The stability and reliability of financial systems throughout the world are seriously threatened by financial fraud. Traditional rule-based fraud detection systems struggle to stay current with evolving fraud patterns because they cannot keep pace with new fraud strategies. As a result, using supervised learning algorithms to improve fraud detection skills is becoming more and more popular. The purpose of our study is to compare the efficacy of various machine learning approaches in detecting financial fraud. The study evaluates quantum graph neural network (QGNN) algorithms, including Variational Quantum Classifier (VQC), Quantum Support Vector Classifier (QSVC), Estimator Quantum Neural Network (EQNN), and Sampler Quantum Neural Network (SQNN) for financial fraud detection. The QSVC model excels in performance compared to the other three models. The QSVC achieves an accuracy score of 91.3%, a precision score of 92.6%, a recall score of 86.1%, and an F1-score of 89.2%. As an outcome, it makes sure that many fraudulent transactions are found without labeling an excessive number of valid transactions as fraudulent.