Abstarct: Current silicon transistor technology faces challenging challenges, such as high power consumption and reduced size. Quantum Cellular Automata (QCA) is one of the new proposed technologies that not only provides a solution on a nanoscale, but also a new method for calculating and transferring information. The design approach of these circuits is very different from the traditional design of logical circuits. In CMOS circuits that are composed of AND and OR and NOT, Using a Karnaugh maps (K-maps)-baxsed design will simplify the circuit and optimize the use of the baxse elements. Of course, the key elements of QCA technology are the logical majority gate with inverted (NOT). Therefore, the classic design of QCA-baxsed circuits baxsed on the Carnot table leads to an increase in the number of cells used in the circuit and the design is non-optimal. The genetic algorithm has been considered by researchers as a soft calculation method for reducing the size of the circuit and optimal design. The structure of chromosomes formed in these methods is a tree structure that will also be very complex for a three-input circuit. Of course, the use of some basic information obtained from the Karnaugh's symmetry feature can solve this problem. In this thesis, first, the basic patterns for optimal design of circuits with three inputs and one output are found. Using these baxse patterns reduces the complexity of the chromosomal structure and, as a result, increases the speed of the genetic algorithm in solving the optimal design problem for QCA circuits. It should be noted that by finding baxse patterns for more input circuits, this method can be generalized to them. The results are investigated by QCA designer software. Which indicates the accuracy of the designs and accuracy in the implementation.