Artificial intelligence-based approaches for optimization of quantum circuits

Quantum computing has emerged as a field that has attracted attention in recent years with its potential to revolutionize information processing technologies. This technology, which surpasses the limitations of traditional computers, offers unique advantages, especially in solving complex problems. However, the design and optimization of quantum circuits pose significant challenges for researchers working in this field. This thesis aims to develop innovative AI-based methods for the optimization of reversible quantum circuits in quantum computing models. The study is built on three main components and provides a comprehensive approach from the analysis of quantum circuits to their optimization and transformation into classical circuits. In the first stage, a pixel-based image processing method is developed for automatic recognition and classification of quantum circuits. KNN algorithm was applied on a comprehensive dataset consisting of 9,250 circuits with 3-7 inputs and 1-8 gates in MATLAB Simulink environment and an extraordinary accuracy rate of 99.94% was achieved. This method provided an effective solution for analyzing quantum circuits quickly and with high accuracy. In the second component, two different methodologies are developed for the transformation of quantum circuits into classical logic circuits. Boolean functions derived from quantum state tables using the Quine-McCluskey algorithm yielded results that are 100% compatible with classical circuits implemented in MATLAB Simulink. In parallel, the transformation of 2-4 input quantum circuits to logic circuits is achieved by Karnaugh mapping method and the practical applicability of this method is proven. In the third and last component, advanced meta-heuristic algorithms for quantum circuit optimization are compared. The developed adaptive genetic algorithm has achieved significant success by reducing the number of gates by 26.76% and the quantum cost by 12.88% in 24 different comparison circuits. In addition, as a result of the comprehensive comparison of ACO, PSO, ABC and GA methods, ACO has been found to be the most stable and high-performance algorithm with 2.39 standard deviation. This thesis presents original contributions such as image processing based high accuracy circuit recognition system, Quine-McCluskey and Karnaugh based methodologies for quantum-classical circuit transformation, and proven optimization techniques with meta-heuristic algorithms. The results obtained provide an important infrastructure for practical applications of quantum computing and are a guide for future research. This work was supported by TUBITAK under the 1001 project number 121E439 and Fırat University Scientific Research Projects Unit under the FUBAP project number TEKF.24.03.