Towards learning the disordered Hamiltonian with graph neural networks from experimental snapshots*

Quantum simulators promise to solve problems that are not accessible for classical computers, such as quantum many-body problems with many degrees of freedom and large-scale entanglement. To achieve this goal, quantum simulators must be fully controllable and efficiently validated. In particular, inferring the experimentally realized Hamiltonian through a scalable number of measurements constitutes the challenging task of Hamiltonian learning, which is especially important in the presence of experimental noise, like disordered positions of optical tweezers.

In this work, we present a scalable approach to Hamiltonian learning with graph neural networks (GNNs). Using numerically simulated snapshots of a quantum system across its time evolution as input data, we infer the underlying interactions between the spins on an example of the experimentally relevant two-dimensional transverse-field Ising model. The input-size invariance of GNNs should allow training them on numerically simulated data of varying size and applying them to larger-scale experimental snapshots, e.g., to infer the disordered interactions between Rydberg atoms in optical tweezers.