In the current technology node, purely classical numerical simulators lack the precision needed to obtain valid results. At the same time, the simulation of fully quantum models can be a cumbersome task in certain studies such as device variability analysis, since a single simulation can take up to weeks to compute and hundreds of device configurations need to be analyzed to obtain statistically significative results. A good compromise between fast and accurate results is to add corrections to the classical simulation that are able to reproduce the quantum nature of matter. In this context, we present a new approach of Schrödinger equation-based quantum corrections. We have implemented it using Message Passing Interface (MPI) in our in-house built semiconductor simulation framework called VENDES, capable of running in distributed systems that allow for more accurate results in a reasonable time frame. Using a 12 nm gate length Gate-AllAround Nanowire FET (GAA NW FET) as an application example, the new implementation shows an almost perfect agreement in the output data with less than a 2% difference between the cases using 1 and 16 processes. Also, a reduction of up to 98% in the computational time has been found comparing the sequential and the 16 process simulation. For a reasonably dense mesh of 150k nodes, a variability study of 300 individual simulations, can be now performed with VENDES in approximately 2.5 days instead of an estimated sequential execution of 137 days.