The integration of quantum computing and artificial intelligence change the way of prediction modeling and data analysis field. This study looks at the basic ideas, design concepts, and mathematical equations behind QML, with a focus on quantum kernel techniques and quantum neural networks. Tests that compare these new approaches to the old ones reveal that they are substantially more accurate and faster at doing mathematical framework to support study. When quantum systems are mixed with regular AI models, it shows how QML can be used to solve issues that were not possible before in fields like banking, healthcare, and science study.