Explore the dynamics of open quantum systems in quantum computing through this insightful lecture presented at IPAM's Quantum Algorithms for Scientific Computation Workshop. Delve into the challenges posed by environmental noise on quantum gate operations and its impact on algorithm outcomes. Discover efficient methods for simulating open quantum system dynamics, learn how quantum channels can be utilized to represent non-Markovian quantum dynamics, and investigate the potential for scaling noise within quantum circuits using these simulation techniques. Gain valuable insights into the broader implications of open quantum systems beyond the conventional time-dependent Schrödinger equation, and understand their significance in real-world quantum computing scenarios.