In this study, we propose a quantum algorithm to calculate the probability distribution of cloud droplet sizes that describes their growth through collision and coalescence. The algorithm is based on a linear probability equation, and by utilizing a key quantum property called superposition, it can handle large probability distributions efficiently.

Even though the quantum algorithm used in financial engineering needs to store the full distribution at each time step, our algorithm reduces this cost by encoding only the history of transitions. While classical methods require exponentially high computational cost, our analysis shows that the number of quantum operations in our algorithm scales quadratically with the number of size bins.

Although this is still a theoretical study, the results suggest that quantum computing may be applicable to cloud microphysics in the future.