Quantum Algorithms for Nonlinear Dynamics: Revisiting Carleman Linearization with No Dissipative Conditions

• DOI: 10.48550/arxiv.2405.12714
• Publication Date: 2024-05-21
• Authors: Hsuan-Cheng Wu; Jingyao Wang; Xiantao Li
• Keywords: Linearization; Dynamics

In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous error bounds and convergence for linearization, which facilitated identification quantum advantages in simulating large-scale systems. Our analysis extends these findings by exploring beyond traditional condition, thereby broadening scope computational benefits to a new class regimes. This novel regime is defined resonance prove how condition leads with respect truncation level $N$ linearization. We support our theoretical advancements numerical experiments on variety models, including Burgers' equation, Fermi-Pasta-Ulam (FPU) chains, Korteweg-de Vries (KdV) equations, validate demonstrate practical implications.