Speaker: George Vahala

Title: Qubit Lattice Algorithm for the Electromagnetic Pulse Propagation in Scalar Dielectric Media

Abstract: There is much interest in examining plasma problems that will be amenable to error-correcting quantum computers. For some years, we have been developing Qubit Lattice Algorithms (QLA) for the solution of nonlinear physics – in particular the Nonlinear Schrodinger Equation (NLS)/Gross Pitaevskii equation in 1D-2D-3D. The 1D soliton physics benchmarked our algorithms, while in 3D we examined scalar quantum turbulence, finding 3 energy cascades on a 5760³ grid using 11k processors (2009). For spinor BEC simulations the QLA were ideally parallelized on classical supercomputers (tested to over 760k cores on IBM Mira). QLA is a mesoscopic representation of interleaved non-commuting sequence of collision/streaming operators which in the continuum limit perturbatively reproduce the physics equations of interest. The collision operators entangle the local on-site qubits, while the streaming operators spread this entanglement throughout the lattice. For plasma physics we are developing QLA for Maxwell equations in a dielectric medium. The QLA collision operators were readily determined following the connection of Maxwell equations in a vacuum to the free particle Dirac equation. Even for 1D propagation of an electromagnetic pulse normal to a dielectric interface we find interesting results: our QLA simulations reproduces all the standard Fresnel relations for a plane wave, except that the transmission amplitude is augmented by a factor (n₂ /n₁ )¹/² over the Fresnel plane wave result. We will discuss our recent QLA results of scattering of a 1D electromagnetic pulse from a 2D scalar dielectric cylinder. For sharp dielectric boundary layers, and small pulse widths one finds multiple reflections within the dielectric cylinder leading to re-radiation of fields from the dielectric region and quite complex field structures.
In collaboration with Min Soe (RSU), Linda Vahala (ODU), Abhay K. Ram (MIT)

Please register here to receive the ZOOM link on the 25th February 2022
https://docs.google.com/forms/d/e/1FAIpQLSf00PKRDrSuIH_ch9RdfMekI8UO9Y4pOkptfnED02k9TZymag/viewform