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URSI General Assembly and Scientific Symposium

Quantum Simulation of Maxwell's Equations

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

Published Jan 1, 2026• 0 citations
Publisher

Abstract

We investigate Hamiltonian simulations of Maxwell's equations, establishing a unified framework in which classical electromagnetic dynamics are mapped onto quantum-native time evolution operators.By introducing the Riemann-Silberstein-Weber (RSW) vector, which combines the electric and magnetic fields into a single complexvalued field, Maxwell's equations can be recast into a Schroedinger-like evolution equation governed by a Hermitian Maxwell Hamiltonian [1].

DOI
10.46620/ursigass26/ficn1461

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We investigate Hamiltonian simulations of Maxwell's equations, establishing a unified framework in which classical electromagnetic dynamics are mapped onto quantum-native time evolution operators.By introducing the Riemann-Silberstein-Weber (RSW) vector, which combines the electric and magnetic fields into a single complexvalued field, Maxwell's equations can be recast into a Schroedinger-like evolution equation governed by a Hermitian Maxwell Hamiltonian [1].
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.
We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schrödingersation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system evolving under unitary dynamics, via a warped phase transformation that maps the equation into one higher dimension. In this paper, our quantum algorithms are based on either a direct approximation of Maxwell's equations combined with Yee's algorithm, or a matrix representation in terms of Riemann-Silberstein vectors combined with a spectral approach and an upwind scheme. We implement these algorithms with physical boundary conditions, including perfect conductor and impedance boundaries. We also solve Maxwell's equations for a linear inhomogeneous medium, specifically the interface problem. Several numerical experiments are performed to demonstrate the validity of this approach. In addition, instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework, which allows the quantum simulation of Maxwell's equations in analog quantum simulation.
We present quantum algorithms for electromagnetic fields governed by Maxwell’s equations. The algorithms are based on the Schrödingerisation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system evolving under unitary dynamics, via a warped phase transformation that maps the equation into one higher dimension. In this paper, our quantum algorithms are based on either a direct approximation of Maxwell’s equations combined with Yee’s algorithm, or a matrix representation in terms of Riemann–Silberstein vectors combined with a spectral approach and an upwind scheme. We implement these algorithms with physical boundary conditions, including perfect conductor and impedance boundaries. We also solve Maxwell’s equations for a linear inhomogeneous medium, specifically the interface problem. Several numerical experiments are performed to demonstrate the validity of this approach. In addition, instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework, which allows the quantum simulation of Maxwell’s equations in analog quantum simulation.
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.
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.