VQIL: Visible Quantum Interference Learning for Perturbation Response Ranking on Graphs

Learning how local perturbations affect a network is important for identifying which components drive or absorb a system's response. We formulate this as seed-conditioned response ranking: given a perturbation at one seed node, ranking all other nodes by response strength. This is challenging when the model is given only the interaction topology, while the mechanism governing how perturbations propagate must be learned from data. We present VQIL (Visible Quantum Interference Learning), a trainable Szegedy quantum walk for seed-conditioned ranking. Edge weights, link phases, and per-node phase rotations are optimized end-to-end by backpropagation while the walk operator remains unitary throughout training. Node scores are obtained from a geometrically discounted coherent sum of quantum-walk amplitudes, enabling quantum interference before the final squared-norm readout. Because each learned parameter is attached to a named edge or node, the trained model provides directly inspectable hypotheses about the roles of individual graph components in the propagation mechanism. On AC power-flow perturbations over six transmission grids, with electrical parameters withheld from the model, VQIL improves Spearman rank correlation from 0.147 for the untrained walk to 0.831 and outperforms an identically trained random-walk model. On gene perturbation over five protein-protein interaction networks with Perturb-seq supervision, VQIL improves rank correlation from 0.171 to 0.620, outperforming the strongest learned classical and neural baselines. These results show that trainable quantum-walk interference provides a scalable and interpretable inductive bias for learning seed-conditioned response rankings on graphs.