QGraphGAN: Quantum Graph Softmax for Adversarial Link Prediction via BFS-Tree Variational Circuits

GraphGAN generates graph neighbors by walking a BFS tree, scoring each branch with a classical softmax. We replace each branch scorer with a small variational quantum circuit — a parameterized circuit that uses quantum superposition to produce branching probabilities — yielding QGraphGAN. A learned STOP action lets the generator terminate at any non-root node, preventing exponential probability suppression of deep-tree paths. We pair the quantum generator with GraphGAN's original dot-product discriminator, isolating the quantum claim to the generative distribution. Training uses REINFORCE with baseline subtraction. Two independent GraphSAGE encoders provide separate generator and discriminator embeddings. Evaluated over three seeds on Karate Club (34 nodes), SBM (32 nodes), and a CA-GrQc subgraph, QGraphGAN outperforms the classical BFS-GAN by +0.08 to +0.32 AUC across datasets. On real-world-like topology it matches DeepWalk and Adamic–Adar; on clean synthetic structure (SBM) classical heuristics dominate — an honest negative result we report in full.