Modeling Wavelet Transformed Quantum Support Vector for Network Intrusion Detection

TL;DR

This work tackles network intrusion detection in IoT environments by integrating a noise-resilient Quantum Support Vector Machine (QSVM) with a Quantum Haar Wavelet Packet Transform (QWPT) for multiscale feature extraction on NISQ devices. It advances QSVM applicability through amplitude encoding, QRAM-assisted data loading, shallow circuitry, fidelity-based quantum kernels, and SPSA-driven hybrid optimization, augmented by behavioral analysis via energy entropy and Chi-square testing. The hybrid pipeline comprises quantum state preparation, QWPT feature extraction, behavioral analysis, and enhanced QSVM classification, achieving 96.67% accuracy on BoT-IoT and 89.67% on IoT-23 under noiseless conditions and demonstrating resilience under depolarizing noise, with an 8-qubit configuration delivering favorable accuracy-noise trade-offs. The results establish a measurable quantum advantage over classical SVM baselines and prior quantum methods, underscoring the potential of quantum-enhanced anomaly detection for real-world cybersecurity workloads on near-term hardware.

Abstract

Network traffic anomaly detection is a critical cybersecurity challenge requiring robust solutions for complex Internet of Things (IoT) environments. We present a novel hybrid quantum-classical framework integrating an enhanced Quantum Support Vector Machine (QSVM) with the Quantum Haar Wavelet Packet Transform (QWPT) for superior anomaly classification under realistic noisy intermediate-scale Quantum conditions. Our methodology employs amplitude-encoded quantum state preparation, multi-level QWPT feature extraction, and behavioral analysis via Shannon Entropy profiling and Chi-square testing. Features are classified using QSVM with fidelity-based quantum kernels optimized through hybrid training with simultaneous perturbation stochastic approximation (SPSA) optimizer. Evaluation under noiseless and depolarizing noise conditions demonstrates exceptional performance: 96.67% accuracy on BoT-IoT and 89.67% on IoT-23 datasets, surpassing quantum autoencoder approaches by over 7 percentage points.

Figures (9)

• Figure 1: Optimized Quantum Circuit Architecture for Noise-Resilient Anomaly Detection.
• Figure 2: Comprehensive view of the proposed Architecture of the Quantum-Enhanced NIDS Framework
• Figure 3: Optimal Convergence Behavior: Across runs, moderate learning rates (0.5) achieve fast, stable loss reduction whereas very low or very high rates either slow progress or induce oscillatory dynamics. Panel (a) shows the per-iteration training loss (rolling mean ±1 std); panel (b) overlays training and testing loss to indicate relative scaling and generalization behavior; panel (c) plots convergence-rate oscillations (positive/negative drift) that mark unstable gradient dynamics at extreme rates; panel (d) presents parameter norm and update magnitudes which explain the large parameter jumps and resulting oscillations at high learning rates.
• Figure 4: Training Loss Dynamics: (a) normalized and log-scaled views of the loss trajectory highlight different aspects of progress and spikes; (b) distribution of per-iteration training loss with KDE to show central tendency and tails; (c) empirical CDF of training loss to show cumulative distribution and quantiles.
• Figure 5: Noise-Resilient Optimization: Under depolarizing noise, moderate learning rates maintain stable convergence while extreme values either fail to overcome noise effects (e.g., LR=0.05) or amplify them through excessive parameter updates (e.g., LR=1.0). (a) Testing loss (rolling mean ± std) for Ideal vs Depolarizing Noise. (b) Example clean vs noisy run with shaded noise-penalty area. (c) Distribution summarizing noise penalty across runs.