Quantum Algorithm for Electromagnetic Field Analysis
Hiroyuki Tezuka, Yuki Sato · International Journal for Numerical Methods in Engineering · 2026
ABSTRACT Partial differential equations (PDEs) form the mathematical foundation of computational electromagnetics (CEM) and photonic device design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a rigorous framework for mapping PDEs into unitary time evolution, offering a scalable approach to electromagnetic analysis. In this work, we formulate Maxwell's equations in the potential representation and embed governing equations, boundary conditions, and observables consistently into a Hamiltonian form. A major challenge arises from the exponential growth of Hamiltonian terms for complex geometries. We examine this issue and demonstrate that logical compression can significantly reduce the number of required terms, particularly in periodic or symmetric configurations. As a proof of concept, we simulate optical wave propagation through a metalens and illustrate that the proposed method can capture wavefront shaping and focusing behavior, suggesting its applicability to optical design optimization. This work highlights the feasibility of Hamiltonian‐based quantum simulation for electromagnetic and photonic systems, and identifies structural conditions favorable for efficient execution.