Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2110.05480

Two Dimensional Electromagnetic Scattering form Dielectric Objects using Qubit Lattice Algorithm

G. Vahala, Min Soe, Linda L. Vahala, Abhay K. Ram

Published Oct 10, 2021• 0 citations
arXivHTMLPDF

Abstract

A qubit lattice algorithm (QLA) is developed for Maxwell equations in a two-dimensional Cartesian geometry. In particular, the initial value problem of electromagnetic pulse scattering off a localized 2D dielectric object is considered. A matrix formulation of the Maxwell equations, using the Riemann-Silberstein-Weber vectors, forms a basis for the QLA and a possible unitary representation. The electromagnetic fields are discretized using a 16-qubit representation at each grid point. The discretized QLA equations reproduce Maxwell equations to second order in an appropriate expansion parameter $ε$. The properties of scattered waves depend on the scale length of the transition layer separating the vacuum from the core of the dielectric. The time evolution of the fields gives interesting physical insight into scattering when propagating fields are excited within the dielectric medium. Furthermore, simulations show that the QLA recovers Maxwell equations even when $ε\sim 1$.

DOI
10.48550/arxiv.2110.05480

Related papers

Quantum Computing Framework for Transient Scattering of Electromagnetic Waves by Dielectric Structures

Min Soe, Abhay K. Ram, Efstratios Koukoutsis +3 more

Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic waves in a dielectric medium are described by Maxwell equations. The qubit lattice algorithm consists of a series of alternating unitary streaming and entanglement operators acting on qubit amplitudes constructed from the electric and magnetic fields. It is not a direct discretization of Maxwell equations, but recovers the desired equations to second order in lattice grid spacing. The resulting algorithm is implemented on a present-day supercomputer and is the basis of studying scattering of electromagnetic waves by an elliptical dielectric. As opposed to the steady state description of Mie scattering in frequency domain, the temporal evolution provides insights into transient scattering. The QLA simulations, reveal that a spatially localized wave packet propagating past an elliptic dielectric, embedded in vacuum, leads to several reflections generated by wave fields trapped within the dielectric. The physics insight brought forth by these simulations is not apparent from frequency domain studies of scattering. A complimentary simulation on transient scattering of a wave packet by an elliptical vacuum bubble inserted in a uniform dielectric demonstrates a stark contrast with respect to scattering off an elliptical dielectric in vacuum. Essentially, there is only a single internal reflection in which the field amplitudes are significantly smaller than those for side and forward scattering. A simple model based on the Kirchhoff tangent plane approximation helps explain the differences between these two scattering examples.

arXiv:2604.21128•Apr 22, 2026•0 citations

One and Two Dimensional Quantum Lattice Algorithms for Maxwell Equations in Inhomogeneous Scalar Dielectric Media I: Theory

George Vahala

A quantum lattice algorithm (QLA) is developed for Maxwell equations in scalar dielectric media using the Riemann-Silberstein representation on a Cartesian grid. For x-dependent and y-dependent dielectric inhomogeneities, the corresponding QLA requires a minimum of 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the local collisional entanglement of these qubits. However, z-dependent inhomogeneities require a QLA with a minimum of 16 qubits/lattice site since the Pauli spin matrix σz is diagonal. For 2 dimensional inhomogeneities, one can readily couple the 8-8 qubit schemes for x-y variations. z-x and y-z variations can be treated by either a 16-8 qubit scheme or a 16-16 qubit representation.

•Jan 1, 2022•0 citations

One- and two-dimensional quantum lattice algorithms for Maxwell equations in inhomogeneous scalar dielectric media I: theory

George Vahala, Linda L. Vahala, Min Soe +1 more

A quantum lattice algorithm (QLA) is developed for Maxwell equations in scalar dielectric media using the Riemann–Silberstein representation on a Cartesian grid. For x-dependent and y-dependent dielectric inhomogeneities, the corresponding QLA requires a minimum of 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the local collisional entanglement of these qubits. However, z-dependent inhomogeneities require a QLA with a minimum of 16 qubits/lattice site since the Pauli spin matrix σz is diagonal. For two-dimensional inhomogeneities, one can readily couple the 8–8 qubit schemes for x−y variations. z−x and y−z variations can be treated by either a 16–8 qubit scheme or a 16–16 qubit representation.

Radiation effects and defects in solids•Feb 1, 2021•12 citations

The Effect of the Pauli Spin Matrices on the Quantum Lattice Algorithm for Maxwell Equations in Inhomogeneous Media

George Vahala, Linda L. Vahala, Min Soe +1 more

A quantum lattice algorithm (QLA) is developed for the solution of Maxwell equations in scalar dielectric media using the Riemann-Silberstein representation. For x-dependent and y-dependent inhomogeneities, the corresponding QLA requries 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the collisional entanglement of two qubits. However, z-dependent inhomogeneities require a QLA with 16 qubits/lattice site since the Pauli spin matrix $σ_z$ is diagonal. QLA simulations are performed for the time evolution of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. There is excellent agreement between all three representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions are imposed at the continuous, but sharply increasing, boundary layer.

arXiv:2010.12264•Oct 23, 2020•1 citation

Quantum computing perspective for electromagnetic wave propagation in cold magnetized plasmas

Efstratios Koukoutsis, Kyriakos Hizanidis, George Vahala +3 more

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.

arXiv:2309.12492•Physics of Plasmas•Dec 1, 2023•13 citations

One- and two-dimensional quantum lattice algorithms for Maxwell equations in inhomogeneous scalar dielectric media. II: Simulations

George Vahala, Min Soe, Linda L. Vahala +1 more

Long-time quantum lattice algorithm (QLA) simulations are performed for the multiple reflection–transmission of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. For these one-dimensional (1D) simulations, there is excellent agreement between x-, y- and z-representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions are imposed at the continuous, but sharply increasing, dielectric boundary layers. Two-dimensional (2D) QLA scattering simulations in the x–z plane are performed for an electromagnetic pulse interacting with a conical dielectric obstacle for the 8–16 qubit model.

Radiation effects and defects in solids•Feb 1, 2021•9 citations
A qubit lattice algorithm (QLA) is developed for Maxwell equations in a two-dimensional Cartesian geometry. In particular, the initial value problem of electromagnetic pulse scattering off a localized 2D dielectric object is considered. A matrix formulation of the Maxwell equations, using the Riemann-Silberstein-Weber vectors, forms a basis for the QLA and a possible unitary representation. The electromagnetic fields are discretized using a 16-qubit representation at each grid point. The discretized QLA equations reproduce Maxwell equations to second order in an appropriate expansion parameter εεε. The properties of scattered waves depend on the scale length of the transition layer separating the vacuum from the core of the dielectric. The time evolution of the fields gives interesting physical insight into scattering when propagating fields are excited within the dielectric medium. Furthermore, simulations show that the QLA recovers Maxwell equations even when ε∼1ε\sim 1ε∼1.
Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic waves in a dielectric medium are described by Maxwell equations. The qubit lattice algorithm consists of a series of alternating unitary streaming and entanglement operators acting on qubit amplitudes constructed from the electric and magnetic fields. It is not a direct discretization of Maxwell equations, but recovers the desired equations to second order in lattice grid spacing. The resulting algorithm is implemented on a present-day supercomputer and is the basis of studying scattering of electromagnetic waves by an elliptical dielectric. As opposed to the steady state description of Mie scattering in frequency domain, the temporal evolution provides insights into transient scattering. The QLA simulations, reveal that a spatially localized wave packet propagating past an elliptic dielectric, embedded in vacuum, leads to several reflections generated by wave fields trapped within the dielectric. The physics insight brought forth by these simulations is not apparent from frequency domain studies of scattering. A complimentary simulation on transient scattering of a wave packet by an elliptical vacuum bubble inserted in a uniform dielectric demonstrates a stark contrast with respect to scattering off an elliptical dielectric in vacuum. Essentially, there is only a single internal reflection in which the field amplitudes are significantly smaller than those for side and forward scattering. A simple model based on the Kirchhoff tangent plane approximation helps explain the differences between these two scattering examples.
A quantum lattice algorithm (QLA) is developed for Maxwell equations in scalar dielectric media using the Riemann-Silberstein representation on a Cartesian grid. For x-dependent and y-dependent dielectric inhomogeneities, the corresponding QLA requires a minimum of 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the local collisional entanglement of these qubits. However, z-dependent inhomogeneities require a QLA with a minimum of 16 qubits/lattice site since the Pauli spin matrix σz is diagonal. For 2 dimensional inhomogeneities, one can readily couple the 8-8 qubit schemes for x-y variations. z-x and y-z variations can be treated by either a 16-8 qubit scheme or a 16-16 qubit representation.
A quantum lattice algorithm (QLA) is developed for Maxwell equations in scalar dielectric media using the Riemann–Silberstein representation on a Cartesian grid. For x-dependent and y-dependent dielectric inhomogeneities, the corresponding QLA requires a minimum of 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the local collisional entanglement of these qubits. However, z-dependent inhomogeneities require a QLA with a minimum of 16 qubits/lattice site since the Pauli spin matrix σz is diagonal. For two-dimensional inhomogeneities, one can readily couple the 8–8 qubit schemes for x−y variations. z−x and y−z variations can be treated by either a 16–8 qubit scheme or a 16–16 qubit representation.
A quantum lattice algorithm (QLA) is developed for the solution of Maxwell equations in scalar dielectric media using the Riemann-Silberstein representation. For x-dependent and y-dependent inhomogeneities, the corresponding QLA requries 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the collisional entanglement of two qubits. However, z-dependent inhomogeneities require a QLA with 16 qubits/lattice site since the Pauli spin matrix σzσ_zσz​ is diagonal. QLA simulations are performed for the time evolution of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. There is excellent agreement between all three representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions are imposed at the continuous, but sharply increasing, boundary layer.
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.
Long-time quantum lattice algorithm (QLA) simulations are performed for the multiple reflection–transmission of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. For these one-dimensional (1D) simulations, there is excellent agreement between x-, y- and z-representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions are imposed at the continuous, but sharply increasing, dielectric boundary layers. Two-dimensional (2D) QLA scattering simulations in the x–z plane are performed for an electromagnetic pulse interacting with a conical dielectric obstacle for the 8–16 qubit model.