Explore the fascinating intersection of quantum walks, scattering theory, and universal quantum computation in this one-hour lecture by David Gosset from the University of Waterloo. Delivered as part of the Workshop on Algebraic Graph Theory and Quantum Information at the Fields Institute, delve into advanced topics such as quantum walks on graphs, wave packets, and scattering phenomena. Examine the principles of reflection and universal time evolution, and learn about the S matrix formula. Discover practical applications of scattering theory, including single qubit unitary operations, multiparticle quantum walks, and two-particle scattering and routing. Gain insights into cutting-edge research that bridges the gap between theoretical quantum mechanics and practical quantum computing implementations.