Inclusion-exclusion principle for many-body diagrammatics

Diagrammatic resummation techniques have recently enabled new classes of quantum Monte Carlo algorithms, but are restricted by the need to sum over factorially large sets of diagrams. Here, the authors present a fast algorithm for summing over the diagrams appearing in Inchworm hybridization expansions. The method relies on the inclusion-exclusion principle to reduce the scaling from factorial to exponential. For the Inchworm hybridization expansion, when compared to the previous state of the art, the new algorithm is shown to provide practical performance gains of approximately two orders of magnitude.