Journal Article

Time-Marching Quantum Algorithm for Simulation of Nonlinear Lorenz Dynamics

Koukoutsis, Efstratios, Hizanidis, Kyriakos, Ram, Abhay K., Vahala, George, Soe, Min, Vahala, Linda

2025

Overview

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.

• Publisher: MDPI AG,MDPI
• Subject: Algorithms / Analysis / Attractors (mathematics) / Chaos theory / Differential equations / Fluid dynamics / Hadamard product / linear combination of unitaries / Linear operators / Lorenz system / Nonlinear differential equations / Nonlinear dynamics / nonlinear ordinary differential equations / Ordinary differential equations / Partial differential equations / Physics / Quantum computers / Quantum computing / Quantum mechanics / recursive structure / Simulation / SVD block encoding / time-marching quantum algorithm