Solving problems in nonlinear radiation diffusion through quantum computing

We apply a quantum algorithm for solving systems of nonlinear partial differential equations [1,2] (PDE) to problems in nonlinear radiation diffusion. As a first application we consider the problem of diffusion of radiation energy into an initially cold material through a planar boundary maintained at constant temperature. This leads to propagation of a thermal wavefront (Marshak wave) through the material. We use the quantum PDE algorithm to solve the nonlinear radiation diffusion PDE and compare the resulting solution with that found using a classical PDE solver. Excellent agreement is found between the two solutions. We discuss possible directions for future applications in radiation diffusion and radiation hydrodynamics.

1. F. Gaitan, npj Quantum Inf. 6, 61 (2020).

2. F. Gaitan, Adv. Quantum Tech. 4, 2100055 (2021).