Hardware Realization of a Hamiltonian Simulation Algorithm for Time-Domain Maxwells Equations

TL;DR

This paper demonstrates the first quantum-hardware implementation of a Hamiltonian simulation for time-domain Maxwell's equations, enabling efficient quantum computation of electromagnetic fields.

Contribution

It introduces a novel quantum algorithm using Schrodingerisation for Maxwell's equations, with experimental validation on IonQ hardware and new measurement techniques.

Findings

Quantum simulation matches analytical solutions in 2D and 3D.

Efficient circuit construction via Bell-basis Trotter blocks.

Extended to compute scattered fields with boundary conditions.

Abstract

We present the first quantum-hardware implementation of a Hamiltonian simulation algorithm that produces signed vector-field solutions to the time-domain Maxwells equations using a Schrodingerisation-based approach. The electromagnetic fields are discretized using finite-difference operators, and the resulting non-unitary matrices are mapped to Bell-basis Trotter blocks, enabling efficient circuit construction. We introduce a measurement procedure that retrieves not only field amplitudes, but also physical directions of the electric and magnetic field values at select spatial points. Implementing this logic on quantum hardware relies on relative-phase-based sign reconstruction. Numerical results obtained using IonQ QPU, show good agreement with analytical solutions of benchmark problems in two dimensions and on simulators; in three dimensions. We further extend our approach to compute fields scattered from simple bodies, by enforcing appropriate boundary conditions. Our work lays the foundational steps towards realizing quantum-hardware solutions for computational electromagnetics.