Quantum Computing Algorithms for Nonlinear and History-Dependent Solid Mechanics

Vanderbilt University, Nashville TN

Investigators

Abstract

Quantum computing offers to transform the way engineering computations are performed and promises to allow the engineering community to solve very large and complex mechanics problems that are intractable with classical computers. Using quantum mechanics principles such as superposition and entanglement, quantum computing could lead to both an exponential growth in memory capacity, and algorithmic speed-ups compared to existing “classical” computers. This study looks to devise new quantum computing algorithms for solving mechanics problems that involve rate-dependent, history-dependent and nonlinear materials. Such materials are frequently used in a wide range of applications such as soft robotics, micro-architected structures, and biomedical systems. Increasing predictive modeling and simulation of such important applications is critical to ensuring American competitiveness from commercial and security perspectives. The quantum computing algorithms that look to be devised in this research will be rigorously tested in quantum simulators and real quantum devices to establish the promise and limitations of quantum computing for solving nonlinear mechanics problems. As a part of this study, a computational mechanics community will be established, whose members are collectively committed to advancing quantum computing for mechanics. This community building will be performed in collaboration with existing technical and professional organizations. This study seeks to (1) develop and characterize variational quantum algorithms to simulate the deformation response of hyperelastic and elasto-viscoplastic solids; and (2) implement, verify and validate these algorithms and understand the relationships between the characteristics of the quantum algorithms and their performance in terms of accuracy and efficiency. The research looks to establish the computational and algorithmic complexity of the algorithms and quantify the computational speedup possible over classical solvers. This research aims to discover quantum algorithms integrated with nonlinear finite element method, which will account for the Lagrangian nature of the solid mechanics problems and the morphological complexity of typical problem domains. This research also intends to uncover efficient solution methodologies for incorporating the complex nonlinear constitutive forms associated with hyperelastic and elasto-viscoplastic material behavior, and account for the presence of history variables in quantum setting. 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.