NISQ Computing the Climate

Classical nonlinear dynamical systems can often be characterized by steady-state probability distribution functions (PDFs). PDFs can be obtained by accumulating statistics from simulation, or alternatively as a solution to the linear Fokker-Planck equation (FPE). Numerical solution of the FPE, however, becomes exponentially hard as the number of dimensions increase. We investigate the utility of Noisy Intermediate Scale Quantum (NISQ) devices as an alternative to classical computation. In particular, we employ the Quantum Phase Estimation (QPE), Variational Quantum Deflation, and Variational Quantum Singular Value Decomposition algorithms to obtain the steady-state statistics of the 3D Lorenz-63 chaotic dynamics using a dimensionally-reduced FPE operator [arXiv:2304.03362]. The same approach is used to investigate the Held-Suarez climate model. The algorithms are implemented on publicly available IBM hardware to test their efficacy. Furthermore, we demonstrate the efficacy of dynamical decoupling as a tool to mitigate errors within the QPE circuit.