Quantum Quasi-Monte Carlo

Understanding the quantum many-body problem and its applications to correlated materials, cold atoms and nanoelectronic devices is a central problem of physics. Nonetheless, few numerical techniques can simulate strongly correlated systems in an accurate and controlled way, especially when far from equilibrium. Perturbation theory has seen an unexpected recent revival, based on Quantum Monte Carlo approaches that calculate all Feynman diagrams up to large orders. Here we show that integration based on low-discrepancy sequences can be adapted to this problem and greatly outperforms state-of-the-art diagrammatic Monte Carlo methods. In relevant practical applications, we show a speed-up of several orders of magnitude. We demonstrate convergence with scaling as fast as $1/N$ in the number of sample points $N$, parametrically faster than the $1/\sqrt{N}$ of Monte Carlo methods. Our approach enables a new scale of high-precision computation for strongly interacting quantum many-body systems. We illustrate it with a solution of the Kondo ridge in quantum dots.