One- and two-dimensional quantum lattice algorithms for Maxwell equations in inhomogeneous scalar dielectric media I: theory

ABSTRACT

A quantum lattice algorithm (QLA) is developed for Maxwell equations in scalar dielectric media using the Riemann–Silberstein representation on a Cartesian grid. For x-dependent and y-dependent dielectric inhomogeneities, the corresponding QLA requires a minimum of 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the local collisional entanglement of these qubits. However, z-dependent inhomogeneities require a QLA with a minimum of 16 qubits/lattice site since the Pauli spin matrix ${\sigma }_z$ is diagonal. For two-dimensional inhomogeneities, one can readily couple the 8–8 qubit schemes for x−y variations. z−x and y−z variations can be treated by either a 16–8 qubit scheme or a 16–16 qubit representation.

Keywords:

• Wave reflection
• Maxwell equations
• dielectric media
• qubits

Acknowledgments

LV was partially supported by an AFRL STTR Phase I with Semicyber LLC contract number FA864919PA049. GV, LV and MS were partially supported by an AFRL STTR Phase 2 with Semicyber LLC contract number FA864920P0419. AKR was supported by DoE Grant Number DE-FG02-91ER-54109 and DE-SC0018090.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Air Force Research Laboratory [FA864919PA049,FA864920P0419] and U.S. Department of Energy [DE-FG02-91ER-54109,DE-SC0018090].

Notes on contributors

George Vahala

George Vahala is a Professor of Physics at William & Mary, Williamsburg, VA. The author received his MS and PhD (Physics) from the University of Iowa and a BSc (Applied Math) from the University of Western Australia. The author's areas of research include turbulence modeling in plasma physics, wave propagation in tokamaks, lattice Boltzmann and quantum lattice algorithms for the study of solitons, quantum vortices in scalar and spinor BECs and in plasmas.

Linda Vahala

Linda Vahala is an Associate Professor of Electrical & Computer Engineering at Old Dominion University. Norfolk, VA. The author received her PhD (Physics) from Old Dominion University, MS (Physics) from the University of Iowa and BS (Phsyics) from the University of Illinois. The author's areas of research include cell phone transmission effects in aircraft fuselage, neural networks, wave propagation in tokamaks, lattice algorithms for nonlinear physics and for plasmas.

Min Soe

Min Soe is a Professor in the Department of Mathematics and Physical Sciences at Rogers State University, Claremore, OK. The author received his PhD (Physics) from William & Mary, MS (mathematics) from Hampton University, and BSc (Physics) from Rangoon University, Rangoon, Burma. The author's area of research spans magnetohydrodynamics and plasma physics, kinetic theory of turbulence modeling, mesoscale simulation methods and optimizations for large-scale parallel computing.

Abhay K. Ram

Abhay K. Ram is a Principal Research Scientist at the Plasma Science and Fusion Center, MIT, Cambridge, MA. He received his PhD from MIT and the BSc from the University of Nairobi, Kenya. His research encompasses a broad range of topics in wave propagation and scattering in plasma physics and controlled fusion.