Explore quantum computation fundamentals in this lecture from the University of Chicago's Bill Fefferman, focusing on the theory of near-term quantum advantage and its implications for experimental quantum computing. Delve into the critical goal of demonstrating quantum computations that surpass classical computer capabilities, examining both theoretical foundations and practical applications. Learn about current evidence supporting near-term quantum experiments' potential to solve classically intractable problems, while gaining insights into classical simulation algorithms for these experiments. Access comprehensive lecture notes and problem sets to reinforce understanding of quantum computing concepts, linear algebra applications, and quantum theory in high complexity scenarios. Part of the 2023 PCMI Graduate Summer School program, this lecture connects to a broader curriculum covering quantum learning, information theory, error-correcting codes, and Hamiltonian complexity.