Exploiting quantum chaos diagnostics in QAOA for enhanced hybrid quantum classical deep learning classification

The Quantum Approximate Optimization Algorithm (QAOA) is repurposed here as a feature map within a hybrid quantum-classical classifier, augmented by a chaos-informed diagnostic. We extract a scalar chaos feature by evaluating an Out-Of-Time-Ordered correlators (OTOC) along parameter-scaling rays through the trained circuit, computing spacings between local minima, and standardizing them via a pre-fitted lognormal model. To probe finite-size effects, we sweep the number of qubits [Formula: see text] at fixed depth [Formula: see text] and train two models on a balanced 1,000-sample MNIST subset: a StandardHybrid using the [Formula: see text] local Pauli-[Formula: see text] expectations, and a ChaosAwareHybrid which appends the OTOC-derived scalar. We perform multi-run, 5-fold cross-validation with a paired design (identical seeds/folds across models) and report mean±SD, paired mean differences Δ, 95% t- and bootstrap CIs, exact permutation/sign tests, win-rates (Wilson 95% CI), and paired effect sizes. Across [Formula: see text] for [Formula: see text], the chaos-aware variant significantly improves test accuracy at [Formula: see text] with [Formula: see text]-[Formula: see text], all 95% CIs excluding zero, permutation [Formula: see text], high win-rates (86-100%), and large paired effects ([Formula: see text]-2.3). At [Formula: see text] the effect reverses ([Formula: see text], 2% win-rate, [Formula: see text]), indicating over-sensitivity. The best average accuracy occurs at [Formula: see text] ([Formula: see text]; [Formula: see text]; 100% wins). Per-epoch panels (train/val/test; mean±1 SD) reveal a "Goldilocks" width at which expressivity and sensitivity are balanced. These results show that a calibrated chaos diagnostic can enhance hybrid quantum-classical classifiers in resource-limited regimes and provide a principled knob to match circuit expressivity to many-body sensitivity.