Past Event: Oden Institute Seminar

FEq: finite elements on quantum annealers

Suvranu De, J. Erik Jonsson '22 Distinguished Professor of Engineering, Department Head and Director, Center for Modeling, Simulation and Imaging in Medicine, Rensselaer Polytechnic Institute

Abstract

** This seminar will be presented LIVE in person in POB 6.304 and streamed via Zoom. **

Quantum computing is a rapidly developing area of research with potential applications extending over scientific and engineering computations. Current work in quantum computing for partial differential equations is sparse and limited in scope with presently available Noisy Intermediate Scale Quantum (NISQ) hardware. Quantum annealers are NISQ devices designed to minimize the Ising Hamiltonian. Current demonstrated applications of quantum annealers suffer from various inefficiencies. Here, we explore the application of quantum annealing to finite element problems and develop a unified general framework to iteratively solve linear partial differential equations with example problems solved on the D-Wave quantum annealer. A general methodology to map finite element problems to the Ising Hamiltonian is developed. Novel iterative procedures - single step “2N  Search” and “3N  Search” approaches, and a two-step “Hyperoctant Search” approach are developed to iteratively solve the finite element minimization problem using quantum annealers. An exponential increase in cosine measures is demonstrated, highlighting the potential for quantum annealing to iteratively solve minimization problems with classically intractable number of unknowns.

Biography

Suvranu De is the J Erik Jonsson ’22 Distinguished Professor of Engineering at Rensselaer Polytechnic Institute, where he serves as Head of the Department of Mechanical, Aerospace and Nuclear Engineering (MANE) and Director of the Center for Modeling, Simulation and Imaging in Medicine (CeMSIM). His research interests include the development of novel, robust, and reliable computational technology to solve challenging and high-impact problems in engineering, medicine, and biology. He is the recipient of the ONR Young Investigator Award (2005), Rensselaer School of Engineering Research Excellence Award (2008), the James M. Tien ’66 Early Career Award for Faculty (2009), the Rensselaer School of Engineering Outstanding Research Team Award (2012), the J. Tinsley Oden Medal of the U.S. Association for Computational Mechanics (2019) and the Edwin F. Church Medal of the ASME (2022). He currently serves on the editorial boards of multiple journals as well as scientific committees of numerous national and international conferences. He is a Senior Member of IEEE and serves as Vice-Chair (Awards) of the IEEE Technical Committee on Haptics and leads/co-leads several committees of the Society of American Gastrointestinal and Endoscopic Surgeons (SAGES). He is an elected Fellow of four professional societies: the American Society of Mechanical Engineers (ASME), the American Institute for Medical and Biological Engineering (AIMBE), the International Association for Computational Mechanics (IACM), and the United States Association for Computational Mechanics (USACM)