Quantum lattice gas approach for the Maxwell equations

Abstract

We show that a quantum lattice gas approach can provide a viable means for numerically solving the classical Maxwell equations. By casting the Maxwell equations in Dirac form, the propagator may be discretized, and we describe how the accuracy relative to the time step may be systematically increased. The quantum lattice gas form of the discretization is suitable for implementation on hybrid classical-quantum computers. We discuss a number of extensions, including application to inhomogeneous media.

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

“…2003 a , b , 2011, 2012 a , b , 2019 a , b , 2020 a , b ). Other spinor representations of Maxwell equations were also attempted by Moses (1959), Coffey (2008) and Kulyabov et al. (2017).…”

“…Extension of QLA for Maxwell equations to three dimensions is expected to follow the standard procedures we have utilized in earlier QLA for 1-D and 3-D simulations of the nonlinear Schrodinger equation (Vahala et al 2003a(Vahala et al ,b, 2011(Vahala et al , 2012a(Vahala et al ,b, 2019a(Vahala et al ,b, 2020a. Other spinor representations of Maxwell equations were also attempted by Moses (1959), Coffey (2008) and Kulyabov et al (2017). The vista for further applications is boundless as the field of electromagnetic wave propagation in different dielectric media, such as a 3D magnetized plasma, lies before us.…”

“…derived a relativistic covariant representation of the Schrodinger equation with positive-definite probability density by, in essence, taking the square root of the Klein-Gordon wave equation. With the introduction of Dirac spinors, there were immediate attempts to connect Maxwell's equations with the Dirac equation (Laporte & Uhlenbeck 1931;Oppenheimer 1931;Moses 1959), particularly with the introduction of the Riemann-Silberstein (RS) vector (Bialynicki-Birula 1996;Coffey 2008) for the electromagnetic field. More recent attempts have further coupled the Maxwell equations to various field theories (Yepez 2002(Yepez , 2005(Yepez , 2016Kulyabov, Kolokova & Sevatianov 2017;Jestadt et al 2018).…”

The Effect of the Pauli Spin Matrices on the Quantum Lattice Algorithm for Maxwell Equations in Inhomogeneous Media

“…Soon after Dirac [23] was able to determine the square root of the Klein-Gordon wave operator and thus obtain a relativistically invariant counterpart to the Schrödinger equation, interest developed in making a formal theoretical connection between the relativistically invariant Maxwell equations and the Dirac equation [24][25][26][27][28]. One particularly intriguing approach has been through the use of the Riemann-Silberstein vectors [21,24]…”