Development of deep learning based circuit analysis and fault detection methods in quantum computing models

The number of studies on quantum computers has been increasing rapidly in recent years due to their potential to overcome complex problems. Quantum circuits are formed by the combination of qubits. While traditional gates such as AND, OR, NAND, NOR, XOR, and XNOR are used in combinational circuits, Feynman, Toffoli, and Fredkin gates are used in quantum circuits. These gates have specific entrances and exits. Quantum circuits with different input, output, and gate numbers are created using quantum gates. Today, studies are being carried out in many application areas using quantum circuits. Quantum circuits are designed and tested through simulation programs. During testing, errors may occur on quantum circuits and the truth table may be produced incorrectly. In this thesis study, deep learning-based methods have been developed for circuit analysis and error detection in quantum circuits. Within the scope of the thesis, scientific contributions are made on three main points. Firstly, a data set was created for analyzing quantum circuits and fault detection. 9250 sample "tfc" files were created using the MATLAB2020A program. Quantum circuit diagrams were obtained from these "tfc" files using the "RCViewer" simulation program. Quantum circuits are labeled according to the number of gates and inputs. Gates and inputs were detected for the analysis of the labeled quantum circuits. The number of gates and inputs in quantum circuits was calculated using the YOLO algorithm. The proposed YOLO algorithm was run for 2800 iterations and 87.1% mAP was obtained for the training-test data ratio of 80:20. Secondly, feature extraction in quantum circuits using deep learning-based models and the number of inputs and gates were determined with a Support Vector Machine. AlexNet, DarkNet, GoogleNet, Vgg, and ResNet models were used and feature extraction was performed from quantum circuit images. The data set used consists of 9250 circuits with 3-7 input numbers and 1-8 gate numbers. In the proposed method, results were obtained for a total of 40 classes by using the gate and input numbers together. The highest accuracy of 99.81% was calculated for the DarkNet53 + SVM algorithm and 99.78% for the ResNet101 + SVM algorithm. Finally, an error detection method has been developed using truth tables in quantum circuits. The number of gates and inputs in quantum circuits was determined and a truth table was produced. The truth table of the quantum circuit for which the truth table is produced is also obtained by "RCViewer" simulation from the "tfc" file. The truth table obtained in the developed application is compared with the truth table obtained from the "RCViewer" simulation and errors are detected. As a result, in this master's thesis study, methods have been developed for the analysis and error detection of quantum circuits. Performance results of the proposed methods are presented. The studies carried out within the scope of the thesis were supported by TÜBİTAK 1001 project No. 121E439.