Bayesian Quantum Neural Networks

Quantum Machine Learning (QML) is an emerging field at the intersection of quantum computing and machine learning, aiming to enhance classical machine learning methods by leveraging quantum mechanics principles such as entanglement and superposition. However, skepticism persists regarding the practical advantages of QML, mainly due to the current limitations of noisy intermediate-scale quantum (NISQ) devices. This study addresses these concerns by extensively assessing Quantum Neural Networks (QNNs)-quantum-inspired counterparts of Artificial Neural Networks (ANNs), demonstrating their effectiveness compared to classical methods. We systematically construct and evaluate twelve distinct QNN configurations, utilizing two unique quantum feature maps combined with six different entanglement strategies for ansatz design. Experiments conducted on a wind energy dataset reveal that QNNs employing the $\mathbf{Z}$ feature map achieve up to $93 \%$ prediction accuracy when forecasting wind power output using only four input parameters. Our findings show that QNNs outperform classical methods in predictive tasks, underscoring the potential of QML in real-world applications.

Recent advances in quantum computing and machine learning have brought about a promising intersection of these two fields, leading to the emergence of quantum machine learning (QML). However, the integration of quantum computing and machine learning poses several challenges. One of the prominent challenges lies in the presence of barren plateaus (BP) in QML algorithms, particularly in quantum neural networks (QNNs). Recent studies have successfully identified the fundamental causes underlying the existence of BP in QNNs. This paper presents a framework designed to explore the interplay of multiple factors contributing to the BP problem in quantum neural networks (QNNs), which poses a critical challenge for the practical applications of QML. We focus on the combined influence of data encoding, qubit entanglement, and ansatz expressibility in hybrid quantum neural networks (HQNNs) for multi-class classification tasks. Our framework aims to empirically analyze the joint impact of these factors on the training landscape of HQNNs. Our results show that the occurrence of the BP problem in HQNNs is contingent upon the expressibility of the underlying ansatz and the type of the adopted data encoding technique. Additionally, we observe that qubit entanglement also plays a role in exacerbating the BP problem. Leveraging various evaluation metrics for classification tasks, we systematically evaluate the performance of HQNNs and provide recommendations tailored to different constraint scenarios. Our findings emphasize the significance of our framework in addressing the practical success of QNNs.

In this work, we studied the use of Quantum Machine Learning (QML) algorithms for binary classification and compared their performance with classical Machine Learning (ML) methods. QML merges principles of Quantum Computing (QC) and ML, offering improved efficiency and potential quantum advantage in data-driven tasks and when solving complex problems. In binary classification, where the goal is to assign data to one of two categories, QML uses quantum algorithms to process large datasets efficiently. Quantum algorithms like Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN) exploit quantum parallelism and entanglement to enhance performance over classical methods. This study focuses on two common QML algorithms, Quantum Support Vector Classifier (QSVC) and QNN. We used the Qiskit software and conducted the experiments with three different datasets. Data preprocessing included dimensionality reduction using Principal Component Analysis (PCA) and standardization using scalers. The results showed that quantum algorithms demonstrated competitive performance against their classical counterparts in terms of accuracy, while QSVC performed better than QNN. These findings suggest that QML holds potential for improving computational efficiency in binary classification tasks. This opens the way for more efficient and scalable solutions in complex classification challenges and shows the complementary role of quantum computing.

Quantum computing is emerging as a powerful computational paradigm capable of solving infeasible problems for classical computers. This review explores the intersection of quantum computing and artificial intelligence (AI), focusing on how quantum algorithms can enhance AI applications. The purpose of this review is to provide a comprehensive analysis of current advancements in quantum machine learning (QML), quantum optimization, and quantum neural networks, highlighting their implications for data processing, cryptography, and decision-making systems. The scope of the literature includes peer-reviewed articles, conference papers, and technical reports from 2020 to 2025, focusing on quantum algorithms, applications in AI, and hardware limitations. Key findings indicate that quantum computing can significantly accelerate data processing tasks, optimize complex problem-solving techniques, and improve the efficiency of AI models. However, challenges such as quantum noise, error correction, and hardware scalability remain substantial barriers to widespread adoption. This review concludes with discussing future research directions, including hybrid quantum-classical systems and advanced quantum error correction methods. This study serves as a foundational reference for researchers and practitioners aiming to leverage quantum computing for AI-driven applications. 3. Keywords Quantum Computing, Artificial Intelligence, Quantum Machine Learning, Quantum Algorithms, Data Processing, Optimization, Quantum Neural Networks

With the rapid advancement of quantum computing, research on quantum machine learning (QML) algorithms has grown significantly. Among these, the Quantum Neural Network (QNN) stands out as one of the promising algorithms that integrates the principles of quantum computing with artificial neural networks to process data. Inspired by applications of QNN across fields, we investigate their use in software testing for the Cancer Registry of Norway (CRN), part of the Norwegian Institute of Public Health (NIPH), responsible for cancer statistics among the Norwegian population. CRN develops a complex socio-technical software system, Cancer Registration Support System ( \(\mathtt{CaReSS}\) ), interacting with many entities (e.g., hospitals, medical laboratories, and other patient registries) to achieve its task. For cost-effective testing of \(\mathtt{CaReSS}\) , CRN has employed \(\mathtt{EvoMaster}\) , an AI-based REST API testing tool combined with an integrated classical machine learning model \(\mathtt{EvoClass}\) . Within this context, we propose \(\mathtt{EvoQlass}\) to investigate the feasibility of using, inside \(\mathtt{EvoMaster}\) , a QNN classifier, instead of the existing classical machine learning model. Results indicate that \(\mathtt{EvoQlass}\) can achieve performance comparable to that of \(\mathtt{EvoClass}\) . We further explore the effects of various QNN configurations on performance and offer recommendations for optimal QNN settings for future QNN developers.

As the limits of classical machine learning (ML) become increasingly evident—especially in terms of computational scalability and data processing—quantum computing emerges as a promising frontier capable of addressing these challenges. Quantum Machine Learning (QML) represents the intersection of quantum computing and traditional ML, aiming to leverage quantum phenomena such as superposition, entanglement, and quantum parallelism to enhance learning capabilities, accelerate training, and solve complex problems that are intractable for classical algorithms. This paper provides a comprehensive overview of the evolving field of QML, beginning with the theoretical foundations of quantum computing and its synergy with classical machine learning principles. We explore key QML algorithms, including quantum support vector machines (QSVM), variational quantum classifiers (VQC), quantum neural networks (QNN), and hybrid quantum-classical approaches that exemplify the practical integration of both paradigms. We further examine real-world applications of QML across domains such as drug discovery, finance, climate modeling, and optimization, where quantum enhancements have begun to show early but promising results. Despite its theoretical potential, QML faces substantial limitations, including quantum hardware instability, limited qubit scalability, noise sensitivity, and unresolved challenges in quantum data encoding and interpretability. In synthesizing recent advancements and persistent obstacles, this paper highlights the importance of continued interdisciplinary research, algorithmic refinement, and hardware evolution. We also outline future directions that could lead QML from experimental promise to practical utility, including developments in quantum error correction, benchmarking standards, and application-specific quantum architectures

The increasing convergence of quantum computing (QC) and advanced robotic control is giving rise to a new class of intelligent automation systems. Utilizing quantum-inspired computational principles, contemporary robotic platforms demonstrate greater optimization efficiency, superior perceptual processing, and improved decision-making performance. This survey outlines the principal quantum-oriented control methodologies utilized in robotics, with particular emphasis on approaches that incorporate Quantum Neural Networks (QNN), Quantum Machine Learning (QML), and Quantum-behaved Particle Swarm Optimization (QPSO). The investigation systematically reviews recent advances in quantum-assisted adaptive control, trajectory planning, and optimization frameworks, spotlighting their contributions to improved robustness, precision, and energy efficiency. By analyzing research in quantum reinforcement learning, distributed Noisy Intermediate-Scale Quantum (NISQ) computing, and hybrid quantum-classical approaches, this review clarifies how quantum principles are transforming both theoretical and practical aspects of robotic control. Likewise, several real-world implementations ranging from industrial manipulators to autonomous and cognitive robotic systems demonstrate the growing feasibility of quantum-enhanced decision-making. The review concludes that while remarkable progress has been made in quantum-inspired control for robotics, most existing studies remain constrained to simulations with restricted experimental validation on physical platforms. Addressing this gap will be essential in future research to transition from theoretical and simulated models toward hardware-level implementations, enabling the realization of scalable, fault-tolerant quantum control architectures.

Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks—including state-of-the-art models, such as Transformers—in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality—informally, a quantitative notion of semantic ambiguity—is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.

Advances in Quantum Machine Learning and Deep Learning for Image Classification: A Survey

The rapid evolution of cyber threats has rendered conventional security approaches inadequate for managing increasingly sophisticated risks. This study introduces a Quantum Machine Learning Cybersecurity Framework that leverages quantum computing and machine learning to enhance cybersecurity across multiple dimensions. The research employs a structured methodology, beginning with the integration of Quantum Key Distribution (QKD) for secure key exchange and progressing through the deployment of Quantum Neural Networks (QNN) and Quantum Support Vector Machines (QSVM) for anomaly detection and adversarial threat management. The framework also incorporates Quantum Reinforcement Learning (QRL) for autonomous incident response, a Quantum Authentication module for securing identity verification using biometric and behavioral data, and a Policy Compliance Interface powered by Quantum Compliance Analyzers for regulatory adherence. Experimental results demonstrated substantial improvements in cybersecurity metrics, including a 96% accuracy in threat detection, a 28% reduction in incident response time, and a 96% success rate in compliance simulations. These findings underscore the framework's capacity to offer adaptive, scalable, and efficient cybersecurity solutions tailored to modern challenges. This study provides a significant step toward integrating quantum technologies into practical cybersecurity applications, paving the way for future innovations in intelligent, secure, and adaptable defense systems.

Quantum Machine Learning (QML) is an emerging interdisciplinary field that integrates quantum computing with classical machine learning techniques to enhance computational efficiency and solve complex problems beyond the capabilities of classical systems. This paper explores fundamental QML algorithms, including quantum-enhanced data processing, quantum neural networks, and quantum support vector machines. We discuss how quantum speedup can be achieved through quantum parallelism and entanglement, leading to improvements in optimization and data classification tasks. Additionally, we highlight applications of QML in areas such as drug discovery, financial modeling, and cryptography. While current quantum hardware imposes limitations, ongoing advancements in quantum algorithms and error correction techniques suggest a promising future for QML. We conclude with a discussion on the challenges and future directions in the field, emphasizing the need for hybrid quantum-classical approaches and scalable quantum hardware.

This PhD thesis combines two of the most exciting research areas of the last decades: quantum computing and machine learning. We introduce dissipative quantum neural networks (DQNNs), which are designed for fully quantum learning tasks, are capable of universal quantum computation and have low memory requirements while training. These networks are optimised with training data pairs in form of input and desired output states and therefore can be used for characterising unknown or untrusted quantum devices. We not only demonstrate the generalisation behaviour of DQNNs using classical simulations, but also implement them successfully on actual quantum computers. To understand the ultimate limits for such quantum machine learning methods, we discuss the quantum no free lunch theorem, which describes a bound on the probability that a quantum device, which can be modelled as a unitary process and is optimised with quantum examples, gives an incorrect output for a random input. Moreover we expand the area of applications of DQNNs in two directions. In the first case, we include additional information beyond just the training data pairs: since quantum devices are always structured, the resulting data is always structured as well. We modify the DQNN's training algorithm such that knowledge about the graph-structure of the training data pairs is included in the training process and show that this can lead to better generalisation behaviour. Both the original DQNN and the DQNN including graph structure are trained with data pairs in order to characterise an underlying relation. However, in the second extension of the algorithm we aim to learn characteristics of a set of quantum states in order to extend it to quantum states which have similar properties. Therefore we build a generative adversarial model where two DQNNs, called the generator and discriminator, are trained in a competitive way.

Emotion Recognition (ER) is an important capability that is increasingly being used to enhance the user experience in various fields such as, Human-Computer interaction, Cognitive Neuroscience, Neurofeedback, Robotics, Artificial Intelligence, Augmented Reality, Virtual Reality, Mental Health, etc. Emotions are generated in the limbic system, a set of brain structures that are involved in emotional processing, memory, and motivation. ER from electroencephalography (EEG) signals has gained attention from researchers in recent years as it provides a more accurate and non-intrusive way of understanding human emotions. This research paper presents a comprehensive study of the use of Quantum Support Vector Machines (QSVMs) and Quantum Neural Networks (QNNs) for ER using EEG signals. The aim of this study is to investigate the potential of quantum machine learning algorithms in improving the performance of ER tasks compared to classical Machine Learning (ML) algorithms. The model was simulated using IBM Qiskit due to the limited resources of quantum computers. Intriguingly, the experimental results contradict the speed-up claims of Quantum Computing (QC) by exhibiting longer computation times and lesser accuracy when compared to traditional methods. SVM and NN yield 68.5% and 69.2% accuracy while the quantum version gives 63% and 65.2% accuracy on the benchmark dataset SEED. This research provides evidence that Quantum Machine Learning (QML) algorithms need to be improved for ER from EEG signals and provide a reliable and non-intrusive way of understanding human emotions.

Quantum Machine Learning (QML) is emerging as a transformative technology in cybersecurity, particularly in anomaly detection for cyber security audits. Traditional machine learning models are effective but face scalability and efficiency limitations as cyber threats grow more sophisticated. QML, leveraging quantum computing’s ability to process and analyze large datasets in parallel, offers potential breakthroughs in identifying anomalous patterns that could signify cyber threats such as data breaches, insider threats, or unauthorized access. Content Analysis Research Methodology used in this research work. This paper explores the integration of QML into anomaly detection systems for cyber security audits, where detecting deviations from normal behavior is crucial. Quantum algorithms, particularly those based on Quantum Support Vector Machines (QSVM), Quantum Neural Networks (QNN), and Quantum Principal Component Analysis (QPCA) can enhance the detection of subtle anomalies that classical algorithms may overlook due to noise or the complex, high-dimensional nature of cyber data. The inherent properties of quantum computing, such as superposition and entanglement, allow for more efficient feature selection and optimization, potentially leading to faster and more accurate anomaly detection. The impact of implementing QML in cyber security audits is profound. First, it enhances detection capabilities by identifying anomalies with greater precision, reducing false positives, and improving response times to cyber incidents. Second, quantum algorithms’ ability to manage exponentially large datasets makes them ideal for environments with extensive data logs, such as enterprise networks and cloud infrastructures. Third, as cyber threats become increasingly adaptive and stealthy, QML offers a dynamic solution that evolves alongside these threats by continuously learning from new patterns of attack. However, practical challenges remain, including the need for quantum hardware advancements, the development of hybrid quantum-classical models, and ensuring the interpretability of quantum models in audit scenarios. Despite these challenges, early research and experimental implementations demonstrate the potential of QML to revolutionize anomaly detection in cybersecurity audits. This paper concludes that while QML is still in its early stages, its application to anomaly detection holds promise for significantly enhancing the effectiveness of cyber security audits. The impact of this technology, when fully realized, could redefine how organizations protect their networks and data from ever-evolving cyber threats, making QML a critical area for future research and development in cybersecurity.

This review paper examines state-of-the-art algorithms and techniques in quantum machine learning (QML) with potential applications in finance. We discuss QML techniques in supervised learning tasks, such as quantum variational classifiers, quantum Kernel estimation, and quantum neural networks, along with quantum generative AI techniques like quantum transformers and quantum graph neural networks. The financial applications considered include risk management, credit scoring, fraud detection, and stock price prediction. We also provide an overview of the challenges, potential, and limitations of QML, both in these specific areas and more broadly across the field. We hope that this can serve as a quick guide for data scientists, professionals in the financial sector, and enthusiasts in this area to understand why quantum computing and QML in particular could be interesting to explore in their field of expertise.