The intricate nature of lung cancer treatment poses considerable challenges upon diagnosis. Early detection plays a pivotal role in mitigating its escalating global mortality rates. Consequently, there are pressing demands for robust and dependable early detection and diagnostic systems. However, the technological limitations and complexity of the disease make it challenging to implement an efficient lung cancer screening system. AI-based CT image analysis techniques are showing significant contributions to the development of computer-assisted detection (CAD) systems for lung cancer screening. Various existing research groups are working on implementing CT image analysis systems for assessing and classifying lung cancer. However, the complexity of different structures inside the CT image is high and comprehension of significant information inherited by them is more complex even after applying advanced feature extraction and feature selection techniques. Traditional and classical feature selection techniques may struggle to capture complex interdependencies between features. They may get stuck in local optima and sometimes require additional exploration strategies. When applied to a prominent feature space, traditional techniques may also struggle with combinatorial optimization problems. This paper proposed a methodology to overcome the existing challenges by applying feature extraction using Vision Transformer (FexViT) and Feature selection using the Quadratic unconstrained binary optimization (FSelQUBO) technique. This algorithm shows better performance when compared with other existing techniques. The proposed methodology showed better performance as compared to other existing techniques when evaluated by applying necessary output measures, such as accuracy, Area under roc (receiver operating characteristics) curve, precision, sensitivity, and specificity, obtained as 94.28%, 99.10%, 96.17%, 90.16% and 97.46%. The further advancement of CAD systems is essential to meet the demand for more reliable detection and diagnosis of cancer, which can be addressed by leading the proposed quantum computation and growing AI-based technology ahead.