Understanding and predicting the behavior of complex quantum systems is a fundamental challenge in physics, chemistry, and materials science. Accurately modeling strongly correlated materials, catalysts, and superconductors requires solving computationally intractable quantum many-body problems, where classical methods face exponential scaling. In this talk, I will present how High-Performance Computing (HPC), Artificial Intelligence (AI)/Machine Learning (ML), and Quantum Algorithms might revolutionize computational approaches to quantum matter. HPC enables large-scale quantum simulations, AI/ML can accelarate optimization and yield data-driven insights, while quantum computing offers novel paradigms to potentially tackle problems beyond classical feasibility. I will discuss applications ranging from transition metal clusters releven to molecular catalysts and model systems for superconductors and quantum materials, highlighting how these computational techniques complement experimental and theoretical research.