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Unitary quantum lattice simulations for Maxwell equations in vacuum and in dielectric media

Published online by Cambridge University Press:  28 October 2020

George Vahala Open the ORCID record for George Vahala [Opens in a new window] ,
Linda Vahala ,
Min Soe  and
Abhay K. Ram
George Vahala*
Affiliation:
Department of Physics, William & Mary, Williamsburg, VA23185, USA
Linda Vahala
Affiliation:
Department of Electrical & Computer Engineering, Old Dominion University, Norfolk, VA23529, USA
Min Soe
Affiliation:
Department of Mathematics and Physical Sciences, Rogers State University, Claremore, OK74017, USA
Abhay K. Ram
Affiliation:
Plasma Science and Fusion Center, MIT, Cambridge, MA02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

Utilizing the similarity between the spinor representation of the Dirac and the Maxwell equations that has been recognized since the early days of relativistic quantum mechanics, a quantum lattice algorithm (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 (2-D) propagation of a Gaussian pulse in a uniform medium whereas for normal (1-D) incidence of an electromagnetic Gaussian wave packet onto a dielectric interface requires 8-component spinors because of the coupling between the two electromagnetic polarizations. 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.

Keywords

plasma wavesplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 5 , October 2020 , 905860518
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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