Quantum ESPRESSO is an integrated suite of Open-Source computer codes for electronic-structure calculations and materials modeling at the nanoscale. It is based on density-functional theory, plane waves, and pseudopotentials.
There is no minimum, the resources only limits the size of the systems you can explore.
QE Runs on almost every conceivable current architecture (really! also cell phones and playstation): from large parallel machines to workstations and single PCs running Linux, Windows, Mac OS-X, including clusters of 32-bit or 64-bit Intel or AMD processors with various connectivity .