Project management is changing drastically due to the integration of artificial intelligence (AI) and quantum computing (QC), redefining traditional methods. This study explores Quantum AI (QAI) and AI-driven solutions to tackle enduring issues, including resource inefficiencies, schedule delays, and budget overruns. These technologies significantly enhance project outcomes by leveraging predictive analytics, dynamic scheduling, and high-dimensional optimization. A comparative analysis of prominent case studies, including the Crossrail Project, East Side Access, and the Montreal Olympics, highlights the superior performance of AI and QAI techniques compared to conventional methods. The study shows that QAI can cut delays by 60%, optimize resource allocation with 83% efficiency, and eliminate cost overruns by up to 40% using Monte Carlo simulations and Failure Mode Effects Analysis. These results demonstrate that quantum artificial intelligence is a ground-breaking tool for handling intricate, interconnected project settings. Additionally, this study emphasizes how QAI is scalable and applicable across industries, especially in fields that need real-time optimization and high-dimensional data processing. The proposed hybrid quantum-classical paradigm provides practical solutions and sets a benchmark for efficiency, scalability, and risk mitigation in project management.