Hypothesis: Integrating minibatch optimal transport reflow into GNN-based surrogate models will generate valid molecular docking configurations for QUBO optimization with significantly fewer inference steps than standard diffusion or flow-matching models.

Replacing the standard denoising/flow-matching sampler in a GNN-based molecular docking surrogate with a minibatch optimal-transport (OT) reflow procedure will produce ligand-protein pose predictions that (a) achieve ≥90% of the pose validity rate (RMSD ≤ 2.0 Å vs. crystal structure, or equivalent physically-valid QUBO-encodable configuration) of a baseline diffusion/flow-matching model, while (b) requiring ≤10 inference steps versus ≥50 for the baseline, on a held-out benchmark of protein-ligand complexes (e.g., PDBbind core set, n≥250), with the resulting coordinate/rotamer distributions feeding a QUBO formulation that quantum or quantum-inspired solvers (D-Wave, simulated annealing, or QAOA-on-simulator) can solve to comparable binding-energy accuracy (ΔG within 1.5 kcal/mol RMSE of baseline) in equal or fewer solver calls.

Minimum viable test: train two models with identical GNN backbone (e.g., EGNN or SE(3)-equivariant GNN, ~5–10M parameters) — one using standard conditional flow-matching, one using minibatch-OT reflow distillation — on CrossDocked2020 training split; evaluate both on PDBbind core set (285 complexes) measuring pose validity, RMSD, inference steps (1/2/5/10/20/50), wall-clock latency, and downstream QUBO binding-energy accuracy when poses are converted to QUBO variables and solved via simulated annealing (as quantum-hardware proxy) and, if budget allows, one D-Wave Advantage run for a validation subsample (n=20).

# Baseline: GNN flow-matching docking model
class FlowMatchDock(nn.Module):
    encoder: EGNN(protein_graph, ligand_graph) -> joint_embedding
    velocity_field: MLP(x_t, t, embedding) -> dx/dt
    train: sample t~U(0,1), x_t = (1-t)*x0_noise + t*x1_data
           loss = MSE(velocity_field(x_t,t), x1-x0)
    sample: ODE_solve(velocity_field, steps=N) # N=50-100 baseline

# OT-Reflow variant
class OTReflowDock(FlowMatchDock):
    train:
        for batch in dataloader:
            x0 = sample_prior(batch_size)
            x1 = batch.data
            # minibatch OT coupling (Sinkhorn or exact for small batch)
            pi = compute_ot_coupling(x0, x1, cost=pairwise_dist)
            x0_matched = resample_via_coupling(x0, pi)
            t ~ U(0,1); x_t = (1-t)*x0_matched + t*x1
            loss = MSE(velocity_field(x_t,t), x1 - x0_matched)
        # reflow distillation round 2+: regenerate (x0,x1) pairs by
        # running current model, retrain on straightened trajectories
    sample: ODE_solve(velocity_field, steps=N) # N=1-10 target

# Downstream QUBO
poses = OTReflowDock.sample(protein, ligand, steps=10)
qubo_vars = discretize_pose(poses, torsion_bins=8, translation_bins=6)
Q_matrix = build_qubo(qubo_vars, scoring_fn=vina_score_approx)
solution = solve_qubo(Q_matrix, solver=SimulatedAnnealing or DWaveSampler)
binding_energy = evaluate(solution, reference_structure)