Diverse cases regarding the impact, with its related factors, of the COVID-19 pandemic on mental health have been reported in previous studies. In this study, multivariable datasets were collected from 751 college students who could be easily affected by pandemics based on the complex relationships between various mental health factors. We utilized quantum annealing (QA)-based feature selection algorithms that were executed by commercial D-Wave quantum computers to determine the changes in the relative importance of the associated factors before and after the pandemic. Multivariable linear regression (MLR) and XGBoost models were also applied to validate the QA-based algorithms. Based on the experimental results, we confirm that QA-based algorithms have comparable capabilities in factor analysis research to the MLR models that have been widely used in previous studies. Furthermore, the performance of the QA-based algorithms was validated through the important factor results from the algorithms. Pandemic-related factors (e.g., confidence in the social system) and psychological factors (e.g. decision-making in uncertain situations) were more important in post-pandemic conditions. Although the results should be validated using other mental health variables or national datasets, this study will serve as a reference for researchers regarding the use of the quantum annealing approach in factor analysis with validation through real-world survey dataset analysis.