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Time Domain Field Simulations on Quantum Computers via Riemann-Silberstein Formulation

Emanuel Colella, Franco Moglie, Valter Mariani Primiani, Gabriele Gradoni

Published May 18, 2025• 0 citations
Publisher

Abstract

This work presents a novel approach for simulating electromagnetic (EM) wave propagation by leveraging quantum computing techniques. By reformulating Maxwell's equations through the Riemann-Silberstein formalism, we cast the problem into a Schrödinger-like framework, enabling the application of Hamiltonian simulation methods. In particular, we employ the Trotter-Suzuki decomposition to approximate the time evolution operator, facilitating efficient quantum simulation of EM wave generated by a Gaussian pulse propagating within a two-dimensional metallic cavity. Our results illustrate the potential of quantum algorithms to address complex electrodynamics problems, offering promising avenues for future advancements in electromagnetics engineering.

DOI
10.23919/aces66556.2025.11052509

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This work presents a novel approach for simulating electromagnetic (EM) wave propagation by leveraging quantum computing techniques. By reformulating Maxwell's equations through the Riemann-Silberstein formalism, we cast the problem into a Schrödinger-like framework, enabling the application of Hamiltonian simulation methods. In particular, we employ the Trotter-Suzuki decomposition to approximate the time evolution operator, facilitating efficient quantum simulation of EM wave generated by a Gaussian pulse propagating within a two-dimensional metallic cavity. Our results illustrate the potential of quantum algorithms to address complex electrodynamics problems, offering promising avenues for future advancements in electromagnetics engineering.
This work presents a novel approach for simulating electromagnetic (EM) wave propagation by leveraging quantum computing techniques. By reformulating Maxwell's equations through the Riemann-Silberstein formalism, we cast the problem into a Schrödinger-like framework, enabling the application of Hamiltonian simulation methods. In particular, we employ the Trotter-Suzuki decomposition to approximate the time evolution operator, facilitating efficient quantum simulation of EM wave generated by a Gaussian pulse propagating within a two-dimensional metallic cavity. Our results illustrate the potential of quantum algorithms to address complex electrodynamics problems, offering promising avenues for future advancements in electromagnetics engineering.
In this work, we present a quantum-computing framework for time-domain simulation of Maxwell's equations. By defining the Riemann-Silberstein vector, Maxwell's curl equations reduce to a single Schrödinger-like evolution equation. The solution requires computing the exponential of the curl (Hamiltonian). On quantum hardware, matrix exponentials correspond to sequences of unitary gates. Therefore decomposing the Hamiltonian using the Trotter-Suzuki decomposition it is possible to simulate electrodynamics. To validate the method, we simulate the propagation of transverse-magnetic (TM) waves in a two-dimensional free-space domain. Results show accurate field propagation highlighting the potential advantage of quantum computing for solving electromagnetic problems.
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.
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.
Electromagnetic waves are an inherent part of all plasmas—laboratory fusion plasmas or astrophysical plasmas. The conventional methods for studying properties of electromagnetic waves rely on discretization of Maxwell equations suitable for implementing on classical, present day, computers. The traditional methodology is not efficient for quantum computing implementation—a future computational source offering a tantalizing possibility of enormous speed up and a significant reduction in computational cost. This paper addresses two topics relevant to implementing Maxwell equations on a quantum computer. The first is on formulating a quantum Schrödinger representation of Maxwell equations for wave propagation in a cold, inhomogeneous, and magnetized plasma. This representation admits unitary, energy preserving, evolution and conveniently lends itself to appropriate discretization for a quantum computer. Riding on the coattails of these results, the second topic is on developing a sequence of unitary operators which form the basis for a qubit lattice algorithm (QLA). The QLA, suitable for quantum computers, can be implemented and tested on existing classical computers for accuracy as well as scaling of computational time with the number of available processors. In order to illustrate the QLA for Maxwell equations, results are presented from a time evolving, full wave simulation of propagation and scattering of an electromagnetic wave packet by non-dispersive dielectric medium localized in space.