Quantum linear system algorithm for the two-dimensional radiative transfer equation: Gate-level resource estimation

The radiative transfer equation (RTE) governs the propagation of radiation through atmospheres and is essential in climate modeling and weather prediction. Because the RTE involves spatial, angular, and spectral degrees of freedom, discretizing it results in huge linear systems whose direct computational cost in classical algorithms scales as only linearly with the number of spatial grid points. This is the motivation of our research to search for quantum algorithms that could alleviate this computational bottleneck.

We develop an explicit quantum circuit that solves the steady-state, two-dimensional RTE in a cloudy atmosphere with a quantum linear system algorithm (QLSA). We construct the full circuit from elementary one- and two-qubit gates, enabling a concrete resource count in terms of gate depth and qubit number.

Our analysis shows that the gate count and qubit count scale logarithmically with the number of spatial grid points in a simplified setting. We demonstrate that RTE is one of the promising targets of quantum computing in the atmospheric science.