Simulating the behavior of non-equilibrium matter in extreme conditions of energy and density lies beyond the capabilities of classical computation alone. Toward realizing Feynman’s vision, the remarkable advances in quantum information science and technology continue to profoundly change how we understand and explore quantum many-body systems, and have brought us to the point where we are working toward simulating essential aspects of such systems using quantum computers (embedded in large HPC systems). I will discuss this progress, along with the opportunities and challenges ahead.