With the increasing complexity of projects and the volume of data in Software Engineering (SE), the need for efficient and accurate data analysis techniques has become crucial. Classification algorithms play a vital role in various SE tasks, such as bug detection, software quality prediction, and requirements classification. Quantum computing offers a new paradigm with the potential to overcome classical computational limitations for certain types of problems. This research proposes the design and implementation of a kernel-based quantum classification algorithm (also known as Quantum Support Vector Machine - QSVM) tailored for data analysis in the SE domain. We will discuss the fundamental principles behind quantum feature mapping and quantum kernel matrices, and demonstrate its implementation using quantum computing libraries. As a case study, the designed algorithm will be tested on a software bug detection dataset, comparing its performance with classical kernel-based classification algorithms like Support Vector Machine (SVM). The result of the comparison show that QSVM is superior in terms of accuracy, precision, recall, and F1-score compared to SVM.