Quantum computing presents a transformative approach to solving complex optimization problems. It has the ability to increase the computational power by solving complex real-life problems far efficiently than classical methods. This chapter explores the integration of quantum computing and bioinspired algorithms to address challenges in optimization and machine learning. By leveraging the unique principles of quantum mechanics, the capability of bioinspired techniques such as genetic algorithms and neural networks can be enhanced, leading to significant performance improvements, particularly in high-dimensional problems with complex constraints. By conducting thorough theoretical analysis and analyzing case studies, we showcase how quantum-enhanced algorithms can tackle complex, real-world problems across various fields. We examine the role of quantum genetic algorithms in optimizing solution diversity and convergence, alongside the application of quantum computing to neural networks, which can accelerate training and enhance pattern recognition. The chapter highlights how these advancements create new paths for solving real-world problems in artificial intelligence, robotics, and beyond, while also identifying future research opportunities in this evolving area.