Optimizing tensor contractions for nuclear correlation functions

Abstract

Nuclear correlation functions reveal interesting physical properties of atomic nuclei, including ground state energies and scattering potentials. However, calculating their values is computationally intensive due to the fact that the number of terms from quantum chromodynamics in a nuclear wave function scales exponentially with atomic number. In this thesis, we demonstrate two methods for speeding up this computation. First, we represent a correlation function as a sum of the determinants of many small matrices, and exploit similarities between the matrices to speed up the calculations of the determinants. We also investigate representing a correlation function as a sum of functions of bipartite graphs, and use isomorph-free exhaustive generation techniques to find a minimal set of graphs that represents the computation.