Di Fang - How Mathematical Analysis can help better understand quantum algorithms - IPAM at UCLA

Recorded 28 April 2025. Di Fang of Duke University presents "How Mathematical Analysis can help better understand quantum algorithms" at IPAM's Dynamics of Density Operators Workshop.
Abstract: The simulation of quantum dynamics, originally envisioned as a primary motivation for quantum computing, remains one of its most significant applications. It also serves as a crucial subroutine in many quantum algorithms for scientific computing. In this talk, we will explore two instances where mathematical analysis provides deeper insights into quantum algorithms for dynamics simulation. First, we will discuss how semiclassical analysis and discrete microlocal analysis help explain the surprising superconvergence phenomena observed in quantum Magnus algorithms for unbounded Hamiltonian simulation. In the second part, we will discuss how hypocoercivity, a concept from kinetic theory, can be leveraged to gain a better understanding of the dynamics of open quantum systems.