Generative Quantum Search for Combinatorial Optimization: A Preregistered Falsification Study of Shallow QAOA-Derived Proposal Distributions for Classically Refined Solution Subspaces

We port the Generative Quantum Eigensolver + Quantum-Selected Configuration Interaction (GQE+QSCI) architecture from quantum chemistry to combinatorial graph optimization. Our framework, GQO+QSS (Generative Quantum Optimization + Quantum-Selected Search), formalizes the key quantity as recovery-basin mass p_r(q,G) = Pr[x ~ q contains a state in A_r(G)], where A_r(G) is the set of states whose r-flip expansion after repair intersects the optimal solution set. We test whether shallow quantum samplers (QAOA, learned generative policy) can place more probability mass in the recovery basin than strong classical samplers for MWIS (Maximum Weighted Independent Set). All 150 ground truths are certified with CBC + brute-force verification. Exact recovery-basin masks are enumerated for all n<=20 instances. Nine samplers are compared on a preregistered held-out test set. Result: Scenario C (falsification). Tabu search dominates (p_r=0.82-0.94), SA is second, and all quantum samplers lose to both at every problem size. The learned classical policy matches oracle QAOA, confirming no structural quantum advantage. The earlier positive oracle result was an artifact of per-instance best-of-50 configuration selection. We claim no quantum advantage.