Student Chapter
Student Chapter
This chapter is a nationwide chapter to help promote computational mechanics to young researchers and improve student engagement and professional development within our community.
USACM Student Chapter Seminar Series
July 14, 2025; 2PM EDT
Join via Zoom: https://us06web.zoom.us/j/82464478256?pwd=ZMkJVFdjMJzadgnVWFPqsdUSs4qTaY.
Eigenvalue analysis of stochastic structural systems: A quantum computing approach
Speaker: Ilias G. Mavromatisa, Columbia University
Abstract
A quantum computing approach is developed for solving eigenvalue problems of relevance to stochastic mechanics applications, such as modal response analysis of structural systems. The motivation relates to the fact that the computational complexity of the numerical solution of a deterministic eigenvalue problem, using a classical computer, is of the order of O(n3), where n is the dimension of the considered matrix [1]. Clearly, if the eigenvalue problem is random originating, for instance, from a stochastic finite element formulation of the governing equations of motion, the computational cost increases further. Indeed, considering a standard Monte Carlo simulation (MCS) solution treatment, the cost becomes of the order of O(Nn3), where N is the number of realizations in the MCS scheme. Obviously, the cost becomes prohibitive for large-scale finite element models of complex structural systems [2]. To address this challenge, the potential of quantum computers for performing complex tasks vastly more efficiently than classical computers is explored herein. Specifically, two distinct variational quantum algorithms, i.e., the subspace-search variational quantum eigensolver [3] and the variational quantum deflation [4], are employed and tailored for treating eigenvalue problems of interest in engineering mechanics. The performance of the algorithms, in terms of accuracy and efficiency, is assessed in conjunction with various numerical examples.
[1] J. H. Wilkinson, 1988. The algebraic eigenvalue problem, Oxford University Press, Oxford, UK.
[2] H.J. Pradlwarter, G.I. Schueller, G.S. Szekely, 2002. Random eigenvalue problems for large systems, Computers and Structures 80 (2002) 2415–2424.
[3] K. M. Nakanishi, K. Mitarai and K. Fujii, 2019. Subspace-search variational quantum eigensolver for excited states, Physical Review Research 1 (3) (2019) 33062.
[4] O. Higgott, D. Wang, S. Brierley, Variational quantum computation of excited states, Quantum 3 (2019) 1–11.
Bio
Dr. Ilias Mavromatis is a Postdoctoral Research Scientist in the Stochastic Engineering Dynamics Laboratory at Columbia University. He earned his PhD and MPhil in Civil Engineering and Engineering Mechanics from Columbia, after completing a Diploma in Naval Architecture and Marine Engineering at the National Technical University of Athens. His research has primarily focused on developing path integration techniques, originating from theoretical physics, to determine the response and assess the reliability of complex stochastic dynamical systems subjected to diverse excitations such as wind, earthquake, and sea waves. More broadly, his research lies at the intersection of applied mathematics, computer science, and engineering, with ongoing efforts to incorporate quantum computing tools to tackle computationally challenging engineering problems. He has authored five peer-reviewed publications and received recognition including Columbia’s Mindlin Scholar award and the ASCE-EMI Best Student Paper prize.
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Organization
2023-2025
Mentors
Jessica Zhang, Carnegie Mellon University
John Evans, University of Colorado Boulder
David Littlewood, Sandia National Laboratories
Patrick Diehl, Los Alamos National Laboratory
Osama Raisuddin, Rensselaer Polytechnic Institute
Student Leadership
Chair: Yanrong Xiao, Yale University
Vice-Chair: Joan Ejeta, North Carolina A&T State University
Member-at-Large: Joseph Amponsah, Iowa State University
Elaheh Mehdizadeh, University of Pittsburgh
Dila Kandel, University of Utah
Executive Members
Xuan Hu, University of California, Berkeley
Ozge Ozbayram, Johns Hopkins University