Introduction to HHL Quantum Matrix Solver for Electromagnetic Analysis

Quantum computing presents promising opportunities for the future of computational science. By leveraging qubits that store data as superpositions of possible states, quantum algorithms enable exponential computational gains with only linear increases in resources. Quantum hardware is rapidly advancing, with small but functional systems already accessible to the public. In computational electromagnetics (CEM), quantum computing offers potential solutions to inefficiencies, particularly in matrix-based algorithms. Key examples include the Method of Moments (MoM) for integral equation discretization and the Finite Element Method (FEM). These problems often lack inherent structures that simplify quantum implementation, making the versatility of quantum algorithms crucial. A notable approach is the Harrow-Hassidim-Lloyd (HHL) algorithm, which efficiently solves matrix equations with logarithmic complexity for well-conditioned matrices, significantly outperforming classical methods. A fundamental aspect of HHL is Hamiltonian simulation, which involves applying the unitary operator. While efficient simulations of general Hamiltonians remain an active area of research, we will discuss two approaches to how such simulations can be performed. Despite challenges in general applicability, early implementations of quantum-assisted MoM and FEM solutions show promising results.