Physics Quantum Science & Engineering Seminar | Title: End-to-End Quantum PDE Algorithms for Direct Observable Estimation | Speaker: Dr. Xiantao Li (Pennsylvania State University)

Assessing quantum advantage for partial differential equations requires accounting for data preparation, quantum computation, and the estimation of physical observables such as averages, fluxes, and energies. Spatial derivatives can introduce substantial mesh dependence in both the solver and the readout, even when only a few quantities of interest are needed. This talk presents multilevel quantum algorithms that estimate these quantities directly for elliptic and parabolic PDEs. The key idea is to encode fine–coarse cancellation before measurement, allowing small corrections to offset mesh-dependent costs. Under suitable approximation and quantum-access assumptions, the resulting algorithms reduce polynomial dependence on spatial resolution to polylogarithmic dependence. I will discuss connections with multigrid, hierarchical bases, and quantum preconditioning, and outline opportunities in stochastic dynamics, PDE inference, and design under uncertainty.

Bio: 

Dr. Xiantao Li is a Professor of Mathematics at Pennsylvania State University. He obtained his Ph.D. from the University of Wisconsin-Madison. His research lies at the intersection of applied mathematics and computational physics, focusing on developing rigorous mathematical foundations for complex computational problems. Prof. Li’s current research specializes in the design and numerical analysis of quantum computing algorithms, with applications to scientific computing.