Time-Marching Quantum Algorithm for Simulation of Nonlinear Lorenz Dynamics
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entropy-27-00871-v2.pdf
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2.67 MB
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Author(s)
Koukoutsis, Efstratios
Vahala, George
Soe, Min
Hizanidis, Kyriakos
Vahala, Linda
Ram, Abhay K.
Date Issued
August 17, 2025
Journal
Entropy
Publisher
Multidisciplinary Digital Publishing Institute
Citation
Koukoutsis, E.; Vahala, G.; Soe, M.; Hizanidis, K.; Vahala, L.; Ram, A.K. Time-Marching Quantum Algorithm for Simulation of Nonlinear Lorenz Dynamics. Entropy 2025, 27, 871.
Version
Final published version
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 an explicit 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, which 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.
MIT Department
Massachusetts Institute of Technology. Plasma Science and Fusion Center
Terms of Use
Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.3390/e27080871
