Machine learning universal bosonic functionals

The one-body reduced density matrix $γ$ plays a fundamental role in describing and predicting quantum features of bosonic systems, such as Bose-Einstein condensation. The recently proposed reduced density matrix functional theory for bosonic ground states establishes the existence of a universal functional F[γ] that recovers quantum correlations exactly. Based on a novel decomposition of $γ$, we have developed a method to design reliable approximations for such universal functionals: our results suggest that for translational invariant systems the constrained search approach of functional theories can be transformed into an unconstrained problem through a parametrization of an Euclidian space. This simplification of the search approach allows us to use standard machine-learning methods to perform a quite efficient computation of both F[γ] and its functional derivative. For the Bose-Hubbard model, we present a comparison between our approach and Quantum Monte Carlo.