Q Learning with Quantum Neural Networks

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.

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.

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.

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.

In recent years, near-term noisy intermediate scale quantum (NISQ) computing devices have become available. One of the most promising application areas to leverage such NISQ quantum computer prototypes is quantum machine learning. While quantum neural networks are widely studied for supervised learning, quantum reinforcement learning is still just an emerging field of this area. To solve a classical continuous control problem, we used continuous-variable quantum machine learning. We introduce proximal policy optimization for photonic variational quantum agents and also study the effect of the data re-uploading. We present performance assessment via empirical study using Strawberry Fields, a photonic simulator Fock backend and a hybrid training framework connected to an OpenAI Gym environment and TensorFlow. For the restricted CartPole problem, the two variations of the photonic policy learning achieve comparable performance levels and a faster convergence than the baseline classical neural network of same number of trainable parameters.

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.

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.

The astounding acceleration in Artificial Intelligence and Quantum Computing advances naturally gives rise to a line of research, which unrolls the potential advantages of quantum computing on classical Machine Learning tasks, known as Quantum Machine Learning or Quantum Machine Intelligence. The typical objectives are either (1) exploring the potential quantum advantages on classical learning tasks or (2) levering well-established classical ML algorithms to tackle quantum-related problems on Noisy Intermediate-Scale Quantum (NISQ) devices. Along the second research direction, we study Quantum Neural Networks (QNNs) to accomplish the purpose of Bayesian learning. By observing a wide range of studies on QNNs, in which the sole training method is based on frequentist training, we find that Bayesian learning benefits QNNs from two aspects. First, Bayesian-trained models enjoy a high level of generalization due to the prior and posterior distribution usage compared to frequentist training, which will be justified by this paper’s theoretical study of model capacity. Second, Bayesian Inference offers epistemic uncertainty estimation, which merits the decision-making process. It is worth mentioning that frequentist-trained QNNs generally lack this desirable property. Under the Bayesian training procedure, our derived models can be considered a new class of QNNs (called BayesianQNNs) which possesses both desirable properties of Bayesian Inference while maintaining comparable predictive performance as frequentist counterparts. The proposed Bayesian Quantum Neural Networks is justified by empirical evidence from numerical experiments.

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.

Variational quantum machine learning algorithms have become the focus of recent research on how to utilize near-term quantum devices for machine learning tasks. They are considered suitable for this as the circuits that are run can be tailored to the device, and a big part of the computation is delegated to the classical optimizer. It has also been hypothesized that they may be more robust to hardware noise than conventional algorithms due to their hybrid nature. However, the effect of training quantum machine learning models under the influence of hardware-induced noise has not yet been extensively studied. In this work, we address this question for a specific type of learning, namely variational reinforcement learning, by studying its performance in the presence of various noise sources: shot noise, coherent and incoherent errors. We analytically and empirically investigate how the presence of noise during training and evaluation of variational quantum reinforcement learning algorithms affect the performance of the agents and robustness of the learned policies. Furthermore, we provide a method to reduce the number of measurements required to train Q-learning agents, using the inherent structure of the algorithm.

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

Introduction Reinforcement learning formalizes the concept of learning from interactions.1 Broadly, reinforcement learning focuses on a setting in which an agent (decision maker) sequentially interacts with an environment that is partially unknown to them. At each stage, the agent takes an action and receives a reward. The objective of the agent is to maximize rewards accumulated in the long run. There are many situations in health care where decisions are made sequentially for which reinforcement learning approaches could prove useful for decision making. Throughout this article, we consider treatment prescription as an archetypical example to connect reinforcement learning concepts to a health care setting. In this setting, the care provider, the prescribed treatment, and the patients can be viewed as the agent, the action, and the environment, respectively, as depicted in Figure 1.Figure 1: Sequential treatment of AKI or CKD complications modeled as a reinforcement learning problem.Background In this section, with the objective of making reinforcement learning literature more accessible to a clinical audience, we briefly introduce related fundamental concepts and approaches. We refer the interested reader to Sutton and Barto1 for a comprehensive introduction to reinforcement learning. Markov Decision Processes Markov decision processes (MDPs) are a formalism of the sequential decision-making problem that has been central to the theoretical and practical advancements of reinforcement learning. In each stage of an MDP, the agent observes the state of the environment and takes an action, which, in turn, results in a change of the state. This change of state is assumed to be probabilistic with the next state being determined only by the preceding state, the chosen action, and the transition probability. The agent also receives a reward that is a function of the taken action, the preceding state, and the subsequent state. In an MDP, the objective of the agent is to maximize the return defined as the reward accumulated over a time horizon. In some applications, it is common to consider the horizon to be infinite, in which case the future rewards are discounted by a factor smaller than one. The selection of action by the agent on the basis of the observed state is known as the policy. More formally, a policy is a probabilistic mapping from states to each possible action. Because the policy and the reward are a function of the state, it is critical to estimate the utility of being in a certain state. More specifically, the value function is defined as the expected return starting from a given state under the chosen policy. Under this formalism, the objective of the agent is to find the optimal policy that maximizes the value function for all states. Reinforcement Learning Methods Action-value methods are a class of reinforcement learning methods in which the actions are chosen on the basis of the estimation of their long-term value. A prominent example of an action-value method is Q-learning in which the agent iteratively takes actions with the highest estimated values and updates the action-state value function on the basis of new observations. Policy gradient methods are another class of reinforcement learning methods that seek to optimize the policy directly instead of choosing actions on the basis of their respective estimated value. Such methods could be advantageous in health care applications that entail a large number of possible actions, e.g., when recommending a wide range of drug dosages or treatment options. Clinical Applications Reinforcement learning frameworks and methods are broadly applicable to clinical settings in which decisions are made sequentially. A prominent clinical application of reinforcement learning is for treatment recommendation, which has been studied across a variety of diseases and treatments including radiation and chemotherapy for cancer, brain stimulation for epilepsy, and treatment strategies for sepsis.2–5 In such treatment recommendation settings, a policy is commonly known as a dynamic treatment regime. There are various other clinical applications of reinforcement learning including diagnosis, medical imaging, and decision support tools (see refs. 2–5 and the references therein). Reinforcement Learning in Nephrology Although there have been recent applications of machine learning in nephrology,6,7 to the best of the authors' knowledge, the application of reinforcement learning to nephrology has been primarily limited to optimizing the erythropoietin dosage in hemodialysis patients.8,9 However, there are other settings where reinforcement learning has the potential to improve patient care in nephrology. For example, reinforcement learning methods can be adopted in the treatment of the complications of AKI or CKD (Figure 1). In this problem, the state models the conditions of the patient (e.g., vital signs, laboratory test results including urine and blood tests, and urine output measurements). The action refers to the treatment options (e.g., the dosage of medications such as sodium polystyrene sulfonate, and hemodialysis). The reward models the improvement in patient conditions. Similarly, reinforcement learning can help automate and optimize the dosage of immunosuppressive drugs in kidney transplants. Challenges and Opportunities Despite the success of reinforcement learning in several simplified clinical settings, their large-scale application to patient care faces several open challenges. The complexity of human biology complicates modeling clinical decision making as a reinforcement learning problem. The state space in such settings is often enormous, which could make a purely computational approach infeasible. Moreover, modeling all potential objectives a priori as a reward function may not be feasible. To overcome these challenges and realize the potential of reinforcement learning, clinical insight can play a pivotal role. More specifically, restricting the state space to only include highly relevant clinical variables could greatly reduce the computational complexity. Furthermore, using inverse reinforcement learning,2 relevant reward functions can be learned from retrospective studies assuming the optimality of clinical decisions. Another critical challenge is addressing moral and ethical concerns. It is imperative to ensure that reinforcement learning methods do not cause harm to the patient. To this end, there exists a need for a thorough validation of such methods before their use in patient care. Hence, there is a need to go beyond retrospective studies that have been used for the proof of concept of most existing reinforcement learning methods in health care applications.2,3 The lessons learned from the success of reinforcement learning in other application areas (e.g., self-driving cars) can help navigate the path to realizing its potential in health care. Accessible open-source simulation environments that enable researchers to compare various approaches are essential to the field of reinforcement learning. OpenAI Gym is currently the leading toolkit containing a wide range of simulated environments, e.g., surgical robotics.10 The development of high-quality and reliable simulation environments for nephrology and other health care applications can facilitate the development and validation of reinforcement learning methods beyond limited retrospective studies. The adoption of methods validated in such simulation environments in actual clinical settings will require clinicians' oversight. Similar to how self-driving cars require a human driver to ensure collision avoidance, clinicians' oversight is critical to ensure the safety of the patients, especially in the early stages of the adoption of reinforcement learning methods. The data from clinicians' decisions (e.g., overruling the automated treatment recommendation) can be used to improve the reliability of autonomous systems over time and reduce the burden of clinicians' oversight.

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.

Partially observable Markov decision processes (POMDPs) are widely used for planning under uncertainty. In many applications, the huge size of the POMDP state space makes straightforward optimization of plans (policies) computationally intractable. To solve this, we introduce an efficient POMDP planning algorithm. Many current methods store the policy partly through a set of “value vectors” which is updated at each iteration by planning one step further; the size of such vectors follows the size of the state space, making computation intractable for large POMDPs. We store the policy as a graph only, which allows tractable approximations in each policy update step: for a state space described by several variables, we approximate beliefs over future states with factorized forms, minimizing Kullback-Leibler divergence to the non-factorized distributions. Our other speedup approximations include bounding potential rewards. We demonstrate the advantage of our method in several reinforcement learning problems, compared to four previous methods.

Robots had a great impact on the manufacturing industry ever since the early seventies when companies such as KUKA and ABB started deploying their first industrial robots. These robots merely performed very specific tasks in specific ways within well-defined environments. Still, they proved to be very useful as they could exceed human performance at these tasks. However, in order to enable robots to enter our daily life, they need to become more versatile and need to operate in much less structured environments. This thesis is partly devoted to stretching these limitations by means of learning, namely imitation learning (IL) and inverse reinforcement learning (IRL). Reinforcement learning (RL) is a powerful approach to enable robots to solve a task in an unknown environment. The practitioner describes a desired behavior by specifying a reward function and the robot autonomously interacts with the environment in order to find a control policy that generates high accumulated reward. However, RL is not suitable for teaching new tasks by non-experts because specifying appropriate reward functions can be difficult. Demonstrating the desired behavior is often easier for non-experts. Imitation learning can be used in order to enable the robot to reproduce the demonstrations. However, without explicitly inferring and modeling the intentions of the demonstrations, it can become difficult to solve the task for unseen situations. Inverse reinforcement learning (IRL) therefore aims to infer a reward function from the demonstrations, such that optimizing this reward function yields the desired behavior even for different situations. This thesis introduces a unifying approach to solve the inverse reinforcement learning problem in the same way as the reinforcement learning problem. This is achieved by framing both problems as information projection problems, i.e., we strive to minimize the relative entropy between a probabilistic model of the robot behavior and a given desired distribution. Furthermore, a trust region on the robot behavior is used to stabilize the optimization. For inverse reinforcement learning, the desired distribution is implicitly given by the expert demonstrations. The resulting optimization can be efficiently solved using state-of-the-art reinforcement learning methods. For reinforcement learning, the log-likelihood of the desired distribution is given by the reward function. The resulting optimization problem corresponds to a standard reinforcement learning formulation, except for an additional objective of maximizing the entropy of the robot behavior. This entropy objective adds little overhead to the optimization, but can lead to better exploration and more diversified policies. Trust-region I-projections are not only useful for training robots, but can also be applied to other machine learning problems. I-projections are typically used for variational inference, in order to approximate an intractable distribution by a simpler model. However, the resulting optimization problems are usually optimized based on stochastic gradient descent which often suffers from high variance in the gradient estimates. As trust-region I-projections where shown to be effective for reinforcement learning and inverse reinforcement learning, this thesis also explores their use for variational inference. More specifically, trust-region I-projections are investigated for the problem of approximating an intractable distribution by a Gaussian mixture model (GMM) with an adaptive number of components. GMMs are highly desirable for variational inference because they can yield arbitrary accurate approximations while inference from GMMs is still relatively cheap. In order to make learning the GMM feasible, we derive a lower bound that enables us to decompose the objective function. The optimization can then be performed by iteratively updating individual components using a technique from reinforcement learning. The resulting method is capable of learning approximations of significantly higher quality than existing variational inference methods. Due to the similarity of the underlying optimization problems, the insights gained from our variational inference method are also useful for IL and IRL. Namely, a similar lower bound can be applied also for the I-projection formulation of imitation learning. However, whereas for variational inference the lower bound serves to decompose the objective function, for imitation learning it allows us to provide a reward signal to the robot that does not depend on its behavior. Compared to reward functions that are relative to the current behavior of the robot---which are typical for popular adversarial methods---behavior-independent reward functions have the advantages that we can show convergence even for greedy optimization. Furthermore, behavior-independent reward functions solve the inverse reinforcement learning problem, thereby closing the gap between imitation learning and IRL. However, algorithms derived from our non-adversarial formulation are actually very similar to existing AIL methods, and we can even show that adversarial inverse reinforcement learning (AIRL) is indeed an instance of our formulation. AIRL was derived from an adversarial formulation, and we point out several problems of that derivation. In contrast, we show that AIRL can be straightforwardly derived from out non-adversarial formulation. Furthermore, we demonstrate that the non-adversarial formulation can be also used to derive novel algorithms by presenting a non-adversarial method for offline imitation learning.