Swift GW beyond 10,000 electrons using sparse stochastic compression

We introduce the concept of sparse stochastic compression, an efficient stochastic sampling of any general function. The technique uses sparse stochastic orbitals (SSOs), short vectors that sample a small number of space points. As a first demonstration, SSOs are applied in conjunction with simple direct projection to accelerate our recent stochastic GW technique; the new developments enable accurate prediction of G0W0 quasiparticle energies and gaps for systems with up to Ne>10,000 electrons, with small statistical errors of ±0.05eV and using less than 2000 core CPU hours. Overall, stochastic GW scales now linearly (and often sublinearly) with Ne.