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A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then developed perturbatively to…
Utilizing the similarity between the spinor representation of the Dirac equation and the Maxwell equations that has been recognized since the early days of relativistic quantum mechanics, a quantum lattice (QLA) representation of unitary…
A quantum lattice representation (QLA) is devised for the initial value problem of one-dimensional (1D) propagation of an electromagnetic disturbance in a scalar dielectric medium satisfying directly only the two curl equations of Maxwell.…
Qubit lattice algorithm (QLA) simulations are performed for a two-dimensional (2D) spatially bounded pulse propagating onto a plane interface between two dielectric slabs. QLA is an initial value scheme that consists of a sequence of…
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…
$\bf{Abstract}$: A qubit lattice algorithm (QLA), which consists of a set of interleaved unitary collision-streaming operators, is developed for electromagnetic wave propagation in tensor dielectric media. External potential operators are…
It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit…
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…
The effect of the thickness of the dielectric boundary layer that connects a material of refractive index $n_1$ to another of index $n_2$ is considered for the propagation of an electromagnetic pulse. For very thin boundary layer the…
An initial value algorithm is utilized to examine the time dependent evolution of the electromagnetic fields arising from oblique scattering of bounded pulses from an infinite planar dielectric interface. Since the qubit lattice algorithm…
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…
We derive a new eight dimensional matrix representation of the Maxwell equations for a linear homogeneous medium and extend it to the case of a linear inhomogneous medium. This derivation starts ab initio with the Maxwell equations and uses…
We continue our analysis of the physics of quantum lattice gas automata (QLGA). Previous work has been restricted to periodic or infinite lattices; simulation of more realistic physical situations requires finite sizes and non-periodic…
The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA, see quant-ph/0406180. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local…
We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the…
A novel quantum algorithm for solving the Boltzmann-Maxwell equations of the 6D collisionless plasma is proposed. The equation describes the kinetic behavior of plasma particles in electromagnetic fields and is known for the classical…
Quantum algorithms based on the variational principle have found applications in diverse areas with a huge flexibility. But as the circuit size increases the variational landscapes become flattened, causing the so-called Barren plateau…
Starting from the Maxwell-Juettner equilibrium distribution, we develop a relativistic lattice Boltzmann (LB) algorithm capable of handling ultrarelativistic systems with flat, but expanding, spacetimes. The algorithm is validated through…
The local approach to computing electrostatic interactions proposed by Maggs and adapted by Pasichnyk for molecular dynamics simulations is extended to situations where the dielectric background medium is inhomogeneous. We furthermore…
The progress in two-dimensional materials has led to rapid experimental developments in quantum plasmonics, where light is manipulated using plasmons. Although numerical methods can be used to quantitatively describe plasmons in spatially…