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In this study, we present ScoreFormer, a novel graph transformer model designed to accurately predict molecular docking scores, thereby optimizing high-throughput virtual screening (HTVS) in drug discovery. The architecture integrates Principal Neighborhood Aggregation (PNA) and Learnable Random Walk Positional Encodings (LRWPE), enhancing the model's ability to understand complex molecular structures and their relationship with their respective docking scores. This approach significantly surpasses traditional HTVS methods and recent Graph Neural Network (GNN) models in both recovery and efficiency due to a wider coverage of the chemical space and enhanced performance. Our results demonstrate that ScoreFormer achieves competitive performance in docking score prediction and offers a substantial 1.65-fold reduction in inference time compared to existing models. We evaluated ScoreFormer across multiple datasets under various conditions, confirming its robustness and reliability in identifying potential drug candidates rapidly.