Abstract :
[en] Taking advantage of quantum computing 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. Looking for a minimum state is of particular interest in computational mechanics as this is naturally the solution of a variational formulation. Therefore, a hybrid classical computer - quantum annealer approach [1] is developed by reformulating the elasto-plastic finite-element method as a double minimisation process built around the variational updates formulation [2].
In particular, since the potentials resulting from an elasto-plastic material model are non-quadratic, a series of Hamiltonian quadratic potentials is constructed 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.
REFERENCES
[1] Nguyen V.D., Remacle F., Wu L., Noels L. A quantum annealing-sequential quadratic programming assisted finite element simulation for non-linear and history-dependent mechanical problems. European Journal of Mechanics – A/solids, Vol. 105, 105254, 2024.
[2] Ortiz M., Stainier L. The variational formulation of viscoplastic constitutive updates, Computer methods in applied mechanics and engineering, Vol. 171, 419-444, 1999.
