Explore the fascinating intersection of quantum physics and statistical mechanics in this 23-minute lecture on integrable quantum circuits. Delve into the fundamental concepts of out-of-equilibrium physics in quantum many-body systems and quantum integrability. Discover how recent research utilizes methods from statistical mechanics of lattice models, including Yang-Baxter relation and star-triangle relation, to construct integrable quantum circuits. Learn about key topics such as solvable models, integrability, tensorization, transfer matrices, and time evolution operators. Gain insights into the theoretical foundations and practical applications of this cutting-edge field, presented by Yuan Miao at the Galileo Galilei Institute.