Performance Study of Variational Quantum Linear Solver for Linear Elastic Problems

In this study, we pioneer the application of the variational quantum linear solver (VQLS) to address linear elasticity problems. Initially, we derive the finite element discretized equations pertinent to plane strain scenarios. Subsequently, we introduce a modified ansatz tailored for the quantum linear solver. Utilizing this enhanced VQLS, we successfully compute the displacement distribution across each grid node. Our implementation, conducted on the open-source Pennylane library provided by Xanadu, encompasses two toy examples. The outcomes affirm that VQLS delivers a highly accurate resolution of the finite element discretized equations for plane strain problems. Moreover, the modified ansatz demonstrates a marked enhancement in both convergence and computational precision when compared to its predecessor. Presently, the quantum bits employed in our examples are limited due to computational constraints. However, we are committed to further investigating the efficacy of this quantum algorithm in more complex scenarios that necessitate a substantial quantum bit array.