Optimizing QAOA parameters for a two-city traveling salesman problem using machine learning

In this thesis, the solution of the two cities Traveling Salesman Problem (TSP) using the Quantum Approximate Optimization Algorithm (QAOA) and the optimization of QAOA parameters through machine learning are discussed. QAOA is a quantum computing method that provides effective solutions to classical optimization problems. The aim of the study is to optimize the gamma and beta parameters of the QAOA method and predict these parameters effectively using different machine learning models. In the initial phase, quantum circuits were created using the QAOA method for the two-city TSP problem and simulations were performed using Aer Simulator. During the optimization process, various initial values for the gamma and beta parameters were tested, and the parameters that provided the best performance were determined. The optimized gamma and beta values were sampled according to the problem distance and solution probabilities (sol_rates) were calculated. Data for optimization was prepared by performing calculations with 5000 different parameters. The obtained data were scaled using StandardScaler, and Neural Network Regression, Support Vector Machines (SVM), and Random Forest Regression models were created with this data. The models were trained to predict the gamma and beta parameters to make the solution probabilities greater than 0.2 for a given distance value. During the training and testing phases, the performance of the models was evaluated, and very low R² and very high Mean Squared Error (MSE) values were obtained. The predictions of the SVM and Random Forest models were tested on 10 different problems using quantum computers and Aer Simulation. As a result, it was observed that the SVM model approached the correct solution in 4/10 cases, while the Random Forest model approached the correct solution in 3/10 cases. Despite these low performance values, the results obtained in the study indicate that more successful results can be achieved in the future by optimizing the machine learning parameters and improving the model inputs and outputs. The successful prediction of the parameters obtained with the QAOA method using machine learning methods is considered an important step in solving classical optimization problems with quantum computing methods. This study not only demonstrates the use of the QAOA method in optimization problems but also reveals the potential of integrating quantum and classical computing methods. Future studies can be extended with similar approaches on more complex TSP problems and other optimization problems. Keywords: Quantum computer, Quantum algorithm, Optimization, Travelling Salesman Problem (TSP), Qubit