Thermodynamic sampling of materials using neutral-atom quantum computers
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.
Summary
This paper explores the use of neutral-atom quantum computers for thermodynamic sampling of materials, specifically focusing on nitrogen-doped graphene. The main challenge addressed is mapping the material's energetics, derived from Density Functional Theory (DFT), onto a Rydberg-atom Hamiltonian suitable for quantum annealing on the QuEra Aquila device. A key limitation is the significant difference in energy scales between the DFT calculations and the hardware's capabilities, where the hardware's accessible energy scale is two orders of magnitude smaller than the target two-body interaction in the material. To overcome this, the authors introduce a novel rescaling strategy using a single parameter, α_v, which effectively adjusts the temperature scale. This ensures that the Boltzmann weights sampled by the quantum hardware correspond to those of the material at an effective temperature T' = α_v * T, where T is the device's sampling temperature. This rescaling also establishes a direct mapping between the global laser detuning (Δ_g) and the grand-canonical chemical potential (Δμ). The method is validated on a 28-site graphene nanoflake through exhaustive enumeration and on a larger 78-site system using Monte Carlo sampling, demonstrating preferential sampling of low-energy configurations. This work matters because it provides a practical framework for extracting thermodynamic properties of materials using neutral-atom quantum hardware, bridging the gap between theoretical models and experimental implementations.
Key Insights
- •Rescaling Parameter α_v: The introduction of the rescaling parameter α_v = (R_min_NN / R_DFT_NN)^6 is crucial for mapping DFT-derived energies to the hardware. It allows the hardware to effectively sample the Boltzmann distribution of the material at a rescaled temperature. For their system, α_v ≈ 236.69.
- •Temperature Rescaling: The paper analytically demonstrates that the annealing temperature T on the hardware corresponds to an effective material temperature T' = α_v * T. This allows for tuning the effective temperature by adjusting the interatomic spacing.
- •Chemical Potential Mapping: A direct correspondence is established between the hardware's global laser detuning Δ_g and the grand-canonical chemical potential Δμ, specifically Δ_g = -(V_α_v + Δμ/α_v), linking device control parameters to thermodynamic variables.
- •Validation on 28-site System: Exhaustive enumeration of the 28-site graphene nanoflake validates the method, yielding a best-fit effective sampling temperature of T = 41 μK on the QuEra device.
- •Monte Carlo Comparison on 78-site System: Unbiased Monte Carlo sampling on the 78-site system confirms that the quantum annealer preferentially samples low-energy configurations, consistent with Boltzmann statistics, highlighting the QPU's efficiency in reaching relevant configurations.
- •Limitations: The current implementation is limited to two-dimensional systems due to hardware constraints. The paper uses a finite, non-periodic nanoflake, which deviates from the periodic boundary conditions used in the DFT calculations.
Practical Implications
- •Materials Discovery: This research provides a new avenue for materials discovery by leveraging neutral-atom quantum computers to explore the thermodynamic properties of complex materials, such as solid solutions.
- •Beneficiaries: Materials scientists, computational chemists, and quantum computing researchers can benefit from this framework.
- •Hardware Parameter Tuning: Practitioners can use the derived mapping to tune the hardware parameters (laser detuning and interatomic spacing) to effectively sample desired thermodynamic conditions in materials.
- •Future Research: The authors suggest that the method is readily applicable to three-dimensional materials as hardware capabilities evolve. They also propose that this work represents a potential building block for future hybrid workflows that combine continuous-time annealing and digital quantum algorithms for materials discovery.