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Applied Energy

Aligning quantum kernels for detecting false data injection attacks in power systems

Bin Huang, Jianhui Wang, Xiaoge Huang

Published Jan 8, 2026• 3 citations
Publisher

Abstract

False Data Injection Attacks (FDIAs) are an elusive and impactful security threat in power systems. Existing solutions, such as those based on machine learning methods with classical kernels, suffer from weak noise resistance, extensive parameter tuning, and unstable performance in high-dimensional spaces. This work provides a novel solution to this problem from the perspective of quantum computing, specifically through the use of quantum kernel embedding (QKE). Classical kernels require costly hyperparameter searches that scale poorly with the number of measurements and often fail to separate sparse, overlapping attack patterns inherent in FDIA detection; by contrast, quantum kernel embedding leverages the exponentially large Hilbert space via shallow, fixed-depth circuits to generate highly expressive feature maps with far fewer tunable parameters, enabling more efficient and robust discrimination of subtle false-data-injection patterns. A kernel-alignment framework with a weighted loss function is proposed to tune the quantum circuit parameters so that the quantum kernel captures the imbalanced label structure and more effectively distinguishes attacked from normal data. Additionally, the Nyström approximation is extended to the quantum Hilbert space, utilizing only a subset of training data instead of the entire dataset, which enhances the scalability and computational efficiency of the method. Case studies on test systems and high-performance quantum simulators demonstrate the effectiveness of the method and evaluate its robustness under varying quantum incoherent noise.

DOI
10.1016/j.apenergy.2025.127332

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•Feb 18, 2026•0 citations
False Data Injection Attacks (FDIAs) are an elusive and impactful security threat in power systems. Existing solutions, such as those based on machine learning methods with classical kernels, suffer from weak noise resistance, extensive parameter tuning, and unstable performance in high-dimensional spaces. This work provides a novel solution to this problem from the perspective of quantum computing, specifically through the use of quantum kernel embedding (QKE). Classical kernels require costly hyperparameter searches that scale poorly with the number of measurements and often fail to separate sparse, overlapping attack patterns inherent in FDIA detection; by contrast, quantum kernel embedding leverages the exponentially large Hilbert space via shallow, fixed-depth circuits to generate highly expressive feature maps with far fewer tunable parameters, enabling more efficient and robust discrimination of subtle false-data-injection patterns. A kernel-alignment framework with a weighted loss function is proposed to tune the quantum circuit parameters so that the quantum kernel captures the imbalanced label structure and more effectively distinguishes attacked from normal data. Additionally, the Nyström approximation is extended to the quantum Hilbert space, utilizing only a subset of training data instead of the entire dataset, which enhances the scalability and computational efficiency of the method. Case studies on test systems and high-performance quantum simulators demonstrate the effectiveness of the method and evaluate its robustness under varying quantum incoherent noise.
In recent years, quantum computers have emerged as promising candidates for implementing kernels. Quantum Embedding Kernels embed data points into quantum states and calculate their inner product in a high-dimensional Hilbert Space by computing the overlap between the resulting quantum states. Variational Quantum Circuits (VQCs) are typically used for this end, with Kernel Target Alignment (KTA) as cost function. The optimized kernels can then be deployed in Support Vector Machines (SVMs) for classification tasks. However, both classical and quantum SVMs scale poorly with increasing dataset sizes. This issue is exacerbated in quantum kernel methods, as each inner product requires a quantum circuit execution. In this paper, we investigate KTA-trained quantum embedding kernels and employ a low-rank matrix approximation, the Nyström method, to reduce the quantum circuit executions needed to construct the Kernel Matrix. We empirically evaluate the performance of our approach across various datasets, focusing on the accuracy of the resulting SVM and the reduction in quantum circuit executions. Additionally, we examine and compare the robustness of our model under different noise types, particularly coherent and depolarizing noise.
With cyber-attacks becoming increasingly sophisticated, modern network intrusion detection systems (NIDSs) are relying on machine learning (ML) methods for their flexibility in detecting subtle anomalous patterns in huge amounts of network data. However, classical ML methods such as support vector machines (SVMs) often rely on the conversion of low-dimensional data into a high-dimensional space, creating complex linear systems that are time-consuming to evaluate on large data inputs such as network flow logs. We propose addressing this limitation by employing a hybrid quantum-classical ML model to leverage quantum computing's (QC's) superiority in high-dimensional areas. We constructed a quantum kernel with an SVM model and evaluated it on four different network attacks from a modern intrusion detection dataset. Results reveal an average hardware accuracy rate of 85% with noticeably small deviations between runs, suggesting that quantum kernels may be a noise-resistant solution. We evaluated these results alongside classical and noiseless quantum simulator benchmarks.
Transient stability assessment (TSA) in power systems evaluates the system’s ability to withstand and recover from disturbances, which can be formulated as a classification problem. This paper presents a quantum machine learning-based TSA approach that leverages quantum embedded kernels (QEKs) to map nonlinear power system features into a high-dimensional Hilbert space, where the data becomes linearly separable. By employing a quantum kernel function and Kernel Target Alignment (KTA), we optimize a variational quantum circuit for the stability classification of power systems. Through extensive experiments on both noise-free quantum simulators and noisy quantum environments, we demonstrated the accuracy and noise resilience of the developed algorithm.
Zero-day attacks pose a persistent threat to computing infrastructure by exploiting previously unknown software vulnerabilities that evade traditional signature-based network intrusion detection systems (NIDSs). To address this limitation, machine learning (ML) techniques offer a promising approach for enhancing anomaly detection in network traffic. This study evaluates several ML models on a labeled network traffic dataset, with a focus on zero-day attack detection. Ensemble learning methods, particularly eXtreme gradient boosting (XGBoost), achieved perfect classification, identifying all 6231 zero-day instances without false positives and maintaining efficient training and prediction times. While classical support vector machines (SVMs) performed modestly at 64% accuracy, their performance improved to 98% with the use of the borderline synthetic minority oversampling technique (SMOTE) and SMOTE + edited nearest neighbours (SMOTEENN). To explore quantum-enhanced alternatives, a quantum SVM (QSVM) is implemented using three-qubit and four-qubit quantum circuits simulated on the aer_simulator_statevector. The QSVM achieved high accuracy (99.89%) and strong F1-scores (98.95%), indicating that nonlinear quantum feature maps (QFMs) can increase sensitivity to zero-day exploit patterns. Unlike prior work that applies standard quantum kernels, this study introduces a parameterised quantum feature encoding scheme, where each classical feature is mapped using a nonlinear function tuned by a set of learnable parameters. Additionally, a sparse entanglement topology is derived from mutual information between features, ensuring a compact and data-adaptive quantum circuit that aligns with the resource constraints of noisy intermediate-scale quantum (NISQ) devices. Our contribution lies in formalising a quantum circuit design that enables scalable, expressive, and generalisable quantum architectures tailored for zero-day attack detection. This extends beyond conventional usage of QSVMs by offering a principled approach to quantum circuit construction for cybersecurity. While these findings are obtained via noiseless simulation, they provide a theoretical proof of concept for the viability of quantum ML (QML) in network security. Future work should target real quantum hardware execution and adaptive sampling techniques to assess robustness under decoherence, gate errors, and dynamic threat environments.
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.
Abstract Quantum Machine Learning (QML) is an emerging field at the intersection of quantum computing and artificial intelligence, offering high potential for extracting complex nonlinear patterns from high-dimensional data. However, many quantum kernel-based methods suffer from high computational costs, the requirement for numerous quantum circuit executions, and the limitations of current Noisy Intermediate-Scale Quantum (NISQ) hardware. These challenges, particularly when dealing with large datasets, represent a major barrier to the widespread adoption of these methods in practical applications. In this paper, a hybrid quantum machine learning framework based on Nyström approximation is proposed to effectively reduce the computational complexity of quantum kernels and enhance their scalability. In the proposed framework, classical data is first mapped to the quantum Hilbert space via parameterized quantum circuits, and the quantum kernel is defined based on the overlap of quantum states. Then, utilizing the Nyström approximation technique, the full kernel calculation is restricted to a representative subset of data, and the final learning process is conducted in the classical space. This approach reduces computational complexity from  O(N2)\:O\left({N}^{2}\right)O(N2) to  O(Nm)\:O\left(Nm\right)O(Nm), where N is the number of samples and m is the size of the selected subset. Analytical results and simulations on the Breast Cancer Wisconsin dataset demonstrate that the proposed framework reduces computational costs by over 60% while maintaining the geometric structure of the quantum feature space, with a classification accuracy loss of less than 3%. These results suggest that the proposed method can serve as a practical, scalable, and noise-resilient solution for applying quantum machine learning to real-world data-driven problems.