Accelerating large-scale linear algebra using variational quantum imaginary time evolution

Solving large sparse linear systems is a critical bottleneck in Finite Element Analysis (FEA), often limited by "fill-in" during matrix factorization. Graph partitioning can effectively reduce this fill-in, and we propose a quantum approach to this problem using Variational Quantum Imaginary Time Evolution (VarQITE).

We present a hybrid quantum/classical workflow that integrates VarQITE into the Ansys LS-DYNA multiphysics simulation software. This framework was applied to large-scale engineering challenges, including automotive roof crush, blood pump simulation, and car body vibration analysis, using meshes of up to six million elements.

We report performance results from classical simulations and experiments on IonQ Aria and IonQ Forte quantum hardware. By measuring the end-to-end wall-clock time, we demonstrate that our hybrid workflow can accelerate LS-DYNA by up to 12% on certain problems. We also introduce a classical Fiduccia-Mattheyses-inspired heuristic to refine the partition quality obtained from hardware. These results highlight a practical path for NISQ-era quantum computing to impact large-scale FEA problems.