Thermodynamic sampling of materials using neutral-atom quantum computers

Neutral-atom quantum hardware has emerged as a promising platform for programmable many-body physics. In this work, we develop and validate a practical framework for extracting thermodynamic properties of materials using such hardware. As a test case, we consider nitrogen-doped graphene. Starting from Density Functional Theory (DFT) formation energies, we map the material energetics onto a Rydberg-atom Hamiltonian suitable for quantum annealing by fitting an on-site term and distance-dependent pair interactions. The Hamiltonian derived from DFT cannot be implemented directly on current QuEra devices, as the largest energy scale accessible on the hardware is two orders of magnitude smaller than the target two-body interaction in the material. To overcome this limitation, we introduce a rescaling strategy based on a single parameter, $\alpha_v$, which ensures that the Boltzmann weights sampled by the hardware correspond exactly to those of the material at an effective temperature $T' = \alpha_vT$, where $T$ is the device sampling temperature. This rescaling also establishes a direct correspondence between the global laser detuning $\Delta_g$ and the grand-canonical chemical potential $\Delta\mu$. We validate the method on a 28-site graphene nanoflake using exhaustive enumeration, and on a larger 78-site system where Monte Carlo sampling confirms preferential sampling of low-energy configurations.