Resolution of elasto-plastic finite-elements problems by quantum annealing (Plenary)

Although quantum computing offers the promise to solve particular problems exponentially faster than classical computers, its application in computational mechanics remains challenging partly because the available possible operations that can be performed on a quantum computer are not as versatile as with a classical computer. Quantum annealers, a family of quantum computers, are dedicated in evaluating the minimum state of a Hamiltonian quadratic potential. In order to take advantage of this feature, we develop a hybrid classical computer - quantum annealer approach [1] by reformulating the elasto-plastic finite-element method as a double minimisation process built around the variational updates formulation [2]. In particular, because the potentials resulting from an elasto-plastic material model are non-quadratic, we build a series of Hamiltonian quadratic potentials by approximating the objective function using a quadratic Taylor’s series. Each quadratic minimisation problem of continuous variables is then transformed into a binary quadratic problem that can be encoded on a quantum annealing hardware such as the D-Wave system.
C[1] V. D. Nguyen, F. Remacle, L. Noels. A quantum annealing-sequential quadratic programming assisted finite element simulation for non-linear and history-dependent mechanical problems. European Journal of Mechanics – A/solids, 105 (01 May 2024): 105254. doi: http://dx.doi.org/10.1016/j.euromechsol.2024.105254
[2] M. Ortiz, L. Stainier (1999), The variational formulation of viscoplastic constitutive updates, Computer methods in applied mechanics and engineering, 171, 419-444, doi:
https://doi.org/10.1016/S0045-7825(98)00219-9