Qubit Lattice Algorithm for the Electromagnetic Pulse Propagation in Scalar Dielectric Media
George Vahala (William & Mary)
Friday 25 February 2021
at 16:00 Lisbon time
in Zoom: link distributed on the day of the session to e-mails registered here
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)