Document Type

Article

Publication Date

2025

DOI

10.3390/e27080871

Publication Title

Entropy

Volume

27

Issue

8

Pages

871

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.

Rights

© 2025 by the authors.

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International (CC BY 4.-0) License.

Data Availability

Article states: "The data generated in this study are available upon reasonable request from the authors."

Original Publication Citation

Koukoutsis, E., Vahala, G., Soe, M., Hizanidis, K., Vahala, L., & Ram, A. K. (2025). Time-marching quantum algorithm for simulation of nonlinear Lorenz dynamics. Entropy, 27(8), Article 871. https://doi.org/10.3390/e27080871

ORCID

0000-0003-2704-5316 (Vahala)

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