Principles and methodologies of quantum algorithmic gate-based design on small quantum computer described. The possibilities of quantum algorithmic gates simulation on classical computers discussed. A new approach to a circuit implementation design of quantum algorithm gates for fast quantum massive parallel computing presented. SW & HW support sophisticated smart toolkit of supercomputing accelerator of quantum algorithm simulation on small quantum programmable computer algorithm gate (that can program in SW to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates) described