Learning interactions between Rydberg atoms

TL;DR

This paper presents a scalable method using graph neural networks to accurately learn and control the Hamiltonian parameters of Rydberg-atom quantum simulators, improving their precision despite experimental uncertainties.

Contribution

The authors introduce a GNN-based Hamiltonian learning approach with a theoretical foundation, enabling accurate parameter estimation and system extrapolation in Rydberg-atom arrays.

Findings

GNN accurately predicts Hamiltonian parameters from correlation data.

Method extrapolates beyond training system size and shape.

Theoretical proof of correlation-function and Hamiltonian parameter bijection.

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 tweezers 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 (DMRG) 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, both regarding 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 to 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.