Quantum algorithm for Electromagnetic Field Analysis

TL;DR

The work addresses the high computational cost of CAE electromagnetics by recasting Maxwell's equations in a potential-based Hamiltonian form and embedding them into quantum circuits for time evolution. It derives wave equations for the vector and scalar potentials under the Lorenz gauge, and maps the discretized system to qubits, with qubit requirements scaling as $O(\log N)$. A key contribution is the metalens proof-of-concept showing that quantum simulation can reproduce wave propagation and focusing, and that logical compression dramatically reduces Hamiltonian terms for periodic or symmetric geometries. The study also discusses observables and readout strategies, highlighting practical challenges and the potential for quantum-assisted design workflows in metasurfaces and photonic devices, which could enable more scalable handling of multiscale EM interactions in design optimization.

Abstract

Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to encode PDEs into unitary time evolution and has potential for scalable electromagnetic analysis. We formulate Maxwell's equations in the potential representation and embed governing equations, boundary conditions, and observables consistently into Hamiltonian form. A key bottleneck is the exponential growth of Hamiltonian terms for complex geometries; we examine this issue and show that logical compression can substantially mitigate it, especially for periodic or symmetric structures. As a proof of concept, we simulate optical wave propagation through a metalens and illustrate that the method can capture wavefront shaping and focusing behavior, suggesting its applicability to design optimization tasks. This work highlights the feasibility of Hamiltonian-based quantum simulation for photonic systems and identifies structural conditions favorable for efficient execution.

Figures (5)

• Figure 1: Settings
• Figure 2: Binary-approximated structures. Left: original refractive index distribution (maximum value shown in yellow). Right: binary-approximated distribution.
• Figure 3: Wave propagation calculated by quantum and classical algorithm. In the figure, "Quantum" denotes Hamiltonian simulation and "Classical" denotes finite difference method. The color plots represents the amplitude of $E(\bm{x})$.
• Figure 4: The location dependency of the power intensity $\int_{\mathcal{X}} |E(t, \bm{x})|^2d\bm{x}$ and the accumulated value $\int_t\int_{\mathcal{X}} |E(t, \bm{x})|^2d\bm{x}dt$. The integrated time window is from $t=0$ to $t=70$ to avoid the effect of reflection. The distance is the number of pixels from the bottom edge of the lens.
• Figure 5: Wave propagation for metalenses with varying thicknesses. Colors are normalized in each plot, with the maximum value shown in red and the minimum in blue.