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Applied Soft Computing

Evolutionary tailoring of quantum kernels for cyber-physical anomaly detection: A case study on the SWaT testbed

Giovanni Acampora, Edoardo Giusto, Andrea Senese, Nicola Mazzocca

Published Jun 10, 2026• 0 citations
Publisher

Abstract

Quantum computing represents a promising frontier for machine learning, offering new tools to tackle complex problems by leveraging high-dimensional feature spaces and the unique properties of quantum systems. In this context, quantum kernels have emerged as a particularly compelling technique, capable of revealing structures in data that are difficult to detect using classical methods (Schuld and Killoran, 2019 [5]). However, their practical impact in real-world applications remains largely unexplored. This work proposes a hybrid quantum-classical architecture for anomaly detection in industrial cyber-physical systems, using the SWaT testbed as a case study. In complex environments like SWaT, sophisticated cyber-attacks can mimic normal system behavior, making them difficult to identify (Goh et al., 2016 [1]). Quantum kernels may help distinguish such anomalies by enabling more expressive data representations. Experimental results demonstrate the viability of hybrid quantum approaches, providing promising indications for future developments in quantum-supported industrial system security.

DOI
10.1016/j.asoc.2026.115664

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Quantum computing represents a promising frontier for machine learning, offering new tools to tackle complex problems by leveraging high-dimensional feature spaces and the unique properties of quantum systems. In this context, quantum kernels have emerged as a particularly compelling technique, capable of revealing structures in data that are difficult to detect using classical methods (Schuld and Killoran, 2019 [5]). However, their practical impact in real-world applications remains largely unexplored. This work proposes a hybrid quantum-classical architecture for anomaly detection in industrial cyber-physical systems, using the SWaT testbed as a case study. In complex environments like SWaT, sophisticated cyber-attacks can mimic normal system behavior, making them difficult to identify (Goh et al., 2016 [1]). Quantum kernels may help distinguish such anomalies by enabling more expressive data representations. Experimental results demonstrate the viability of hybrid quantum approaches, providing promising indications for future developments in quantum-supported industrial system security.
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.
Cyber-physical control systems are critical infrastructures designed around highly responsive feedback loops that are measured and manipulated by hundreds of sensors and controllers. Anomalous data, such as from cyber-attacks, greatly risk the safety of the infrastructure and human operators. With recent advances in the quantum computing paradigm, the application of quantum in anomaly detection can greatly improve identification of cyber-attacks in physical sensor data. In this paper, we explore the use of strong pre-processing methods and a quantum-hybrid Support Vector Machine (SVM) that takes advantage of fidelity in parameterized quantum circuits to efficiently and effectively flatten extremely high dimensional data. Our results show an F-1 Score of 0.86 and accuracy of 87% on the HAI CPS dataset using an 8-qubit, 16-feature quantum kernel, performing equally to existing work and 14% better than its classical counterpart.
Increasing digitalization exposes critical infrastructure to sophisticated cyber threats, requiring new approaches to improving security and resilience. While classical machine learning techniques have shown promise in anomaly detection and threat mitigation, emerging quantum-inspired methods offer new opportunities to enhance detection capabilities by leveraging principles derived from quantum computing. The objective of this work is to propose a model for the early detection of Telephony Denial of Service attacks using a combination of classical algorithms and quantum computing-based techniques. Call records are embedded into a low-dimensional quantum feature space using spatial and temporal attributes, mapped through a quantum kernel in two modalities: Quantum-Inspired Kernel or Qiskit-Simulated Quantum Kernel. This approach enables the identification of subtle and complex patterns that can be difficult to capture using classical methods alone, without the need for fully fault-tolerant quantum hardware. The anomaly decision threshold is empirically calibrated, allowing the detector to balance early sensitivity against false-alarm control under the evaluated Public Safety Answering Points (PSAP) traffic conditions. The evaluation shows that the proposed framework can improve threat detection and system resilience in critical infrastructure contexts. The results support the use of kernel-based quantum-inspired representations as a tunable early-warning layer for PSAP traffic monitoring, while also showing that threshold calibration and operational context remain necessary before deployment.
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.
Abstract Modern Industrial Control Systems (ICS) face sophisticated cyber-physical attacks that exploit nonlinear correlations between process variables, rendering traditional linear classifiers ineffective. This paper presents a hardware-agnostic Quantum Support Vector Machine (QSVM) framework employing an 8-qubit ZZFeatureMap kernel for anomaly detection in critical water treatment and thermal power infrastructure. Performance benchmarks were established via noise-free statevector simulation to determine theoretical quantum advantage. Physical realizability was separately validated via circuit execution on IBM's 156-qubit ibm_fez processor, with completed hardware jobs enabling quantitative analysis of the simulation-to-hardware performance gap. Through rigorous cross-testbed validation on the SWaT (Secure Water Treatment) and HAI (Hardware-in-the-Loop Augmented ICS) datasets, our simulated approach achieves an AUC-ROC of 0.9912 ± 0.004 on SWaT and 0.8309 ± 0.050 on HAI, demonstrating consistent quantum advantage of +10.8% AUC over classical RBF-kernel SVMs on the more challenging HAI testbed. Statistical robustness is established through 5-seed cross-validation with stratified sampling. Hardware execution on ibm_fez confirms physical realizability with circuit depth 76 and 28 CNOT gates, while revealing an expected fidelity degradation of approximately 17–20% compared to ideal simulation due to gate errors and decoherence. The quantum kernel's Z i Z j entanglement structure geometrically captures pairwise feature correlations, providing inductive bias well-suited for coupled sensor dynamics. Unlike deep learning approaches that require massive attack datasets unavailable in critical infrastructure domains, our kernel method generalizes effectively from limited training samples. All experimental artifacts are publicly available at https://github.com/Ali-Badami/Quantum-IDS. IBM Quantum job identifiers: d5l9htjh36vs73bgsi3g (SWaT), d5l9huk8d8hc73cfb0pg (HAI).
The growing complexity of cyber threats has revealed the limitations of classical machine learning techniques, motivating the exploration of Quantum Machine Learning in threat detection systems for enhancing detection accuracy and computational efficiency. This study presents a comparative evaluation of two prominent quantum machine learning approaches: quantum kernel methods and variational quantum circuits, applied across diverse threat detection tasks. Our analysis, supported by recent empirical findings, demonstrates that hybrid quantum-classical architectures can reach or surpass classical baselines while requiring few qubits, shallow circuits, and reduced parameter count. Despite these promising results, several challenges remain, including data loading and state preparation overheads, trainability constraints, and limited empirical validation. In response, we propose theoretical guidance and practical criteria to facilitate reproducible and effective application of Quantum Machine Learning in cyber threat detection, bridging the gap between emerging theory and empirical practice.