Quantum Method for Scaling the Finite Element Based Quantum Solutions of Electromagnetic Problems

Quantum computing is a potential approach for addressing computational challenges in solving electromagnetic problems. A quantum method, called the Harrow/Hassidim/Lloyd (HHL) algorithm has recently been applied to solve the equations from finite-element-method (FEM) formulation of electromagnetic problems. Here we address a further step in this direction. Since quantum state vectors always have unit norm, the solution vector from HHL is only proportional to the final electromagnetic solutions. The magnitude of the final electromagnetic solution vector remains unavailable from HHL In this paper, a new quantum formulation is proposed to find the magnitude of the final electromagnetic solutions. The proposed method can be used to scale the HHL results to the correct magnitude of electromagnetic solutions. In this way, the proposed method is a further advance in making the quantum computing more effective in solving electromagnetic problems.