A Variational Quantum Algorithm for Nonlinear Finite Element Analysis of Hyperelastic Materials
For computational mechanics researchers, this is an incremental step toward applying quantum computing to nonlinear elasticity, but limited to simple 1D problems and requiring polynomial approximations.
This work develops a variational quantum algorithm for nonlinear finite element analysis of hyperelastic materials, using polynomial approximations of strain energy to enable NISQ implementation. Numerical experiments on a 1D Neo-Hookean model demonstrate feasibility, with accuracy depending on polynomial order.
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the potential energy structure of hyperelasticity and employs a hybrid quantum classical framework in which the energy functional is evaluated using parameterized quantum circuits and optimized through classical routines. To enable implementation on current quantum hardware, polynomial approximations of the nonlinear strain energy density are introduced, yielding a representation compatible with variational quantum algorithms. The methodology is demonstrated on a one dimensional NeoHookean material model using finite element discretizations with first and second order shape functions and nonhomogeneous boundary conditions. Numerical experiments investigate the influence of the polynomial approximation order on the accuracy and efficiency of the proposed approach, illustrating its feasibility for near term quantum devices.