Q-TAILOR: Tail-Adaptive Quantum Operator Learning for Protein Structure Refinement

Abstract Protein structure refinement is inherently a tail-dominated problem: only a small fraction of conformations lie near the native basin, yet reliable improvement in this regime is critical for downstream accuracy. Most existing learning-based approaches address refinement indirectly through energy prediction or ranking, optimizing average performance rather than worst-case behavior. As a result, difficult near-native conformations often remain poorly treated. In this work, we introduce Q-TAILOR, a tail-adaptive operator learning framework for protein structure refinement. Q-TAILOR formulates refinement as the learning of a structured transformation on conformation space, explicitly optimized for worst-case improvement using a Conditional Value-at-Risk (CVaR) objective. The refinement operator is constrained to a low-rank geometric subspace and parameterized via a nonlinear coefficient generator in spired by quantum expectation values, enabling expressive yet stable refine ment dynamics. An ambiguity-driven adaptive mechanism allocates expres sive capacity selectively to difficult conformations, mitigating optimization pathologies associated with uniformly deep models. We provide theoretical analysis showing that operator learning is better conditioned than scalar energy prediction in tail-dominated landscapes and that CVaR induces gradient concentration on the most informative refinement cases. Controlled experiments on a synthetic refinement task demonstrate that Q-TAILOR achieves substantially stronger improvements in the tail of the quality distribution than in the mean, while maintaining stable refinement across all inputs. Although evaluated in a minimal setting, the results validate the central premise of the approach: reliable protein refinement requires tail-sensitive op erator learning rather than average-case prediction. Q-TAILOR establishes a general framework that can be extended to higher-dimensional protein models and hybrid classical–quantum implementations as computational resources mature