Reversible quantum logic synthesis is to study given quantum gates and quantum circuits of the constraints and limitations and find the smallest or smaller quantum cost to achieve the desired quantum logic circuits. The quantum logic gate functions of the matrix is indicated by the mathematical model. The synthesis and optimization are achieved simultaneously by the genetic algorithm as global search tool. Genetic algorithm is applied to quantum reversible logic synthesis. The fourth-order quantum circuit experiment has achieved good results, and further analysis of this method in high-level synthesis of quantum circuits and its application is completed.