When Do Entangling Gates Add Predictive Signal? A Preregistered Falsification Study for Hybrid Quantum-Classical Combinatorial Optimization

Hybrid quantum-classical optimization requires quantum components to justify scarce quantum-processing-unit time relative to strong classical alternatives. This preregistered falsification study tests whether a shallow entangling circuit can serve as a useful quantum feature oracle for combinatorial-optimization algorithm selection. On 10,000 simulated graphs, the circuit adds a small in-distribution predictive signal beyond cheap graph descriptors, but information-matched classical models substantially outperform the quantum feature map. The signal fails to transfer to most out-of-distribution graph families. Trapped-ion experiments show high simulator-to-hardware feature fidelity, while noise-aware controls distinguish predictive signal from differential noise robustness. The work makes no quantum-advantage claim and provides an evidence-first, resource-aware evaluation of quantum participation in hybrid optimization.