Moment Optimization in the Navascu'es-Pironio-Ac'in Hierarchy
The Navascués–Pironio–Acín (NPA) hierarchy uses semidefinite programming relaxations to bound solutions for quantum optimization problems, but increasing the hierarchy level becomes computationally too expensive due to combinatorial growth in required moments. This work reframes moment selection as a subset selection problem and develops three methods—Parallel Tempering, Restricted Boltzmann Machine (RBM), and Bayesian Optimization—to find the best moments within a fixed computational budget.