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  • Open Access

Learning Interactions between Rydberg Atoms

Olivier Simard1,2,*,†, Anna Dawid3,4,*, Joseph Tindall3, Michel Ferrero1,2, Anirvan M. Sengupta3,5,6, and Antoine Georges1,2,3,7

  • 1Collège de France, Paris Sciences & Lettres (PSL) University, 11 place Marcelin Berthelot, 75005 Paris, France
  • 2Centre de physique théorique (CPHT), CNRS, École Polytechnique, Institut Polytechnique de Paris, F-91128 Palaiseau, France
  • 3Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA
  • 4〈aQaL〉 Applied Quantum Algorithms – Leiden Institute of Advanced Computer Science & Leiden Institute of Physics, Universiteit Leiden, 2333 CA Leiden, The Netherlands
  • 5Center for Computational Mathematics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
  • 6Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
  • 7Department of Quantum Matter Physics (DQMP), Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève, Switzerland

  • *These two authors contributed equally to this work.
  • †Contact author: olivier.simard@polytechnique.edu
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PRX Quantum 6, 030324 – Published 8 August, 2025

DOI: https://doi.org/10.1103/f58h-zxs3

Abstract

Quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully controllable, allowing for precise tuning of the microscopic physical parameters that define their implementation. We consider Rydberg-atom arrays, a promising platform for quantum simulations. Experimental control of such arrays is limited by the imprecision on the optical-tweezer positions when assembling the array, hence introducing uncertainties in the simulated Hamiltonian. In this work, we introduce a scalable approach to Hamiltonian learning using graph neural networks (GNNs). We employ the density-matrix renormalization group to generate ground-state snapshots of the transverse-field Ising model realized by the array, for many realizations of the Hamiltonian parameters. Correlation functions reconstructed from these snapshots serve as input data to carry out the training. We demonstrate that our GNN model has a remarkable capacity to extrapolate beyond its training domain, regarding both the size and the shape of the system, yielding an accurate determination of the Hamiltonian parameters with a minimal set of measurements. We prove a theorem establishing a bijective correspondence between the correlation functions and the interaction parameters in the Hamiltonian, which provides a theoretical foundation for our learning algorithm. Our work could open the road to feedback control of the positions of the optical tweezers, hence providing a decisive improvement of analog quantum simulators.

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Popular Summary

Quantum simulators are emerging as powerful tools to study complex quantum systems, especially those with strong entanglement that are beyond classical computation. They promise to help us understand exotic phases of matter and solve open problems in quantum many-body physics. But to reach this potential, simulators must be highly precise—both in how they are built and how we interpret their behavior.

We focus on Rydberg-atom arrays, where individual atoms are trapped in optical tweezers and interact with each other. Small imperfections in the atom positions introduce disorder in the Hamiltonian of the system, limiting control and predictability. To address this, we develop a Hamiltonian-learning method using graph neural networks (GNNs). Trained on ground-state data from the transverse-field Ising model (generated via the density-matrix renormalization group), the GNN learns to infer interaction parameters from correlation functions. Remarkably, it can extrapolate to larger or differently shaped arrays than those on which it was trained. We also prove a bijective relationship between correlation functions and Hamiltonian parameters, giving a solid theoretical foundation to the method.

This approach moves us closer to experimental feedback and fine-tuned quantum simulations. The network ability to extrapolate bridges the gap between theoretical models and experiments and can be used to solve challenges beyond Hamiltonian learning. In the future, it could enable adaptive control of atom positions, making analog quantum simulators more accurate and ultimately more useful for exploring quantum many-body physics.

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PRX Quantum 6, 030324– Published 8 August, 2025
  • Received 7 January 2025
  • Revised 18 April 2025
  • Accepted 8 July 2025
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