A time-marching quantum algorithm for simulation of the nonlinear Lorenz dynamics

• URL: http://arxiv.org/abs/2506.21354v1
• Date: Thu, 26 Jun 2025 15:08:00 GMT
• Title: A time-marching quantum algorithm for simulation of the nonlinear Lorenz dynamics
• Authors: Efstratios Koukoutsis, George Vahala, Min Soe, Kyriakos Hizanidis, Linda Vahala, Abhay K. Ram,
• Abstract summary: We develop a quantum algorithm that implements the time evolution of a second order time-discretized version of the Lorenz model.<n> Notably, we showcase that it accurately captures the structural characteristics of the Lorenz system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing a quantum algorithm that implements the time evolution of a second order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state with respect to the number of integration time-steps. This provides a significant improvement over previous approaches, while preserving the characteristic quantum speed-up in terms of the dimensionality of the underlying differential equations system, that similar time-marching quantum algorithms have previously demonstrated. Notably, by classically implementing the proposed algorithm, we showcase that it accurately captures the structural characteristics of the Lorenz system, reproducing both regular attractors--limit cycles--and the chaotic attractor within the chosen parameter regime.

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