In this work we present a comparative study of several GPU accelerated elements of a Genetic Algorithm (GA) for the synthesis of quantum circuits on the level of Electro-Magnetic (EM) pulses. The novelty in our approach is in the implementation: a) a completely GPU accelerated quantum simulator, b) GPU accelerated genetic operators and fitness evaluation and finally c) a set of GPU implemented optimizations for GPU accelerated evolutionary search optimization for the synthesis of quantum circuits. The reason for using EM pulses model for synthesis is the observation that this model requires the largest amount of elementary rotations to implement quantumlogic gates and thus provides a good measure to evaluate the efficiency of the acceleration by the GPU processor. The reason to use a GA is the advantage of pseudo evolutionary search in very large problem space such as the one defined by the Ising model where the EM realized quantum circuits are evolved. As a result of the several GPU optimizations several new circuits implementations are presented and their cost is compared to thecurrently known Ising model implementations.