Unitary Quantum Lattice Simulations for Maxwell Equations in Vacuum and in Dielectric Media

Abstract

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 collision stream operators of Maxwell equations is derived for both homogeneous and inhomogeneous media. A second order accurate 4 spinor scheme is developed and tested successfully for two dimensional (2D) propagation of a Gaussian pulse in a uniform medium while for normal (1D) incidence of an electromagnetic Gaussian pulse onto a dielectric interface requires 8 component spinors. In particular, the well-known phase change, field amplitudes and profile widths are recovered by the QLA asymptotic profiles. The QLA simulations yield the time dependent electromagnetic fields as the pulse enters and straddles the dielectric boundary. QLA involves unitary interleaved noncommuting collision and streaming operators that can be coded onto a quantum computer. The noncommutation being the only reason why one perturbatively recovers the Maxwell equations.

20 pages, 20 figures. More explanations on the incorporation of the inhomogeneous dielectric media through Hermitian operators

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• The Effect of the Pauli Spin Matrices on the Quantum Lattice Algorithm for Maxwell Equations in Inhomogeneous Media
• The effect of the width of the incident pulse to the dielectric transition layer in the scattering of an electromagnetic pulse -- a quantum lattice algorithm simulation
• Simulating plasma wave propagation on a superconducting quantum chip
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