A normalizing flow computes a bijective mapping from an arbitrary distribution to a predefined (e.g., normal) distribution. Such a flow can be used to address different tasks, e.g., anomaly detection, once such a mapping has been learned. In this work we introduce normalizing flows for quantum architectures, describe how to model and optimize such a flow, and evaluate our method on example datasets. Our proposed models show competitive performance for anomaly detection compared to classical methods, especially those ones where there are already quantum inspired algorithms available. In the experiments we compare our performace to isolation forests (IF), the local outlier factor (LOF), or single-class SVMs.
A normalizing flow computes a bijective mapping from an arbitrary distribution to a predefined (e.g., normal) distribution. Such a flow can be used to address different tasks, e.g., anomaly detection, once such a mapping has been learned. In this work we introduce normalizing flows for quantum architectures, describe how to model and optimize such a flow, and evaluate our method on example datasets. Our proposed models show competitive performance for anomaly detection compared to classical methods, especially those ones where there are already quantum inspired algorithms available. In the experiments we compare our performace to isolation forests (IF), the local outlier factor (LOF), or single-class SVMs.
Anomaly detection plays a crucial role in identifying rare and critical events, anomalies, or outliers that are not part of the normal data distribution. With the large volume of modern data and the widespread use of sensors and IoT devices, datasets have evolved into high-dimensional structures, posing significant challenges to anomaly detection tasks. In this work, we investigate to employ a hybrid quantum-classical algorithm to help handle such challenges. It is mainly based on Local Outlier Factor (LOF) algorithm to detect anomalies. However, we enhance distance estimation and k-nearest neighbor search via quantum algorithms. The proof-of-principle numerical results demonstrate the performance of the proposed method is competitive to previous algorithm.
The increasingly complex cybersecurity landscape requires more advanced network anomaly detection systems. Although, classical machine learning models are known to be effective, they reach computational bottlenecks when processing high-dimensional data. This study investigates the potential of Quantum Machine Learning (QML) for network traffic anomaly detection by evaluating four distinct Variational Quantum Classifier (VQC) architectures. A synthetic network traffic dataset is generated for the evaluations. The VQC models systematically varied feature encoding methods, parameterized ansatz circuits, quantum neural network types, and classical optimizers. Experimental results show that a trade-off exists between circuit expressivity and optimization stability. Deeper circuits (VQC-4) achieved higher accuracy of upto 89.0\%, while simultaneously being sensitive to training conditions. A shallower variant (VQC-1) under performed, although it had consistent and stable optimization curves. Class-dependent biases were also observed such as in VQC-2, where the model struggled to find an effective decision boundary, and produced a large number of false negatives. The best performing model in this study (VQC-3) combined ZFeatureMap with RealAmplitudes ansatz, optimized using ADAM. Comparative analysis against classical machine learning models such as Support Vector Machine and Random Forest reveal a performance gap, where classical models are able to achieve perfect classification performance on the synthetic data. It is concluded that classical algorithms remain dominant in their ability to classify structured data with relatively simple class separations. However, due to the observed potential of certain VQC configurations to learn decision boundaries to classify data, their utility for future applications in noisier, higher-dimensional problems is highlighted.
Quantum Machine Learning investigates the pos-sibility of quantum computers enhancing Machine Learning algorithms. Anomaly segmentation is a fundamental task in various domains to identify irregularities at sample level and can be addressed with both supervised and unsupervised methods. Autoencoders are commonly used in unsupervised tasks, where models are trained to reconstruct normal instances efficiently, al-lowing anomaly identification through high reconstruction errors. While quantum autoencoders have been proposed in the literature, their application to anomaly segmentation tasks remains unexplored. In this paper, we introduce a patch-based quantum autoencoder (QPB-AE) for image anomaly segmentation, with a number of parameters scaling logarithmically with patch size. QPB-AE reconstructs the quantum state of the embedded input patches, computing an anomaly map directly from measurement through a SWAP test without reconstructing the input image. We evaluate its performance across multiple datasets and parameter configurations and compare it against a classical counterpart.
Anomaly detection has a significant impact on applications such as video surveillance, medical diagnostics, and industrial monitoring, where anomalies frequently depend on context and anomaly-labeled data are limited. Quantum federated learning (QFL) overcomes these concerns by distributing model training among several quantum clients, consequently eliminating the requirement for centralized quantum storage and processing. However, in real-life quantum networks, clients frequently differ in terms of hardware capabilities, circuit designs, noise levels, and how classical data is encoded or preprocessed into quantum states. These differences create inherent heterogeneity across clients - not just in their data distributions, but also in their quantum processing behaviors. As a result, training a single global model becomes ineffective, especially when clients handle imbalanced or non-identically distributed (non-IID) data. To address this, we propose a new framework called personalized quantum federated learning (PQFL) for anomaly detection. PQFL enhances local model training at quantum clients using parameterized quantum circuits and classical optimizers, while introducing a quantum-centric personalization strategy that adapts each client's model to its own hardware characteristics and data representation. Extensive experiments show that PQFL significantly improves anomaly detection accuracy under diverse and realistic conditions. Compared to state-of-the-art methods, PQFL reduces false errors by up to 23%, and achieves gains of 24.2% in AUROC and 20.5% in AUPR, highlighting its effectiveness and scalability in practical quantum federated settings.
Quantum Kernel Methods for Anomaly Detection in High-Velocity Data Streams introduces a novel framework leveraging quantum computing principles to address critical challenges in real-time anomaly detection. By combining the expressive power of quantum-enhanced feature spaces with classical machine learning techniques, the work presents a hybrid architecture capable of identifying subtle anomalies in complex, high-dimensional streaming data. The framework incorporates specialized quantum feature maps that efficiently encode temporal and distributional properties of data streams, while adaptation mechanisms respond to concept drift and evolving patterns. Through systematic experimental evaluation across synthetic and real-world datasets from financial transactions, network security, and industrial systems, the approach demonstrates superior detection performance particularly for complex nonlinear patterns in high-dimensional spaces. The quantum-classical implementation addresses current hardware constraints through optimization techniques and targeted resource allocation, establishing specific conditions where quantum advantage emerges for operational anomaly detection scenarios.
The application and assessment of quantum-based anomaly detection models in cybersecurity are examined in this work. The efficacy of quantum machine learning approaches for detecting several cyber threats, including Denial of Service (DoS), Remote-to-Local (R2L), and botnet penetration, using two well-known intrusion detection datasets: NSL-KDD and CICIDS2017. Angle and amplitude encoding techniques are worn to preprocess and instruct traditional data into quantum-readable formats, making it compatible with quantum circuits. Due to the present constraints of Noisy Intermediate-Scale Quantum (NISQ) devices, the models are developed using Qiskit, using parameterized quantum layers via the TwoLocal ansatz, and simulated on classical hardware using Qiskit Aer. Metrics are used to compare performance to traditional machine learning models, such as Support Vector Machines (SVM), Random Forests (RF), and Multilayer Perceptions (MLP). The quantum SVM (QSVM) performs better in classification on both datasets, according to the results, indicating that quantum computing may be used to improve anomaly detection in cybersecurity applications.