Quantum Computing and Atmospheric Dynamics: Exploring the Lorenz System

Abstract: This paper explores the potential contribution of quantum computing, specifically the Variational Quantum Eigensolver (VQE), into atmospheric physics research and application problems using as an example the Lorenz system, a paradigm of chaotic behavior in atmospheric dynamics. Traditionally, the complexity and non-linearity of atmospheric systems have presented significant computational challenges. However, the advent of quantum computing, and in particular the VQE algorithm, offers a novel approach to these problems. The VQE, known for its efficiency in quantum chemistry for determining ground state energies, is adapted in our study to analyze the non-Hermitian Jacobian matrix of the Lorenz system. We employ a method of Hermitianization and dimensionality augmentation to make the Jacobian amenable to quantum computational techniques. This study demonstrates the application of VQE in calculating the eigenvalues of the Lorenz system's Jacobian, thus providing insights into the system's stability at various equilibrium points. Our results reveal the VQE's potential in addressing complex systems in atmospheric physics. Furthermore, we discuss the broader implications of VQE in handling non-Hermitian matrices, extending its utility to operations like diagonalization and Singular Value Decomposition (SVD), thereby highlighting its versatility across various scientific fields. This research extends beyond the realm of chaotic systems in atmospheric physics, underscoring the significant potential of quantum computing to tackle complex, real-world challenges.