Computational Graph Representation of Multiloop Feynman Diagrams

In quantum field theory, precise calculation of high-order Feynman diagrams and proper implementation of renormalization schemes are crucial yet computationally challenging. We propose a novel computational framework, representing Feynman diagrams as computational graphs—a key structure in deep learning. Utilizing high-order automatic differentiation on these graphs, we streamline the implementation of renormalization. By combining this approach with the diagrammatic Monte Carlo algorithm, we develop an efficient solver for electron liquid field theories, applicable to electronic structure calculations, superconductivity, and magnetization studies. Our work reveals a conceptual alignment between quantum field theory and machine learning. This establishes a new avenue for applying AI techniques in scientific research, widening the scope for machine learning in solving complex problems in quantum physics.