Quantum Computing the Climate?

We investigate the utility of Noisy Intermediate Scale Quantum (NISQ) processors as an alternative to classical computers for the simulation of climate systems by finding steady-state probability distribution functions (PDF) of several idealized models of increasing complexity. PDFs are found through direct statistical simulation (DSS) that solves for the statistics directly instead of following the traditional route of accumulation during numerical simulation. Steady-state solutions of the linear Fokker-Planck equation (FPE) are the form of DSS that we consider here. Numerical solution of the FPE becomes exponentially hard on classical computers as the number of dimensions increase, but this can in principle be overcome using quantum computers. We employ the Quantum Phase Estimation and Variational Quantum Eigensolver algorithms on IBM quantum hardware to find the zero-mode of the FPE operator. The approach is tested on nonlinear 1D Ornstein-Uhlenbeck problems for which comparison to exact analytical PDFs can be made [arXiv:2409.06036]. We then use the machine learning approach introduced by Souza [J. Fluid Mech. 997, A1 & A2 (2024)] to generate dimensionally reduced FPEs for the chaotic Lorenz-63 attractor and the Held-Suarez model of the general circulation. The zero modes found with NISQ machines are compared to numerically exact classical results. We comment on challenges and future prospects for quantum computing components of the climate system such as the atmospheric and oceanic boundary layers.