Abstract 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 n \4, 6, 8, 10\ at fixed depth p=2 and train two models on a balanced 1, 000-sample MNIST subset: a StandardHybrid using the n local Pauli- Z 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, 95% t- and bootstrap CIs, exact permutation/sign tests, win-rates (Wilson 95% CI), and paired effect sizes. Across N_ pairs=\50, 50, 67, 50\ for n=\4, 6, 8, 10\, the chaos-aware variant significantly improves test accuracy at n \4, 6, 8\ with +0. 016 – +0. 018, all 95% CIs excluding zero, permutation p 0, high win-rates (86–100%), and large paired effects (dᵦ 1. 0 –2. 3). At n=10 the effect reverses (=-0. 022, 2% win-rate, dᵦ=-2. 20), indicating over-sensitivity. The best average accuracy occurs at n=8 (0. 9006 0. 0069 ; =+0. 0180 ; 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.
Villalba-Díez et al. (2026) studied this question.