Explore the fundamental concepts of quantum circuit dynamics in this lecture from the "Periodically and Quasi-Periodically Driven Complex Systems" program. Delve into the many-body aspects of quantum circuits as presented by Austen Lamacraft from the International Centre for Theoretical Sciences. Gain insights into the interplay between closed quantum systems, open quantum systems, and gauge theory of coupling between matter and radiation. Learn about topics such as terahertz and infrared driven quantum matter, shaken optical lattices, Floquet time crystals, and localization-delocalization physics in quasi-periodically driven systems. Discover how this interdisciplinary field combines theoretical approaches with experimental quantum simulations to tackle complex problems beyond the reach of brute force numerical calculations.