Quantum algorithm for radiative transfer equations

We report a new quantum algorithm for radiative transfer using the lattice Boltzmann method (LBM). This algorithm encompasses all the essential processes of radiative transfer: absorption, scattering, and emission. The algorithm primarily consists of three sections. The first section calculates the effects of absorption (leading to a decrease) and scattering, while the second section computes the effects of absorption (leading to an increase) and emission. These two sections do not depend on the number of grid points, ensuring that the computational complexity does not increase with the number of grid points. The third section computes the propagation processes. Except for the initial encoding and final measurements, this quantum algorithm accelerates radiative transfer calculations on a logarithmic scale compared to classical algorithms. Furthermore, we present simulation results for a test problem using this algorithm. The close agreement between our computational results and analytical solutions demonstrates the validity of this algorithm.