Quantum Bayesian Machine Learning (QBML) is an emerging field at the intersection of quantum computing, machine learning, and financial sciences. It has enabled the development of more accurate predictive models, optimal risk management, and intelligent portfolio optimization. With the rapid growth of data and increasing complexity of financial markets, classical computational models are no longer sufficient to meet the demands of modern technological needs. Consequently, combining the power of quantum computing with machine learning algorithms has created opportunities to develop models with enhanced accuracy and efficiency. QBML has garnered attention from researchers due to its ability to manage uncertainty precisely and provide probabilistic inferences, particularly in market prediction, risk management, and portfolio optimization. Despite significant theoretical advancements, challenges such as quantum hardware limitations, algorithmic complexity, poor data quality, and the gap between theory and practical applications have hindered widespread adoption of these technologies. Systematic and Bibliometric analyses indicated that while the field is rapidly growing, there remain serious gaps in practical implementation and algorithm performance evaluation. The findings of this study emphasized that fully exploiting the potential of QBML in financial systems requires developing hardware and algorithms, conducting empirical research, and fostering interdisciplinary collaborations. Moreover, the scientific mapping conducted in this study provided a useful framework to guide future research and develop practical applications that can transform analytical and decision-making methods in finance.
