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

arXiv:2606.24219v1 Announce Type: new Abstract: Stochastic quantum neural networks (SQNNs) encode neuronal activations as qubits, synaptic topology as entanglement, and neural noise through a Lindblad master equation. A recent conference study applied a ring-entangled SQNN to collaborative intrusion detection and reached three conclusions: ring entanglement is essential for non-local anomaly detection; an adversarial-resilience bound holds but is conservative; and the depolarising channel fails to act as a dropout-style regulariser, behaving instead as output noise. It left open whether a per-gate stochastic deactivation (``true quantum dropout'') could regularise where the depolarising channel could not, and whether the loose robustness bound could be replaced by a predictive theory. This paper resolves both and extends the framework to real data and to neutral-atom hardware. We give an N-qubit formulation through the stochastic master equation and its vectorised Liouvillian, and prove a decoherence-contraction theorem: a depolarising channel of strength gamma over L entangling layers contracts every weight-w Pauli read-out by a factor (1-4gamma/3)^{wL} (for the weight-1 read-out used here, (1-4gamma/3)^{L}); building on the general noise-as-defence result of Du et al., we make this quantitative and operational for intrusion detection. On the real NSL-KDD dataset under white-box FGSM and PGD attacks, a depolarising SQNN trained with the channel is, over seven seeds under strong ell_infty/ell_2 attacks, significantly more robust than the noiseless circuit (ell_infty PGD-20, p=0.04, large effect) and, critically, never suffers the catastrophic robustness collapse that the noiseless model and gradient-trained classical detectors (which fall from 95% to 47%) do, cutting robustness variance roughly twofold; we show this robustness arises from a noise-reshaped training boundary rather than from attack-time gradient contraction. For generalisation, we derive an adaptive-penalty formula showing that per-gate dropout implements a curvature-weighted L_2 penalty frac{p(1-p)}{2}sumheta^2partial^2_heta L in weight space, maximised at p=1/2, whereas depolarising noise implements an output-space penalty. A 30-seed study confirms the formula's quantitative prediction: both mechanisms reduce the train-test gap by a small but statistically significant margin (approx!0.01; p<10^{-4} and p=0.004), are statistically indistinguishable from each other, and the effect is concentrated where overfitting is largest; increasing the dropout rate past 1/2 does not help, as the formula predicts. The single-seed dichotomy of prior work does not survive replication. We close with a neutral-atom realisation and a feasibility-by-N analysis.

Source: arXiv cs.CL | 2026-06-24