Prof. Caglar Oskay
Department of Civil and Environmental Engineering
Vanderbilt University

Quantum Computing Algorithms for the Finite Element Method

ABSTRACT: In this presentation, the speaker will highlight recent advancements toward achieving the goal of implementing a general-purpose finite element analysis platform suitable for use on hybrid (classical/quantum) and fault-tolerant quantum devices. The hybrid algorithms leverage variational quantum principles, where the discretized system of equations is reformulated as an optimization problem. In this framework, classical optimizers are employed to solve the optimization problem, while the evaluation of the cost function and its gradients are performed on a quantum computer. The speaker will describe algorithms designed to solve both linear problems and nonlinear problems, such as those encountered in hyperelasticity. In addition, the talk will highlight efforts aimed at implementation on future fault-tolerant quantum computers. Specifically, the speaker will explore methods that utilize quantum linear system solvers in conjunction with a novel Pauli string decomposition algorithm. It will be demonstrated that the proposed decomposition algorithm achieves exponential speedup when compared to general-purpose algorithms typically used for sparse solvers.

BIOGRAPHY: Dr. Caglar Oskay is Cornelius Vanderbilt Professor of Engineering, Department Chair and Professor of Civil and Environmental Engineering, and Professor of Mechanical Engineering at Vanderbilt University. Prof. Oskay received Master of Science in Applied Mathematics, and Master of Science and Ph.D. in Civil Engineering from Rensselaer Polytechnic Institute. Professor Oskay’s research focuses on bringing understanding to nonlinear mechanical response of materials and structures through multi-scale computational modeling and simulation, specifically computational characterization of the failure response of heterogeneous systems that involve multiple temporal and spatial scales subjected to extreme and/or dynamic loading conditions, and development of enabling computational methodologies. More recently, his research focus has been on development of algorithms and methodologies for solving mechanics problems in non-traditional computing platforms. Dr. Oskay served as Program Director for the Engineering for Civil Infrastructure Program at the National Science Foundation between 2019-2021. He is a fellow of The American Society of Mechanical Engineers, US Association of Computational Mechanics, and American Society of Civil Engineers' Engineering Mechanics Institute.