sqnn-decoherence-defence

name	sqnn-decoherence-defence
description	Stochastic Quantum Neural Networks (SQNNs) adversarial robustness methodology. Decoherence-contraction theorem for depolarising channels, per-gate dropout as curvature-weighted L2 penalty, and noise-as-defence framework for quantum machine learning. Use when: SQNNs, quantum adversarial robustness, quantum dropout, decoherence contraction, Lindblad master equation, neural network security.
metadata	{"arxiv_id":"2606.24219","published":"2026-06-23","authors":"Gautier-Edouard Filardo","tags":["quantum","machine-learning","adversarial-robustness","sqnn","decoherence"]}

SQNN Decoherence as Defence

Description

Stochastic Quantum Neural Networks (SQNNs) encode neuronal activations as qubits, synaptic topology as entanglement, and neural noise through a Lindblad master equation. This methodology proves that decoherence acts as adversarial defence rather than degradation.

Activation Keywords

• sqnn decoherence defence
• stochastic quantum neural network robustness
• quantum dropout
• decoherence contraction theorem
• depolarising channel regularisation
• quantum adversarial robustness
• lindblad master equation neural
• per-gate stochastic deactivation

Core Contributions

1. Decoherence-Contraction Theorem

A depolarising channel of strength γ over L entangling layers contracts every weight-w Pauli read-out by factor:

(1 - 4γ/3)^(wL)

For weight-1 read-out: (1 - 4γ/3)^L

Key insight: Depolarising noise reshapes the training boundary rather than contracting attack-time gradients. This prevents catastrophic robustness collapse seen in noiseless circuits.

2. Per-Gate Dropout as Curvature-Weighted L2 Penalty

Per-gate dropout implements:

p(1-p)/2 × Σ θ² ∂²_θ L

in weight space, maximised at p=1/2. Depolarising noise implements an output-space penalty instead.

Practical result: Both mechanisms reduce train-test gap by ~0.01 (p<10⁻⁴), statistically indistinguishable. Effect concentrated where overfitting is largest.

3. Empirical Validation

• NSL-KDD dataset under FGSM and PGD attacks
• 30-seed study confirms dropout formula prediction
• Increasing dropout past 1/2 does not help
• Noiseless models fall from 95% to 47% under PGD-20; SQNN never suffers catastrophic collapse

Usage Workflow

Step 1: SQNN Architecture Design

1. Encode neuronal activations as qubits
2. Map synaptic topology to entanglement structure
3. Choose ring topology for non-local anomaly detection

Step 2: Noise Mechanism Selection

Mechanism	Effect	Best For
Depolarising (γ)	Output-space penalty	General robustness
Per-gate dropout (p)	Curvature-weighted L2	Overfitting prevention
Combined	Both penalties	Maximum robustness

Step 3: Training with Noise-as-Defence

1. Apply depolarising channel during training (not just inference)
2. Set dropout rate p ≤ 0.5 (optimal at p=1/2)
3. Monitor robustness variance (should decrease ~2×)
4. Validate under white-box FGSM and PGD attacks

Step 4: Neutral-Atom Realisation

For hardware deployment:

• Map SQNN to neutral-atom architecture
• Perform feasibility analysis by N qubits
• Account for native gate set and connectivity

Pitfalls

1. Depolarising ≠ dropout: Depolarising channel acts as output noise, not dropout-style regulariser. Use per-gate dropout for weight-space effects.
2. Optimal dropout at p=0.5: Increasing beyond 0.5 does not improve generalisation.
3. Single-seed results unreliable: Prior work with single seeds showed false dichotomy; use 30+ seeds.
4. Robustness from boundary reshaping: Robustness comes from noise-reshaped training boundary, not gradient contraction during attack.

Related Skills

• stochastic-quantum-neural-network — SQNN basics (arXiv:2511.11609)
• qmt-quantum-measurement-temperature — QNN training stability (arXiv:2606.22551)
• qpinn-integro-fractional-pde — QPINN methodology (arXiv:2606.26865)
• qml-adversarial-robustness-sok — QML robustness SoK