Quantum Computing Method for Solving Electromagnetic Problems Based on the Finite Element Method

Applying quantum computation to solve electromagnetic (EM) problems is still at an early age. Recently, initial study on applying the finite element method (FEM) equations in EM domain has been made. This article makes a further development beyond study. Specifically, we first develop approach systematically prepare state represent right-hand side (RHS) vector of equation problems. Then, reduce number gates needed preparation process, propose quantum-gate-reduction method, which explores fact that FEM cells input port are small portion total 3-D structure and for depends RHS vector’s sparsity pattern. Based proposed derive upper lower bounds analytically circuit. Furthermore, deal with large condition matrix EM, leverage preconditioner modify original linear equations, so as qubits required using Two examples used illustrate how computing can be find solutions