The ab initio GW plus Bethe-Salpeter equation approach is particularly well-suited for exascale high performance computing systems–more so, for example, than Kohn—Sham Density functional theory (DFT). This chapter describes optimization strategy and optimization process for the BerkeleyGW software package toward performant execution on exascale systems. The ab initio GW method and its implementation within the BerkeleyGW software package captures excited-state properties of materials in quantitatively accurate way, which fundamentally cannot be accomplished with standard Kohn—Sham DFT methods. Calculations beyond Kohn—Sham DFT are required for computation of excited-state material properties such as bandgaps, band-alignments at interfaces between materials, conductivity, and optical absorption spectra. Of the various computational bottlenecks in the BerkeleyGW application, the computation of self-energy within the GPP approximation provides the richest optimization space. In general out-performing Haswell on Knights Landing requires at least two of the following qualities: efficient thread scaling, efficient vectorization and effective use of the high-bandwidth memory, which two depends on the arithmetic intensity of application.