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IEEE Open Journal of the Communications Society

Hybrid Classical–Quantum Kernel Learning for Scalable and Secure Link State Prediction in Software-Defined Networks

Muhammad Afaq

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Software-Defined Networks (SDNs) with their centralized control system and enhanced programmability requires a sophisticated approach to predict link states in complex network topologies. While predictive performance of traditional machine learning (ML) models remains high on static data, they struggle under dynamic and imbalanced network behavior. Although Quantum Machine Learning (QML) offers a promising solution by leveraging quantum-enhanced kernels to discover non-linear patterns, current quantum hardware constraints limit its standalone applicability. This paper presents an extended hybrid classical-quantum learning framework for SDN link state prediction under both benign (stable) and attack (compromised) conditions, integrating classical preprocessing with quantum kernel embedding via the ZZFeatureMap. A tunable parameter α0,1 enables dynamic interpolation between classical Radial Basis Function (RBF) and quantum kernels. On a stratified 5,000-sample subset of the InSDN dataset, which contains both normal and attack traffic flows, the hybrid Quantum Support Vector Machine (QSVM) achieves 85% accuracy, 0.92 ROC–AUC, and 0.73 Average Precision (AP). Scalability experiments on 20,000 samples confirm stable performance using Nyström-approximated kernels. Comparative evaluations with existing core classical, gradient boosting, and deep learning approaches highlight hybrid QSVM’s tunable expressivity, controlled computational scaling, and robustness to data distribution shifts, demonstrating its potential for future quantum-enabled SDN analytics.

DOI
10.1109/ojcoms.2025.3639435

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Software-Defined Networks (SDNs) with their centralized control system and enhanced programmability requires a sophisticated approach to predict link states in complex network topologies. While predictive performance of traditional machine learning (ML) models remains high on static data, they struggle under dynamic and imbalanced network behavior. Although Quantum Machine Learning (QML) offers a promising solution by leveraging quantum-enhanced kernels to discover non-linear patterns, current quantum hardware constraints limit its standalone applicability. This paper presents an extended hybrid classical-quantum learning framework for SDN link state prediction under both benign (stable) and attack (compromised) conditions, integrating classical preprocessing with quantum kernel embedding via the ZZFeatureMap. A tunable parameter α0,1 enables dynamic interpolation between classical Radial Basis Function (RBF) and quantum kernels. On a stratified 5,000-sample subset of the InSDN dataset, which contains both normal and attack traffic flows, the hybrid Quantum Support Vector Machine (QSVM) achieves 85% accuracy, 0.92 ROC–AUC, and 0.73 Average Precision (AP). Scalability experiments on 20,000 samples confirm stable performance using Nyström-approximated kernels. Comparative evaluations with existing core classical, gradient boosting, and deep learning approaches highlight hybrid QSVM’s tunable expressivity, controlled computational scaling, and robustness to data distribution shifts, demonstrating its potential for future quantum-enabled SDN analytics.
Software-Defined Networks (SDNs) significantly enhance network management through centralized control, programmability, and agility. However, accurate link prediction remains challenging due to the complexity and dynamic topology of SDNs. Classical machine learning techniques achieve high accuracy but can struggle to model subtle, nonlinear relationships in rapidly evolving networks. Quantum Machine Learning (QML) techniques exploit quantum phenomena to capture these complex patterns, yet current quantum hardware limitations restrict their standalone applicability. To address these challenges, this paper proposes a hybrid classical-quantum machine learning framework for SDN link prediction. Classical preprocessing, including normalization and feature selection, prepares high-quality input for quantum processing. The selected features are then mapped into quantum states using the ZZFeatureMap, enabling the Quantum Support Vector Machine (QSVM) to detect complex patterns through quantum-enhanced kernels. Rigorous experimentation using synthetic SDN datasets demonstrates that the hybrid QSVM achieves an area under the ROC curve (AUC) of 0.84, an average precision (AP) of 0.74, and an accuracy of 0.84—closely matching classical SVM and approaching the performance of Random Forest (AUC = 0.86, AP = 0.78, Accuracy = 0.88). The QSVM and classical SVM also demonstrate significantly lower training time ( 0.04s) compared to Random Forest ( 0.29s), highlighting the hybrid model's efficiency. These results provide strong evidence that quantum-enhanced techniques can effectively complement classical models, offering improved robustness and scalability for intelligent network systems.
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.
Abstract Support vector machines (SVMs) are widely used for classification, but become computationally expensive as datasets grow and data become high-dimensional or nonlinearly separable. Quantum support vector machines (QSVMs) enhance the traditional SVMs by replacing conventional feature mappings with quantum-implemented embeddings that project data into high-dimensional Hilbert spaces, potentially improving expressive power and efficiency. However, training QSVMs on current noisy intermediate-scale quantum (NISQ) devices remains challenging, as constructing the quantum kernel matrix requires repeated circuit executions and scales quadratically with dataset size. We propose NQ-SVM , a hybrid quantum-classical method that incorporates the Nystr\"om approximation to enhance the scalability of QSVMs. By selecting a small set of landmark points, the Nystr\"om method yields a low-rank kernel approximation, reducing complexity from (O(n2))(O(n^2))(O(n2)) to (O(nm))(O(nm))(O(nm)), while preserving the quantum advantages in handling high-dimensional, non-linear data. Extensive simulations demonstrate that NQ-SVM achieves comparable classification accuracy to classical SVMs and full QSVMs, while substantially reducing training time and kernel evaluation costs. These results underscore the potential of NQ-SVM as a scalable and practical hybrid framework for near-term quantum machine learning (QML).
Modern cyberattacks are increasingly complex, posing significant challenges to classical machine learning methods, particularly when labeled data is limited and feature interactions are highly non-linear. In this study we investigates the potential of hybrid quantum-classical learning to enhance feature representations for intrusion detection and explore possible quantum advantages in cybersecurity analytics. Using the UNSW-NB15 dataset, network traffic is transformed into structured feature vectors through classical preprocessing and normalization. Classical models, including Logistic Regression and Support Vector Machines with linear and RBF kernels, are evaluated on the full dataset to establish baseline performance under large-sample conditions. Simultaneously, a quantum-enhanced pipeline maps classical features into variational quantum circuits via angle encoding and entangling layers, executed on a CPU-based quantum simulator, with resulting quantum embeddings classified using a classical SVM. Experiments show that while classical models achieve higher overall accuracy with large datasets, quantum-enhanced representations demonstrate superior attack recall and improved class separability when data is scarce, suggesting that quantum feature spaces capture complex correlations inaccessible to shallow classical models. These results highlight the potential of quantum embeddings to improve generalization and representation quality in cybersecurity tasks and provide a reproducible framework for evaluating quantum advantages as quantum hardware and simulators continue to advance.
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.
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.