The computational efficiency of a state of the art ab initio quantum transport (QT) solver, capable of revealing the coupled electro-thermal properties of atomically-resolved nano-transistors, has been improved by up to two orders of magnitude through a data centric reorganization of the application. The approach yields coarse-and fine-grained data-movement characteristics that can be used for performance and communication modeling, communication-avoidance, and dataflow transformations. The resulting code has been tuned for two top-6 hybrid supercomputers, reaching a sustained performance of 85.45 Pflop/s on 4,560 nodes of Summit (42.55% of the peak) in double precision, and 90.89 Pflop/s in mixed precision. These computational achievements enable the restructured QT simulator to treat realistic nanoelectronic devices made of more than 10,000 atoms within a 14$\times$ shorter duration than the original code needs to handle a system with 1,000 atoms, on the same number of CPUs/GPUs and with the same physical accuracy.