Nis-Luca van Hülst, Mario Guillaume Cecile, Hai-Yen Van, Tomohiro Hashizume, Eugene de Villiers, Dieter Jaksch
Turbulent thermal convection governs heat transport in systems ranging from stellar interiors to industrial heat exchangers. Two-dimensional Rayleigh-Bénard convection serves as a paradigm for these flows, reproducing key features such as thin boundary layers, large-scale circulation, and sustained plume dynamics. While Matrix Product State (MPS) methods have demonstrated significant compression of isothermal turbulent fields, their application to buoyancy-driven flows with active thermal coupling has remained unexplored. We apply MPS to two-dimensional Rayleigh-Bénard convection with dynamical simulations up to 
. An a priori decomposition of DNS snapshots up to shows that the bond dimension 
required to represent the flow fields grows without saturation, in contrast to the plateauing of reported for velocity fields in isothermal 2D turbulence. Crucially, however, dynamical simulations solving the governing equations directly in the compressed MPS format at fixed show that the required to recover statistical observables, such as the Nusselt number, scales significantly more favorably with than the a priori complexity suggests. At , a relative error of 
in the mean Nusselt number is achieved with a nearly 9-fold reduction in degrees of freedom, using a comparable to that required at 
. Spectral analysis confirms the progressive recovery of spatial and temporal scales with increasing . These findings establish MPS as a scalable tool for simulating thermally driven turbulence, suggesting the method may remain viable for investigations of the ultimate regime at substantially higher .
Cite as BibTex
@misc{vanhülst2026quantuminspiredsimulation2dturbulent,
title={Quantum-Inspired Simulation of 2D Turbulent Rayleigh-B\’enard Convection},
author={Nis-Luca van Hülst and Mario Guillaume Cecile and Hai-Yen Van and Tomohiro Hashizume and Eugene de Villiers and Dieter Jaksch},
year={2026},
eprint={2604.16179},
archivePrefix={arXiv},
primaryClass={physics.flu-dyn},
url={https://arxiv.org/abs/2604.16179},
}