Turbulent Rayleigh-Bénard convection (RBC) is a paradigm for heat transport in geophysical and astrophysical flows. However, Direct Numerical Simulation (DNS) of the extreme Rayleigh numbers Ra found in nature is computationally prohibitive, as the degrees of freedom required to resolve the thermal boundary layer scale polynomially with Ra [1]. In this work, we propose a quantum-inspired approach to overcome this ”curse of dimensionality” by simulating the 2D Boussinesq equations directly within the low-rank manifold of Matrix Product States (MPS). Building on recent success in applying tensor networks to homogeneous turbulence [2, 3] and flow compression [4], we extend the formalism to thermally driven wall-bounded turbulence, where resolving the boundary layer is the primary computational bottleneck. Our preliminary analysis suggests that while the grid resolution required for DNS grows rapidly, the information content, quantified by the bond dimension χ required to maintain a fixed fidelity, could scale significantly more favorably. We present results for RBC up to Ra = 1010 (Re ∼ 105), utilizing an implicit-explicit time-stepping scheme entirely in the MPS framework. Our simulations achieve a parameter compression ratio of > 80% while maintaining key features in global transport statistics. We validate the method against full-state DNS, showing that the MPS ensemble reproduces the Nusselt number probability distribution (Wasserstein distance W1 of ≈ 10%). Furthermore, spectral analysis confirms that the method correctly captures the inertial energy cascade before degrading at the truncation noise floor. These results suggest that quantum-inspired methods offer a scalable pathway to simulate extreme-scale convection regimes currently inaccessible to classical grid-based methods. REFERENCES [1] S. Grossmann and D. Lohse, “Scaling in thermal convection: a unifying theory,” Journal of Fluid Mechanics, vol. 407, pp. 27–56, 2000. [2] N. Gourianov, M. Lubasch, S. Dolgov, Q. Y. van den Berg, H. Babaee, P. Givi, M. Kiffner, and D. Jaksch, “A quantum-inspired approach to exploit turbulence structures,” Nature Computational Science, vol. 2, p. 30, 2022. [3] L. H¨olscher, P. Rao, L. M¨uller, J. Klepsch, A. Luckow, T. Stollenwerk, and F. K. Wilhelm, “Quantum-inspired fluid simulation of 2D turbulence with GPU acceleration,” arXiv preprint arXiv:2406.17823, 2024. [4] S. Pisoni, R. D. Peddinti, E. Tiunov, S. E. Guzman, and L. Aolita, “Compression, simulation, and