Watch a conference talk from TQC 2023 exploring efficient methods for learning ground and thermal states within phases of matter. Dive into advanced quantum information theory as Daniel S. França presents novel techniques for estimating Gibbs state parameterization and learning local observable expectation values in thermal/quantum phases. Learn about exponential improvements in sample complexity for learning properties of quantum systems, including ground states with local topological order and thermal phases showing correlation decay. Explore innovative tools like robust shadow tomography algorithms, Gibbs approximations, and transportation cost inequalities while understanding how to minimize sampling requirements for precise quantum state estimation. Follow along as the presentation covers key topics from Hamiltonian protocols and Lipschitz observables to local indistinguishability and learning algorithms, demonstrating significant advances in quantum state learning efficiency.