of-the-art quantum simulators from IBM Quantum and Xanadu using a variety of standard ML datasets. The experimental results show the favorable characteristics of our proposed techniques compared with existing work with respect to a number of quantitative metrics, such as the number of training parameters, cross-entropy loss, classification accuracy, circuit depth, and quantum gate count. Full article
(This article belongs to the Special Issue Quantum Computation, Communication and Cryptography)
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21 pages, 563 KiB  
Article
A First Approach to Quantum Logical Shape Classification Framework
by Alexander Köhler, Marvin Kahra and Michael Breuß
Mathematics 2024, 12(11), 1646; https://doi.org/10.3390/math12111646 - 24 May 2024
Viewed by 496
Abstract
Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it [...] Read more.
Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to devise suitable applications. This article aims to propose for the first time an approach using quantum logic in image processing for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way, we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification, we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables us to initiate the principal component analysis. Through experiments, we explore the possibility of distinguishing between different geometrical objects and discuss the results in terms of quantum logical interpretation. Full article
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15 pages, 4026 KiB  
Article
Augmentation of Soft Partition with a Granular Prototype Based Fuzzy C-Means
by Ruixin Wang, Kaijie Xu and Yixi Wang
Mathematics 2024, 12(11), 1639; https://doi.org/10.3390/math12111639 - 23 May 2024
Viewed by 501
Abstract
Clustering is a fundamental cornerstone in unsupervised learning, playing a pivotal role in various data mining techniques. The precise and efficient classification of data stands as a central focus for numerous researchers and practitioners alike. In this study, we design an effective soft [...] Read more.
Clustering is a fundamental cornerstone in unsupervised learning, playing a pivotal role in various data mining techniques. The precise and efficient classification of data stands as a central focus for numerous researchers and practitioners alike. In this study, we design an effective soft partition classification method which refines and extends the prototype of the well-known Fuzzy C-Means clustering algorithm. Specifically, the developed scheme employs membership function to extend the prototypes into a series of granular prototypes, thus achieving a deeper revelation of the structure of the data. This process softly divides the data into core and extended parts. The core part can be succinctly encapsulated through several information granules, whereas the extended part lacks discernible geometry and requires formal descriptors (such as membership formulas). Our objective is to develop information granules that shape the core structure within the dataset, delineate their characteristics, and explore the interaction among these granules that result in their deformation. The granular prototypes become the main component of the information granules and provide an optimization space for traditional prototypes. Subsequently, we apply quantum-behaved particle swarm optimization to identify the optimal partition matrix for the data. This optimized matrix significantly enhances the partition performance of the data. Experimental results provide substantial evidence of the effectiveness of the proposed approach. Full article
(This article belongs to the Special Issue New Advances in Data Analytics and Mining)
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14 pages, 13155 KiB  
Article
Optimizing Variational Quantum Neural Networks Based on Collective Intelligence
by Zitong Li, Tailong Xiao, Xiaoyang Deng, Guihua Zeng and Weimin Li
Mathematics 2024, 12(11), 1627; https://doi.org/10.3390/math12111627 - 22 May 2024
Viewed by 775
Abstract
Quantum machine learning stands out as one of the most promising applications of quantum computing, widely believed to possess potential quantum advantages. In the era of noisy intermediate-scale quantum, the scale and quality of quantum computers are limited, and quantum algorithms based on [...] Read more.
Quantum machine learning stands out as one of the most promising applications of quantum computing, widely believed to possess potential quantum advantages. In the era of noisy intermediate-scale quantum, the scale and quality of quantum computers are limited, and quantum algorithms based on fault-tolerant quantum computing paradigms cannot be experimentally verified in the short term. The variational quantum algorithm design paradigm can better adapt to the practical characteristics of noisy quantum hardware and is currently one of the most promising solutions. However, variational quantum algorithms, due to their highly entangled nature, encounter the phenomenon known as the “barren plateau” during the optimization and training processes, making effective optimization challenging. This paper addresses this challenging issue by researching a variational quantum neural network optimization method based on collective intelligence algorithms. The aim is to overcome optimization difficulties encountered by traditional methods such as gradient descent. We study two typical applications of using quantum neural networks: random 2D Hamiltonian ground state solving and quantum phase recognition. We find that the collective intelligence algorithm shows a better optimization compared to gradient descent. The solution accuracy of ground energy and phase classification is enhanced, and the optimization iterations are also reduced. We highlight that the collective intelligence algorithm has great potential in tackling the optimization of variational quantum algorithms. Full article
(This article belongs to the Special Issue Advances in Quantum Key Distribution and Quantum Information)
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16 pages, 725 KiB  
Article
Cyber Risk in Insurance: A Quantum Modeling
by Claude Lefèvre, Muhsin Tamturk, Sergey Utev and Marco Carenzo
Risks 2024, 12(5), 83; https://doi.org/10.3390/risks12050083 - 20 May 2024
Viewed by 878
Abstract
In this research, we consider cyber risk in insurance using a quantum approach, with a focus on the differences between reported cyber claims and the number of cyber attacks that caused them. Unlike the traditional probabilistic approach, quantum modeling makes it possible to [...] Read more.
In this research, we consider cyber risk in insurance using a quantum approach, with a focus on the differences between reported cyber claims and the number of cyber attacks that caused them. Unlike the traditional probabilistic approach, quantum modeling makes it possible to deal with non-commutative event paths. We investigate the classification of cyber claims according to different cyber risk behaviors to enable more precise analysis and management of cyber risks. Additionally, we examine how historical cyber claims can be utilized through the application of copula functions for dependent insurance claims. We also discuss classification, likelihood estimation, and risk-loss calculation within the context of dependent insurance claim data. Full article
(This article belongs to the Special Issue Advancements in Actuarial Mathematics and Risk Theory)
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31 pages, 5192 KiB  
Review
Cupolets: History, Theory, and Applications
by Matthew A. Morena and Kevin M. Short
Dynamics 2024, 4(2), 394-424; https://doi.org/10.3390/dynamics4020022 - 13 May 2024
Viewed by 604
Abstract
In chaos control, one usually seeks to stabilize the unstable periodic orbits (UPOs) that densely inhabit the attractors of many chaotic dynamical systems. These orbits collectively play a significant role in determining the dynamics and properties of chaotic systems and are said to [...] Read more.
In chaos control, one usually seeks to stabilize the unstable periodic orbits (UPOs) that densely inhabit the attractors of many chaotic dynamical systems. These orbits collectively play a significant role in determining the dynamics and properties of chaotic systems and are said to form the skeleton of the associated attractors. While UPOs are insightful tools for analysis, they are naturally unstable and, as such, are difficult to find and computationally expensive to stabilize. An alternative to using UPOs is to approximate them using cupolets. Cupolets, a name derived from chaotic, unstable, periodic, orbit-lets, are a relatively new class of waveforms that represent highly accurate approximations to the UPOs of chaotic systems, but which are generated via a particular control scheme that applies tiny perturbations along Poincaré sections. Originally discovered in an application of secure chaotic communications, cupolets have since gone on to play pivotal roles in a number of theoretical and practical applications. These developments include using cupolets as wavelets for image compression, targeting in dynamical systems, a chaotic analog to quantum entanglement, an abstract reducibility classification, a basis for audio and video compression, and, most recently, their detection in a chaotic neuron model. This review will detail the historical development of cupolets, how they are generated, and their successful integration into theoretical and computational science and will also identify some unanswered questions and future directions for this work. Full article
(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena—2nd Edition)
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