How Mathematical Analysis Can Help Better Understand Quantum Algorithms

Explore a 52-minute lecture by Di Fang from Duke University examining how mathematical analysis enhances our understanding of quantum algorithms, presented at IPAM's Dynamics of Density Operators Workshop at UCLA. Recorded in April 2025, this talk delves into two key areas where mathematical analysis provides deeper insights into quantum dynamics simulation. First, discover how semiclassical analysis and discrete microlocal analysis explain superconvergence phenomena in quantum Magnus algorithms for unbounded Hamiltonian simulation. Then learn how hypocoercivity concepts from kinetic theory can be applied to better understand open quantum systems dynamics. This presentation highlights the intersection of advanced mathematical techniques and quantum computing, demonstrating how theoretical analysis supports one of quantum computing's most significant applications.