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Explore a comprehensive lecture by Scott Aaronson from the University of Texas that outlines a research agenda for advancing quantum computation through three key objectives: implementing quantum computations on near-term NISQ devices, developing algorithms resistant to classical simulation, and ensuring classical verification methods. Learn about the intricate relationship between random quantum circuits and post-selected behaviors, with specific focus on generating verifiable outputs. Delve into concrete open problems within quantum computing advantage, where recent experiments demonstrate quantum computers significantly outperforming classical counterparts. Gain insights into the mathematical foundations necessary for building and analyzing near-term quantum devices, including quantum learning, information theory, linear-algebraic algorithms, quantum error-correcting codes, and the complexity theory of random circuits and Hamiltonians.
