In this study, we develop a novel quantum machine learning (QML) framework to analyze cybersecurity vulnerabilities using data from the 2022 CISA Known Exploited Vulnerabilities catalog, which includes detailed information on vulnerability types, severity levels, common vulnerability scoring system (CVSS) scores, and product specifics. Our framework preprocesses this data into a quantum-compatible format, enabling clustering analysis through our advanced quantum techniques, QCSWAPK-means and QkernelK-means. These quantum algorithms demonstrate superior performance compared to state-of-the-art classical clustering techniques like k-means and spectral clustering, achieving Silhouette scores of 0.491, Davies-Bouldin indices below 0.745, and Calinski-Harabasz scores exceeding 884, indicating more distinct and well-separated clusters. Our framework categorizes vulnerabilities into distinct groups, reflecting varying levels of risk severity: Cluster 0, primarily consisting of critical Microsoft-related vulnerabilities; Cluster 1, featuring medium severity vulnerabilities from various enterprise software vendors and network solutions; Cluster 2, with high severity vulnerabilities from Adobe, Cisco, and Google; and Cluster 3, encompassing vulnerabilities from Microsoft and Oracle with high to medium severity. These findings highlight the potential of QML to enhance the precision of vulnerability assessments and prioritization, advancing cybersecurity practices by enabling more strategic and proactive defense mechanisms.