Decoherence as Defence and the Magnitude of Noise Regularisation: A Rigorous N-Qubit Theory of Stochastic Quantum Neural Networks for Adversarially Robust Network Intrusion Detection

Research Question and Approach

This paper investigates the role of decoherence and stochasticity in quantum neural networks (SQNNs) for network intrusion detection. Specifically, it addresses whether controlled noise, such as a depolarizing channel or per-gate dropout, can serve as a robust regularizer against adversarial attacks. The author develops an N-qubit formulation using the stochastic master equation and a vectorised Liouvillian to provide a rigorous theoretical framework. The study evaluates these mechanisms on the NSL-KDD dataset, comparing them against classical baselines and noiseless quantum circuits under white-box FGSM and PGD attacks.

The paper establishes a 'decoherence-contraction theorem,' which provides a predictive law for how depolarizing noise scales Pauli read-outs. Contrary to prior assumptions that noise only acts as output perturbation, the study demonstrates that training with a depolarizing channel significantly improves adversarial robustness. This robustness is attributed to a noise-reshaped training boundary rather than simple gradient contraction. Furthermore, the author derives an 'adaptive-penalty formula' for per-gate quantum dropout, showing it acts as a curvature-weighted L2 penalty in weight space. A 30-seed study confirms that both depolarizing noise and per-gate dropout reduce the train-test gap by a statistically significant margin, with the effect concentrated where overfitting is most severe.

As machine learning detectors are increasingly integrated into high-stakes, automated security pipelines, hardening them against adversarial evasion is critical. This research moves beyond conservative robustness bounds, offering a predictive, operational theory for noise-induced defense. By identifying the mapping between SQNNs and neutral-atom Rydberg hardware, the paper provides a path toward implementing these robust quantum models on physical hardware, demonstrating that noise can be harnessed as a computational resource rather than just a limitation.