Quantum Algorithms for Numerical PDEsColloquium CRC 1720

by Daniel Peterseim

Tuesday Jan 20, 2026, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Solving partial differential equations (PDEs) numerically leads to very large linear and nonlinear systems, particularly in high-dimensional and multiscale settings, where classical algorithms face significant computational challenges. Quantum computing offers new algorithmic possibilities for addressing such problems. In this talk, we derive examples of quantum algorithms in this context that address key challenges such as nonunitarity, nonlinearity, and preconditioning. For linear elliptic PDEs with multiscale features and high dimensionality, we present quantum solvers inspired by classical multilevel preconditioning techniques. Using targeted amplitude amplification techniques, we also derive quantum algorithms for solving large nonlinear systems. Rigorous runtime bounds establish a theoretical quantum advantage, and proof-of-concept experiments on quantum simulators and noisy quantum hardware provide a practical assessment of current capabilities.