Quantum computing the climate? Preliminary explorations using noisy intermediate-scale quantum hardware

We investigate the utility of Noisy Intermediate Scale Quantum (NISQ) processors as an alternative to classical computers for the simulation of climate models by finding steady-state probability distribution functions (PDF) of several idealized dynamical systems 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 (QPE) and Variational Quantum Eigensolver (VQE) 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 exact PDFs can be found. Comparison to classically computed PDFs using a finite basis of Hermite polynomials is made. We find that the accuracy of QPE and VQE reaches a limit and then deteriorates as the number of basis elements grows [see arXiv:2409.06036]. We investigate the use of the Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (ADAPT-VQE) to increase the accuracy for larger basis sizes. Preliminary simulations and runs on IBM quantum hardware will be presented.