Quantum-enhanced and data-integrated PDE solution methods

Recent advances in quantum computing indicate the potential to solve (spatially/temporally discretized) PDEs with up to exponentially better complexity scaling compared to classical algorithms. While implementations of pure quantum algorithms on real hardware showed that noisy intermediate-scale quantum (NISQ) computers are currently limited to small problem sizes, variational quantum (VQ) methods handle the NISQ setting much better and allow for medium-sized problems to be solved, usually trading exponential for polynomial speedup. VQ circuits and quantum kernel methods naturally fit into machine learning (ML) settings as an entryway into data-integrated problem solving, leading to quantum ML (QML) approaches.

We aim to implement, adapt, and test pure and VQ algorithms as well as QML approaches to solving PDEs from structural mechanics and fluid dynamics, and to identify subroutines of classical solvers that can be outsourced to quantum accelerators especially in heterogeneous HPC settings. The overarching goal is to identify acceleration potentials and near-term applicability by testing the methods on relevant prototypical PDEs and executing them on real devices.