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We present a low-scaling diagrammatic Monte Carlo approach to molecularcorrelation energies. Using combinatorial graph theory to encode many-bodyHugenholtz diagrams, we sample the M{\o}ller-Plesset (MPn) perturbation series,obtaining accurate correlation energies up to n = 5, with quadratic scaling inthe number of basis functions. Our technique reduces the computationalcomplexity of the molecular many-fermion correlation problem, opening up thepossibility of low-scaling, accurate stochastic computations for a wide classof many-body systems described by Hugenholtz diagrams.

Diagrammatic Monte Carlo for electronic correlation in molecules: high-order many-body perturbation theory with low scaling