Learning Interactions between Rydberg Atoms

PRX Quantum, vol. 6

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.

Authors 5

1. Olivier Simard corresponding

   École Polytechnique · Collège de France

   Affiliation as printed

   Collège de France

   École Polytechnique

2. Anna Dawid corresponding Aachen

   Leiden University · Flatiron Institute

   Affiliation as printed

   Flatiron Institute

   Universiteit Leiden

   Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA

3. Joseph Tindall

   Flatiron Institute

   Affiliation as printed

   Flatiron Institute

   Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA

4. Michel Ferrero

   École Polytechnique · Collège de France

   Affiliation as printed

   Collège de France

   École Polytechnique

5. Antoine Georges

   University of Geneva · École Polytechnique · Collège de France · Flatiron Institute

   Affiliation as printed

   Collège de France

   Flatiron Institute

   Université de Genève

   École Polytechnique

   Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA