EAGER: Quantum Algorithms for Solving Computational Mechanics Problems in Hybrid Quantum Computers

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Quantum computing has received tremendous national and international attention in the past few years. This is because research in physics, mathematics, and computer science, as well as hardware and software technology have achieved several critical milestones that demonstrate the potential of quantum computing in revolutionizing many aspects of how and what we compute in engineering, science, and beyond. Despite such significant advancements, solving important engineering problems with quantum computing remains a distant prospect with several fundamental research questions remain to be addressed from the hardware and software, and from the quantum algorithm development perspectives. This Early-Concept Grants for Exploratory Research (EAGER) research award will explore quantum algorithms for solving the mechanical response of engineering materials and structures. The finite element method is the most successful and commonly used approach to predict the mechanical behavior of materials and structures. The focus of this research is to study whether and how novel quantum finite element algorithms could outperform classical finite element algorithms in solving mechanics problems. As part of the grant, educational content will also be developed to introduce the use of quantum computing in solving classical engineering problems to a broad section of the engineering community. The objective of this EAGER research is to devise and investigate quantum computing algorithms for solving continuum mechanics problems in Noisy Intermediate-Scale Quantum computers that are available today or will be available soon. This research will establish and analyze algorithms for evaluating linear elasticity problems subjected to static loading conditions. The specific research objectives to achieve the stated goal are: (1) to develop a framework for the algorithmic structure of quantum finite element method based on the Variational Quantum Linear Solver approach; (2) to analyze the computational performance of the quantum algorithms relative to classical algorithms in terms of complexity, accuracy and convergence; and (3) to verify and validate the performance of the proposed quantum framework using existing quantum computers with gate-based architectures and quantum computing simulators. Since some of the solution procedures for the finite element method either require or are better suited for classical computers, and since currently available quantum computers are limited in the operations they can perform, this research will study algorithms suitable for hybrid (classical-quantum) computers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.