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Search Results (399)

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24 pages, 1681 KiB  
Article
A Hybrid Quantum–Classical Architecture with Data Re-Uploading and Genetic Algorithm Optimization for Enhanced Image Classification
by Aksultan Mukhanbet and Beimbet Daribayev
Computation 2025, 13(8), 185; https://doi.org/10.3390/computation13080185 - 1 Aug 2025
Viewed by 337
Abstract
Quantum machine learning (QML) has emerged as a promising approach for enhancing image classification by exploiting quantum computational principles such as superposition and entanglement. However, practical applications on complex datasets like CIFAR-100 remain limited due to the low expressivity of shallow circuits and [...] Read more.
Quantum machine learning (QML) has emerged as a promising approach for enhancing image classification by exploiting quantum computational principles such as superposition and entanglement. However, practical applications on complex datasets like CIFAR-100 remain limited due to the low expressivity of shallow circuits and challenges in circuit optimization. In this study, we propose HQCNN–REGA—a novel hybrid quantum–classical convolutional neural network architecture that integrates data re-uploading and genetic algorithm optimization for improved performance. The data re-uploading mechanism allows classical inputs to be encoded multiple times into quantum states, enhancing the model’s capacity to learn complex visual features. In parallel, a genetic algorithm is employed to evolve the quantum circuit architecture by optimizing gate sequences, entanglement patterns, and layer configurations. This combination enables automatic discovery of efficient parameterized quantum circuits without manual tuning. Experiments on the MNIST and CIFAR-100 datasets demonstrate state-of-the-art performance for quantum models, with HQCNN–REGA outperforming existing quantum neural networks and approaching the accuracy of advanced classical architectures. In particular, we compare our model with classical convolutional baselines such as ResNet-18 to validate its effectiveness in real-world image classification tasks. Our results demonstrate the feasibility of scalable, high-performing quantum–classical systems and offer a viable path toward practical deployment of QML in computer vision applications, especially on noisy intermediate-scale quantum (NISQ) hardware. Full article
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65 pages, 8546 KiB  
Review
Quantum Machine Learning and Deep Learning: Fundamentals, Algorithms, Techniques, and Real-World Applications
by Maria Revythi and Georgia Koukiou
Mach. Learn. Knowl. Extr. 2025, 7(3), 75; https://doi.org/10.3390/make7030075 - 1 Aug 2025
Viewed by 269
Abstract
Quantum computing, with its foundational principles of superposition and entanglement, has the potential to provide significant quantum advantages, addressing challenges that classical computing may struggle to overcome. As data generation continues to grow exponentially and technological advancements accelerate, classical machine learning algorithms increasingly [...] Read more.
Quantum computing, with its foundational principles of superposition and entanglement, has the potential to provide significant quantum advantages, addressing challenges that classical computing may struggle to overcome. As data generation continues to grow exponentially and technological advancements accelerate, classical machine learning algorithms increasingly face difficulties in solving complex real-world problems. The integration of classical machine learning with quantum information processing has led to the emergence of quantum machine learning, a promising interdisciplinary field. This work provides the reader with a bottom-up view of quantum circuits starting from quantum data representation, quantum gates, the fundamental quantum algorithms, and more complex quantum processes. Thoroughly studying the mathematics behind them is a powerful tool to guide scientists entering this domain and exploring their connection to quantum machine learning. Quantum algorithms such as Shor’s algorithm, Grover’s algorithm, and the Harrow–Hassidim–Lloyd (HHL) algorithm are discussed in detail. Furthermore, real-world implementations of quantum machine learning and quantum deep learning are presented in fields such as healthcare, bioinformatics and finance. These implementations aim to enhance time efficiency and reduce algorithmic complexity through the development of more effective quantum algorithms. Therefore, a comprehensive understanding of the fundamentals of these algorithms is crucial. Full article
(This article belongs to the Section Learning)
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24 pages, 5906 KiB  
Article
In Silico Mining of the Streptome Database for Hunting Putative Candidates to Allosterically Inhibit the Dengue Virus (Serotype 2) RdRp
by Alaa H. M. Abdelrahman, Gamal A. H. Mekhemer, Peter A. Sidhom, Tarad Abalkhail, Shahzeb Khan and Mahmoud A. A. Ibrahim
Pharmaceuticals 2025, 18(8), 1135; https://doi.org/10.3390/ph18081135 - 30 Jul 2025
Viewed by 374
Abstract
Background/Objectives: In the last few decades, the dengue virus, a prevalent flavivirus, has demonstrated various epidemiological, economic, and health impacts around the world. Dengue virus serotype 2 (DENV2) plays a vital role in dengue-associated mortality. The RNA-dependent RNA polymerase (RdRp) of DENV2 is [...] Read more.
Background/Objectives: In the last few decades, the dengue virus, a prevalent flavivirus, has demonstrated various epidemiological, economic, and health impacts around the world. Dengue virus serotype 2 (DENV2) plays a vital role in dengue-associated mortality. The RNA-dependent RNA polymerase (RdRp) of DENV2 is a charming druggable target owing to its crucial function in viral reproduction. In recent years, streptomycetes natural products (NPs) have attracted considerable attention as a potential source of antiviral drugs. Methods: Seeking prospective inhibitors that inhibit the DENV2 RdRp allosteric site, in silico mining of the Streptome database was executed. AutoDock4.2.6 software performance in predicting docking poses of the inspected inhibitors was initially conducted according to existing experimental data. Upon the assessed docking parameters, the Streptome database was virtually screened against DENV2 RdRp allosteric site. The streptomycetes NPs with docking scores less than the positive control (68T; calc. −35.6 kJ.mol−1) were advanced for molecular dynamics simulations (MDS), and their binding affinities were computed by employing the MM/GBSA approach. Results: SDB9818 and SDB4806 unveiled superior inhibitor activities against DENV2 RdRp upon MM/GBSA//300 ns MDS than 68T with ΔGbinding values of −246.4, −242.3, and −150.6 kJ.mol−1, respectively. A great consistency was found in both the energetic and structural analyses of the identified inhibitors within the DENV2 RdRp allosteric site. Furthermore, the physicochemical characteristics of the identified inhibitors demonstrated good oral bioavailability. Eventually, quantum mechanical computations were carried out to evaluate the chemical reactivity of the identified inhibitors. Conclusions: As determined by in silico computations, the identified streptomycetes NPs may act as DENV2 RdRp allosteric inhibitors and mandate further experimental assays. Full article
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20 pages, 2399 KiB  
Article
Exploring Novel Optical Soliton Molecule for the Time Fractional Cubic–Quintic Nonlinear Pulse Propagation Model
by Syed T. R. Rizvi, Atef F. Hashem, Azrar Ul Hassan, Sana Shabbir, A. S. Al-Moisheer and Aly R. Seadawy
Fractal Fract. 2025, 9(8), 497; https://doi.org/10.3390/fractalfract9080497 - 29 Jul 2025
Viewed by 304
Abstract
This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fiber optic communications, nonlinear optics, optical signal processing, and laser–tissue interactions [...] Read more.
This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fiber optic communications, nonlinear optics, optical signal processing, and laser–tissue interactions in medical science. The nonlinear effects exhibited by the model—such as self-focusing, self-phase modulation, and wave mixing—are influenced by the combined impact of the cubic and quintic nonlinear terms. To explore the dynamics of this model, we apply a robust analytical technique known as the sub-ODE method, which reveals a diverse range of soliton structures and offers deep insight into laser pulse interactions. The investigation yields a rich set of explicit soliton solutions, including hyperbolic, rational, singular, bright, Jacobian elliptic, Weierstrass elliptic, and periodic solutions. These waveforms have significant real-world relevance: bright solitons are employed in fiber optic communications for distortion-free long-distance data transmission, while both bright and dark solitons are used in nonlinear optics to study light behavior in media with intensity-dependent refractive indices. Solitons also contribute to advancements in quantum technologies, precision measurement, and fiber laser systems, where hyperbolic and periodic solitons facilitate stable, high-intensity pulse generation. Additionally, in nonlinear acoustics, solitons describe wave propagation in media where amplitude influences wave speed. Overall, this work highlights the theoretical depth and practical utility of soliton dynamics in fractional nonlinear systems. Full article
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25 pages, 579 KiB  
Article
An Internet Messenger Using Post-Quantum Cryptography Algorithms Based on Isogenies of Elliptic Curves
by Beniamin Jankowski, Kamil Szydłowski, Marcin Niemiec and Piotr Chołda
Electronics 2025, 14(14), 2905; https://doi.org/10.3390/electronics14142905 - 20 Jul 2025
Viewed by 431
Abstract
This paper presents the design and implementation of an Internet-based instant messaging application that leverages post-quantum cryptographic algorithms founded on isogenies of elliptic curves. The system employs the CSIDH cryptosystem for key exchange and SeaSign for digital signatures, integrating these with the X3DH [...] Read more.
This paper presents the design and implementation of an Internet-based instant messaging application that leverages post-quantum cryptographic algorithms founded on isogenies of elliptic curves. The system employs the CSIDH cryptosystem for key exchange and SeaSign for digital signatures, integrating these with the X3DH and Double-Ratchet protocols to enable end-to-end encryption for both text messages and binary file transfers. Key generation is supported for new users upon registration, ensuring robust cryptographic foundations from the outset. The performance of the CSIDH and SeaSign algorithms is evaluated at various security levels using a Python-based prototype, providing practical benchmarks. By combining isogeny-based cryptographic schemes with widely adopted secure messaging protocols, this work presents an illustration of a selected quantum-resistant communication solution and offers insights into the feasibility and practicality of deploying such protocols in real-world applications. Full article
(This article belongs to the Special Issue Network Security and Cryptography Applications)
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13 pages, 279 KiB  
Article
Generalized Hyers–Ulam Stability of Bi-Homomorphisms, Bi-Derivations, and Bi-Isomorphisms in C*-Ternary Algebras
by Jae-Hyeong Bae and Won-Gil Park
Mathematics 2025, 13(14), 2289; https://doi.org/10.3390/math13142289 - 16 Jul 2025
Viewed by 194
Abstract
In this paper, we investigate the generalized Hyers–Ulam stability of bi-homomorphisms, bi-derivations, and bi-isomorphisms in C*-ternary algebras. The study of functional equations with a sufficient number of variables can be helpful in solving real-world problems such as artificial intelligence. In this [...] Read more.
In this paper, we investigate the generalized Hyers–Ulam stability of bi-homomorphisms, bi-derivations, and bi-isomorphisms in C*-ternary algebras. The study of functional equations with a sufficient number of variables can be helpful in solving real-world problems such as artificial intelligence. In this paper, we build on previous research on functional equations with four variables to study functional equations with as many variables as desired. We introduce new bounds for the stability of mappings satisfying generalized bi-additive conditions and demonstrate the uniqueness of approximating bi-isomorphisms. The results contribute to the deeper understanding of ternary algebraic structures and related functional equations, relevant to both pure mathematics and quantum information science. Full article
27 pages, 4005 KiB  
Article
Quantum-Enhanced Predictive Degradation Pathway Optimization for PV Storage Systems: A Hybrid Quantum–Classical Approach for Maximizing Longevity and Efficiency
by Dawei Wang, Shuang Zeng, Liyong Wang, Baoqun Zhang, Cheng Gong, Zhengguo Piao and Fuming Zheng
Energies 2025, 18(14), 3708; https://doi.org/10.3390/en18143708 - 14 Jul 2025
Viewed by 257
Abstract
The increasing deployment of photovoltaic and energy storage systems (ESSs) in modern power grids has highlighted the critical challenge of component degradation, which significantly impacts system efficiency, operational costs, and long-term reliability. Conventional energy dispatch and optimization approaches fail to adequately mitigate the [...] Read more.
The increasing deployment of photovoltaic and energy storage systems (ESSs) in modern power grids has highlighted the critical challenge of component degradation, which significantly impacts system efficiency, operational costs, and long-term reliability. Conventional energy dispatch and optimization approaches fail to adequately mitigate the progressive efficiency loss in PV modules and battery storage, leading to suboptimal performance and reduced system longevity. To address these challenges, this paper proposes a quantum-enhanced degradation pathway optimization framework that dynamically adjusts operational strategies to extend the lifespan of PV storage systems while maintaining high efficiency. By leveraging quantum-assisted Monte Carlo simulations and hybrid quantum–classical optimization, the proposed model evaluates degradation pathways in real time and proactively optimizes energy dispatch to minimize efficiency losses due to aging effects. The framework integrates a quantum-inspired predictive maintenance algorithm, which utilizes probabilistic modeling to forecast degradation states and dynamically adjust charge–discharge cycles in storage systems. Unlike conventional optimization methods, which struggle with the complexity and stochastic nature of degradation mechanisms, the proposed approach capitalizes on quantum parallelism to assess multiple degradation scenarios simultaneously, significantly enhancing computational efficiency. A three-layer hierarchical optimization structure is introduced, ensuring real-time degradation risk assessment, periodic dispatch optimization, and long-term predictive adjustments based on PV and battery aging trends. The framework is tested on a 5 MW PV array coupled with a 2.5 MWh lithium-ion battery system, with real-world degradation models applied to reflect light-induced PV degradation (0.7% annual efficiency loss) and battery state-of-health deterioration (1.2% per 100 cycles). A hybrid quantum–classical computing environment, utilizing D-Wave’s Advantage quantum annealer alongside a classical reinforcement learning-based optimization engine, enables large-scale scenario evaluation and real-time operational adjustments. The simulation results demonstrate that the quantum-enhanced degradation optimization framework significantly reduces efficiency losses, extending the PV module’s lifespan by approximately 2.5 years and reducing battery-degradation-induced wear by 25% compared to conventional methods. The quantum-assisted predictive maintenance model ensures optimal dispatch strategies that balance energy demand with system longevity, preventing excessive degradation while maintaining grid reliability. The findings establish a novel paradigm in degradation-aware energy optimization, showcasing the potential of quantum computing in enhancing the sustainability and resilience of PV storage systems. This research paves the way for the broader integration of quantum-based decision-making in renewable energy infrastructure, enabling scalable, high-performance optimization for future energy systems. Full article
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25 pages, 2908 KiB  
Article
Secure and Scalable File Encryption for Cloud Systems via Distributed Integration of Quantum and Classical Cryptography
by Changjong Kim, Seunghwan Kim, Kiwook Sohn, Yongseok Son, Manish Kumar and Sunggon Kim
Appl. Sci. 2025, 15(14), 7782; https://doi.org/10.3390/app15147782 - 11 Jul 2025
Viewed by 440
Abstract
We propose a secure and scalable file-encryption scheme for cloud systems by integrating Post-Quantum Cryptography (PQC), Quantum Key Distribution (QKD), and Advanced Encryption Standard (AES) within a distributed architecture. While prior studies have primarily focused on secure key exchange or authentication protocols (e.g., [...] Read more.
We propose a secure and scalable file-encryption scheme for cloud systems by integrating Post-Quantum Cryptography (PQC), Quantum Key Distribution (QKD), and Advanced Encryption Standard (AES) within a distributed architecture. While prior studies have primarily focused on secure key exchange or authentication protocols (e.g., layered PQC-QKD key distribution), our scheme extends beyond key management by implementing a distributed encryption architecture that protects large-scale files through integrated PQC, QKD, and AES. To support high-throughput encryption, our proposed scheme partitions the target file into fixed-size subsets and distributes them across slave nodes, each performing parallel AES encryption using a locally reconstructed key from a PQC ciphertext. Each slave node receives a PQC ciphertext that encapsulates the AES key, along with a PQC secret key masked using QKD based on the BB84 protocol, both of which are centrally generated and managed by the master node for secure coordination. In addition, an encryption and transmission pipeline is designed to overlap I/O, encryption, and communication, thereby reducing idle time and improving resource utilization. The master node performs centralized decryption by collecting encrypted subsets, recovering the AES key, and executing decryption in parallel. Our evaluation using a real-world medical dataset shows that the proposed scheme achieves up to 2.37× speedup in end-to-end runtime and up to 8.11× speedup in encryption time over AES (Original). In addition to performance gains, our proposed scheme maintains low communication cost, stable CPU utilization across distributed nodes, and negligible overhead from quantum key management. Full article
(This article belongs to the Special Issue AI-Enabled Next-Generation Computing and Its Applications)
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14 pages, 1922 KiB  
Article
Asymmetric Protocols for Mode Pairing Quantum Key Distribution with Finite-Key Analysis
by Zhenhua Li, Tianqi Dou, Yuheng Xie, Weiwen Kong, Yang Liu, Haiqiang Ma and Jianjun Tang
Entropy 2025, 27(7), 737; https://doi.org/10.3390/e27070737 - 9 Jul 2025
Viewed by 302
Abstract
The mode pairing quantum key distribution (MP-QKD) protocol has attracted considerable attention for its capability to ensure high secure key rates over long distances without requiring global phase locking. However, ensuring symmetric channels for the MP-QKD protocol is challenging in practical quantum communication [...] Read more.
The mode pairing quantum key distribution (MP-QKD) protocol has attracted considerable attention for its capability to ensure high secure key rates over long distances without requiring global phase locking. However, ensuring symmetric channels for the MP-QKD protocol is challenging in practical quantum communication networks. Previous studies on the asymmetric MP-QKD protocol have relied on ideal decoy state assumptions and infinite-key analysis, which are unattainable for real-world deployment. In this paper, we conduct a security analysis of the asymmetric MP-QKD protocol with the finite-key analysis, where we discard the previously impractical assumptions made in the decoy state method. Combined with statistical fluctuation analysis, we globally optimized the 10 independent parameters in the asymmetric MP-QKD protocol by employing our modified particle swarm optimization. Through further analysis, the simulation results demonstrate that our work achieves improved secure key rates and transmission distances compared to the strategy with additional attenuation. We further investigate the relationship between the intensities and probabilities of signal, decoy, and vacuum states with transmission distance, facilitating their more efficient deployment in future quantum networks. Full article
(This article belongs to the Section Quantum Information)
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18 pages, 1199 KiB  
Article
Adaptive, Privacy-Enhanced Real-Time Fraud Detection in Banking Networks Through Federated Learning and VAE-QLSTM Fusion
by Hanae Abbassi, Saida El Mendili and Youssef Gahi
Big Data Cogn. Comput. 2025, 9(7), 185; https://doi.org/10.3390/bdcc9070185 - 9 Jul 2025
Viewed by 787
Abstract
Increased digital banking operations have brought about a surge in suspicious activities, necessitating heightened real-time fraud detection systems. Conversely, traditional static approaches encounter challenges in maintaining privacy while adapting to new fraudulent trends. In this paper, we provide a unique approach to tackling [...] Read more.
Increased digital banking operations have brought about a surge in suspicious activities, necessitating heightened real-time fraud detection systems. Conversely, traditional static approaches encounter challenges in maintaining privacy while adapting to new fraudulent trends. In this paper, we provide a unique approach to tackling those challenges by integrating VAE-QLSTM with Federated Learning (FL) in a semi-decentralized architecture, maintaining privacy alongside adapting to emerging malicious behaviors. The suggested architecture builds on the adeptness of VAE-QLSTM to capture meaningful representations of transactions, serving in abnormality detection. On the other hand, QLSTM combines quantum computational capability with temporal sequence modeling, seeking to give a rapid and scalable method for real-time malignancy detection. The designed approach was set up through TensorFlow Federated on two real-world datasets—notably IEEE-CIS and European cardholders—outperforming current strategies in terms of accuracy and sensitivity, achieving 94.5% and 91.3%, respectively. This proves the potential of merging VAE-QLSTM with FL to address fraud detection difficulties, ensuring privacy and scalability in advanced banking networks. Full article
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17 pages, 1566 KiB  
Article
A Method Inspired by One-Dimensional Discrete-Time Quantum Walks for Influential Node Identification
by Wen Liang, Yifan Wang, Qiwei Liu and Wenbo Zhang
Entropy 2025, 27(6), 634; https://doi.org/10.3390/e27060634 - 14 Jun 2025
Viewed by 289
Abstract
Identifying influential nodes in complex networks is essential for a wide range of applications, from social network analysis to enhancing infrastructure resilience. While quantum walk-based methods offer potential advantages, existing approaches face challenges in dimensionality, computational efficiency, and accuracy. To address these limitations, [...] Read more.
Identifying influential nodes in complex networks is essential for a wide range of applications, from social network analysis to enhancing infrastructure resilience. While quantum walk-based methods offer potential advantages, existing approaches face challenges in dimensionality, computational efficiency, and accuracy. To address these limitations, this study proposes a novel method inspired by the one-dimensional discrete-time quantum walk (IOQW). This design enables the development of a simplified shift operator that leverages both self-loops and the network’s structural connectivity. Furthermore, degree centrality and path-based features are integrated into the coin operator, enhancing the accuracy and scalability of the IOQW framework. Comparative evaluations against state-of-the-art quantum and classical methods demonstrate that IOQW excels in capturing both local and global topological properties while maintaining a low computational complexity of O(Nk), where k denotes the average degree. These advancements establish IOQW as a powerful and practical tool for influential node identification in complex networks, bridging quantum-inspired techniques with real-world network science applications. Full article
(This article belongs to the Special Issue Quantum Information and Quantum Computation)
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13 pages, 563 KiB  
Article
Defending Against the Homodyne Detector-Blinding Attack on Continuous-Variable Quantum Key Distribution Using an Adjustable Optical Attenuator
by Yijun Wang, Yanyan Li, Wenqi Jiang and Ying Guo
Entropy 2025, 27(6), 631; https://doi.org/10.3390/e27060631 - 13 Jun 2025
Viewed by 364
Abstract
A homodyne detector, which is also a common element in current telecommunication, is a core component of continuous-variable quantum key distribution (CV-QKD) since it is considered the simplest setup for the distinguishing of coherent states with minimum error. However, the theoretical security of [...] Read more.
A homodyne detector, which is also a common element in current telecommunication, is a core component of continuous-variable quantum key distribution (CV-QKD) since it is considered the simplest setup for the distinguishing of coherent states with minimum error. However, the theoretical security of CV-QKD is based on the assumption that the responses of the homodyne detector are always linear with respect to the input, which is impossible in practice. In the real world, a homodyne detector has a finite linear domain, so the linearity assumption is broken when the input is too large. Regarding this security vulnerability, the eavesdropper Eve can perform the so-called homodyne detector-blinding attack by saturating the homodyne detector and then stealing key information without being detected by the legitimate users. In this paper, we propose a countermeasure for the homodyne detector-blinding attack by using an adjustable optical attenuator with a feedback structure. Specifically, we estimate the suitable attenuation value in the data processing of CV-QKD and feed it back to the adjustable optical attenuator before the detector in real time. Numerical simulation shows that the proposed countermeasure can effectively defend against homodyne detector-blinding attacks and ensure the security of the Gaussian-modulated coherent state protocol with finite-size effect. Full article
(This article belongs to the Special Issue Recent Advances in Continuous-Variable Quantum Key Distribution)
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16 pages, 770 KiB  
Article
The Quantum Measurement Problem
by Erik B. Karlsson
Quantum Rep. 2025, 7(2), 28; https://doi.org/10.3390/quantum7020028 - 13 Jun 2025
Viewed by 1370
Abstract
Measurements play a specific role in quantum mechanics; only measurements allow us to catch a glimpse of the eluding physical reality. However, there is something deeply unsatisfactory with this specificity—a measurement is itself a physical process! Several varying modes of coping with this [...] Read more.
Measurements play a specific role in quantum mechanics; only measurements allow us to catch a glimpse of the eluding physical reality. However, there is something deeply unsatisfactory with this specificity—a measurement is itself a physical process! Several varying modes of coping with this dilemma have been proposed and this article tries to describe how a now-century-long discussion has led to new insights about the transition from the quantum to the classical world. Starting from the pioneer’s view of the quantum measurement problem, it follows the development of formalisms, the interest from philosophers for its new aspects on reality and how different interpretations of quantum mechanics have tried to support our classically working brains in understanding quantum phenomena. Decoherence is a main topic and its role in measurement processes exemplified. The question of whether the quantum measurement problem is now solved is left open for the readers’ own judgment. Full article
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
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35 pages, 382 KiB  
Article
Generalized Pauli Fibonacci Polynomial Quaternions
by Bahadır Yılmaz, Nazmiye Gönül Bilgin and Yüksel Soykan
Axioms 2025, 14(6), 449; https://doi.org/10.3390/axioms14060449 - 6 Jun 2025
Viewed by 396
Abstract
Since Hamilton proposed quaternions as a system of numbers that does not satisfy the ordinary commutative rule of multiplication, quaternion algebras have played an important role in many mathematical and physical studies. This paper introduces the generalized notion of Pauli Fibonacci polynomial quaternions, [...] Read more.
Since Hamilton proposed quaternions as a system of numbers that does not satisfy the ordinary commutative rule of multiplication, quaternion algebras have played an important role in many mathematical and physical studies. This paper introduces the generalized notion of Pauli Fibonacci polynomial quaternions, a definition that incorporates the advantages of the Fibonacci number system augmented by the Pauli matrix structure. With the concept presented in the study, it aims to provide material that can be used in a more in-depth understanding of the principles of coding theory and quantum physics, which contribute to the confidentiality needed by the digital world, with the help of quaternions. In this study, an approach has been developed by integrating the advantageous and consistent structure of quaternions used to solve the problem of system lock-up and unresponsiveness during rotational movements in robot programming, the mathematically compact and functional form of Pauli matrices, and a generalized version of the Fibonacci sequence, which is an application of aesthetic patterns in nature. Full article
(This article belongs to the Special Issue Advances in Applied Algebra and Related Topics)
13 pages, 2141 KiB  
Article
Post-Quantum KEMs for IoT: A Study of Kyber and NTRU
by M. Awais Ehsan, Walaa Alayed, Amad Ur Rehman, Waqar ul Hassan and Ahmed Zeeshan
Symmetry 2025, 17(6), 881; https://doi.org/10.3390/sym17060881 - 5 Jun 2025
Viewed by 989
Abstract
Current improvements in quantum computing present a substantial challenge to classical cryptographic systems, which typically rely on problems that can be solved in polynomial time using quantum algorithms. Consequently, post-quantum cryptography (PQC) has emerged as a promising solution to emerging quantum-based cryptographic challenges. [...] Read more.
Current improvements in quantum computing present a substantial challenge to classical cryptographic systems, which typically rely on problems that can be solved in polynomial time using quantum algorithms. Consequently, post-quantum cryptography (PQC) has emerged as a promising solution to emerging quantum-based cryptographic challenges. The greatest threat is public-key cryptosystems, which are primarily responsible for key exchanges. In PQC, key encapsulation mechanisms (KEMs) are crucial for securing key exchange protocols, particularly in Internet communication, virtual private networks (VPNs), and secure messaging applications. CRYSTALS-Kyber and NTRU are two well-known PQC KEMs offering robust security in the quantum world. However, even when quantum computers are functional, they are not easily accessible. IoT devices will not be able to utilize them directly, so there will still be a requirement to protect IoT devices from quantum attacks. Concerns such as limited computational power, energy efficiency, and memory constraints in devices such as those used in IoTs, embedded systems, and smart cards limit the use of these techniques in constrained environments. These concerns always arise there. To address this issue, this study conducts a broad comparative analysis of Kyber and NTRU, with special focus on their security, performance, and implementation efficiency in such environments (IOT/constrained environments). In addition, a case study was conducted by applying KEMs to a low-power embedded device to analyze their performance in real-world scenarios. These results offer an important comparison for cyber security engineers and cryptographers who are involved in integrating post-quantum cryptography into resource-constrained devices. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics, 2nd Edition)
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