Q-CVaR-Fold: A Quantum CVaR Contrastive LearningFramework for Protein-Folding Decoy Scoring

Abstract Protein structure prediction and decoy ranking remain central challenges in computational biophysics. Classical scoring functions often struggle todiscriminate near-native conformations from large populations of plausible decoys,particularly in the critical low-energy tail of the conformational distribution. Weintroduce Q-CVaR-Fold, a hybrid quantum–classical architecture that integratesa geometric graph neural network encoder with a small parameterized quantumcircuit acting as a nonlinear scoring head. To focus optimization on near-nativeconformations, we combine contrastive ranking with Conditional Value-at-Risk(CVaR) tail reweighting, yielding a risk-sensitive training objective aligned withstructural evaluation metrics.Despite using only four qubits and shallow entangling layers, Q-CVaR-Fold exhibits stable end-to-end training and avoids barren plateaus. On a decoy-rankingbenchmark, the model achieves a ROC-AUC of 0.984 and perfect top-5 nativeenrichment across all sequences, outperforming classical baselines of comparablesize. The score distributions and monotonic reduction of CVaR loss demonstratethat quantum feature transformations, coupled with tail-focused optimization, provide discriminative power beyond standard MLP heads. To our knowledge, this isthe first demonstration of a quantum-enhanced, risk-sensitive scoring model thatachieves near-perfect recovery of native structures in decoy-ranking tasks.Q-CVaR-Fold highlights the potential of hybrid quantum models for energylandscape modeling, fragment selection, and structural refinement, and offers apromising foundation for next-generation quantum–geometric methods in computational structural biology.