Explore quantum algorithms for continuous sampling and optimization problems in this 55-minute lecture by Ruizhe Zhang from the Simons Institute for the Theory of Computing. Delve into quantum speedups for sampling from high-dimensional log-concave distributions and their applications in estimating normalizing constants. Examine the approximately convex optimization problem and its implications for robust optimization and nonconvex optimization. Discover a quantum algorithm that outperforms classical counterparts and its application to the quantum version of the zeroth-order stochastic convex bandit problem. Gain insights into the potential of quantum computing for solving fundamental computational challenges in statistics, machine learning, and physics.