Reduced-density-matrix functional theory, many-body quantum resources, and machine learning

Reduced-density-matrix functional theory (RDMFT) is based on a bijective map between the wave function of an electronic or a bosonic system and the corresponding one-particle reduced density matrix (1-RDM) for ground states. We show that this map can be used to develop a functional-theoretical framework for quantum information. For instance, quantum Fisher information functionals correspond to the derivative of the 1-RDM universal functional with respect to the coupling strengths, revealing thus the ability of the RDMFT to capture itself high-level quantum correlations. We showcase this relation with the Bose-Hubbard model. In addition, based on a decomposition of the 1-RDM we 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 and its functional derivative.