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’s 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 wave packet 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 without the imposition of electromagnetic boundary conditions at the interface. The QLA simulations yield the time-dependent electromagnetic fields as the wave packet enters and straddles the dielectric boundary. QLA involves unitary interleaved non-commuting collision and streaming operators that can be coded onto a quantum computer – the non-commutation being the very reason why one perturbatively recovers the Maxwell equations.