Preliminary study on the boundary element method using quantum algorithms

Abstract

In recent years, the global race to develop quantum computers has intensified. Quantum computers are expected to be applied across various engineering fields, with particularly high expectations for their integration with High Performance Computing (HPC) in the field of the computational mechanics. However, the development of computational mechanics techniques utilizing quantum computers is still unexplored. Therefore, in this study, we conduct a fundamental investigation of the Boundary Element Method (BEM) using quantum algorithms. First, we briefly describe the current state of quantum computing. Then, the general formulation of BEM for 2D Laplace equation targeted in this research is discussed. Subsequently, from an engineering perspective, the quantum algorithms required for solving the BEM for 2-D Laplace equation using a quantum computer are explained. Finally, by presenting numerical examples obtained by using a quantum simulator, we demonstrate the potential for implementing the BEM on quantum computers.