Quantum algorithm for the collision-coalescence of cloud droplets

Quantum computing is gaining attention as a new approach for solving complex problems in many scientific fields. In atmospheric and oceanic sciences, it may help reduce computational costs of simulating large and nonlinear systems. However, research into the use of quantum computers in this area is still in its earlier stage, and suitable applications have not been established yet. This study explores the use of quantum computing for calculating the collision-coalescence process of cloud droplets, which dominates the size growth of liquid particles in the cloud microphysics. Inspired by the quantum algorithms developed in the field of financial engineering, we propose a new algorithm based on a master equation that describes the time evolution of the droplet mass distribution. Our algorithm uses the quantum amplitudes to encode the probability distribution of droplet mass and calculates the expected number of droplets via the quantum amplitude estimation. Our resource analysis shows that the number of T gates scales as O\(N²\), where N is the number of bins of the mass distributions. This is an essential improvement over the classical methods that scale only exponentially with N. This efficiency improvement is achieved by using quantum arithmetic in the superposition and by encoding the transition histories instead of the full distributions at each time step. Our results suggest that the collision-coalescence process is one of the promising targets of quantum computing in the field of atmospheric science.