Large-scale GW calculations are the state-of-the-art approach to accurately describe many-body excited-state phenomena in complex materials. This is critical for novel device design but due to their extremely high computational cost, these calculations often run at a limited scale. In this paper, we present algorithm and implementation advancements made in the materials science code BerkeleyGW to scale calculations to the order of over 10,000 electrons utilizing the entire Summit supercomputer at OLCF. Excellent strong and weak scaling is observed, and a 105.9 PFLOP/s double-precision performance is achieved on 27,648 V100 GPUs, reaching 52.7% of the peak. This work for the first time demonstrates the possibility to perform GW calculations at such scale within minutes on current HPC systems, and leads the way for future efficient HPC software development in materials, physical, chemical and engineering sciences.