Thermodynamic sampling of materials using neutral-atom quantum computers

TL;DR

This work presents a practical framework for thermodynamic sampling of materials by mapping DFT formation energies onto a neutral-atom Rydberg Hamiltonian and using quantum annealing to sample Boltzmann-like configurations. A single rescaling parameter $\alpha_v$ is introduced to reconcile hardware energy scales with material energetics, establishing $T' = \alpha_v T$ and a detuning–chemical potential mapping $\Delta_g \leftrightarrow \Delta\mu$, enabling accurate thermodynamic predictions from hardware. The approach is validated on nitrogen-doped graphene for 28- and 78-site nanoflakes, using exhaustive enumeration and unbiased Monte Carlo benchmarks, and shown to reproduce the expected thermodynamic behavior while highlighting efficiency advantages of quantum sampling in low-energy regions. Temperature control is further demonstrated by tuning the interatomic spacing $R_{NN}$ to realize different effective temperatures, offering a direct, experimentally accessible handle on sampling distributions. The study outlines a pathway toward integrating DFT-based energetics with neutral-atom quantum hardware and points to future extensions for three-dimensional materials and higher-order interactions, paving the way for hybrid classical-quantum workflows in materials discovery.

Abstract

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, $α_v$, which ensures that the Boltzmann weights sampled by the hardware correspond exactly to those of the material at an effective temperature $T' = α_vT$, where $T$ is the device sampling temperature. This rescaling also establishes a direct correspondence between the global laser detuning $Δ_g$ and the grand-canonical chemical potential $Δμ$. 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.

Figures (7)

• Figure 1: Structure of the graphene model used in this study and its mapping to the quantum hardware. a Periodic structure employed for the CRYSTAL DFT calculations. b Graphene nanoflake with 28 atoms used in the exhaustive search simulations (Section \ref{['subsec:es']}). c Graphene nanoflake with 78 atoms used in the Monte Carlo simulations (Section \ref{['subsec:mc']}). d Zoom-in illustrating the distance between lattice sites in terms of the distance between nearest neighbours $R_{\mathrm{NN}}$. e Mapping of the structure in panel c onto neutral atoms using $R_{\mathrm{NN}} = 4.0\,\mu$m.
• Figure 2: Effect of scaling on the energy levels in the material and the hardware. Top left: energy levels of pure graphene (C$_{\text{M}}$) and graphene doped with one (C$_{(\text{M}-1)}$N) or two (C$_{(\text{M}-2)}$N$_2$) nitrogen atoms. $V^{\mathrm{DFT}}$ denotes the nitrogen on-site energy, and $V_{\mathrm{NN}}^{\mathrm{DFT}}$ the two-body potential between neighbouring sites. Top right: $\alpha_v$ is the scaling factor used to map the DFT energies onto the hardware, subject to its constraints. $V_{\mathrm{NN}}^{\alpha_v}$ is the scaled two-body potential between neighbouring sites, and $V^{\alpha_v}$ is the nitrogen on-site energy scaled consistently. Bottom: visual comparison (not to scale) of the energy levels with and without scaling in the material and the hardware. The term $\pm \Delta_g^{\mathrm{max}}$ represents the global detuning range of the annealer. $\Delta\mu$ is the chemical potential range explored in terms of the DFT energy levels of the material, while $\Delta\mu^{\alpha_v}$ is the corresponding range scaled by $\alpha_v$.
• Figure 3: QPU and exhaustive search data for the 28-site structure shown in Fig. \ref{['fig:graphene_model']}b. Panel a reports the average nitrogen concentration as a function of $\Delta\mu$ (bottom $x$-axis) and $\Delta_g$ (top $x$-axis). Black dots indicate QPU data obtained at $R_{\mathrm{NN}} = 4 \mu$m. Blue and red curves correspond to exhaustive search results at $T = 1 \mu$K and $T = 60 \mu$K, respectively, with the grey shaded area marking the range between these two temperatures. The dashed black line shows the result at $T = 41 \mu$K, which minimises the RMSE with respect to the QPU data, as highlighted by the red dot in panel b. Each subplot in panel c corresponds to a different value of the chemical potential and displays the distribution of nitrogen concentration. The orange and blue dashed vertical lines mark the average concentration obtained from the QPU and from the exhaustive search at $T = 41 \mu$K, respectively. Solid bars of the same colours illustrate the spread of concentrations around these mean values. Panels d and e display the number of states explored by the annealer (orange line) and by the exhaustive search (blue line) for the distribution at $\Delta\mu=-3.81\times10^{-4}$ eV and $\Delta\mu=-3.61\times10^{-4}$ eV, respectively.
• Figure 4: QPU and Unbiased Monte Carlo (UMC) data for the 78-site structure shown in Fig. \ref{['fig:graphene_model']}c. Panel a shows the average nitrogen concentration as a function of $\Delta\mu$ (bottom $x$-axis) and $\Delta_g$ (top $x$-axis). Black dots and lines indicate QPU data obtained at $R_{\mathrm{NN}} = 4\,\mu$m, while coloured curves correspond to UMC results at $T = 41\,\mu$K for increasing sample sizes. Panel b compares the number of states explored by the annealer (orange line) and by the UMC (blue line) for $\Delta_g = 0$ eV. Note that the $y$-axes have different orders of magnitude. Panel c shows the fraction of states per nitrogen concentration explored by the QPU (orange bars) and by the UMC (blue bars) at $\Delta_g = 0$ eV.
• Figure 5: Panel a shows the average nitrogen concentration in the 78-site graphene structure depicted in Fig. \ref{['fig:graphene_model']}c as a function of the chemical potential $\Delta\mu$ at different interatomic distances in the hardware. The inset in this panel shows an example of structure returned by the annealer in the plateau region of the $R_{\mathrm{NN}}=5\mu$m (blue) line. Panel b displays how the chemical potential varies as a function of the global detuning $\Delta_g$ for the three interatomic separations obtained according to Eq. \ref{['eq:def_Delta_mu^alpha_v']}