Exploiting Quantum Computing Advantages: A Hybrid Multiscale Approach

• Applicants: Professor Dr.-Ing. Markus Kästner; Professor Dr. Daniel Peterseim
• Subject Area: Mechanics ; Mathematics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 571768116

The integration of quantum computing with classical high-performance simulations promises to transform the field of computational mechanics. While finite element methods are central to current simulation methods, they often struggle to capture the complex multiscale phenomena and statistical microstructures essential for increasingly accurate materials modeling. To address this limitation, this proposal exploits quantum parallelism within a hybrid quantum-classical framework specifically tailored for multiscale mechanical simulations, while carefully mitigating the inherent challenges of quantum systems, which are prone to hardware noise and measurement uncertainties. Our approach focuses on three main goals. First, we will develop a quantum finite element method by designing efficient quantum algorithms for both linear and nonlinear elasticity, addressing challenges such as variable coefficients and nontrivial domains, while incorporating effective preconditioners. Second, we aim to generate synthetic material microstructures on quantum computers by adapting classical reconstruction techniques, compressing detailed material information into a few key statistical parameters, and using quantum random number generation and statistical estimation to exploit quantum parallelism. Third, we propose to establish a hybrid FE^2 multiscale framework that integrates quantum computation of representative volume elements with classical macroscopic finite element simulations. In our approach, only effective quantities such as averaged strains and stresses are measured from the quantum simulation, thus preserving the quantum advantage while overcoming the information bottleneck at the quantum-classical interface. This research, based on an interdisciplinary collaboration between experts in computational mechanics and mathematics, is timely given the expected scale-up of quantum hardware. Although current noisy intermediate-scale quantum (NISQ) devices have limited accuracy, our hybrid strategy is designed to make effective use of these early-stage systems, serving as a proof-of-concept that will improve significantly as quantum hardware matures.

• DFG Programme: Research Grants