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Feynman's diagrammatic series is a common language for a formally exacttheoretical description of systems of infinitely-many interacting quantumparticles, as well as a foundation for precision computational techniques. Herewe introduce a universal framework for efficient summation of connected orskeleton Feynman diagrams for generic quantum many-body systems. It is based onan explicit combinatorial construction of the sum of the integrands by dynamicprogramming, at a computational cost that can be made only exponential in thediagram order on a classical computer and potentially polynomial on a quantumcomputer. We illustrate the technique by an unbiased diagrammatic Monte Carlocalculation of the equation of state of the $2D$ $SU(N)$ Hubbard model in anexperimentally relevant regime, which has remained challenging forstate-of-the-art numerical methods.

Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model