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

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