  The one-body reduced density matrix $\gamma$ 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 $\mathcal{F}[\gamma]$ that recovers quantum correlations
exactly. Based on a novel decomposition of $\gamma$, 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 $\mathcal{F}[\gamma]$ and its
functional derivative. For the Bose-Hubbard model, we present a comparison
between our approach and Quantum Monte Carlo.

Quantum Physics;Computational Physics