Data-Driven Quantum Simulation of Artificial Quantum Materials with Rydberg Atoms

Programmable quantum simulators based on Rydberg atom arrays provide a versatile platform for data-driven quantum simulation of strongly correlated systems, combinatorial optimization problems, and artificial quantum materials. In this review, we present a unified perspective on how materials-inspired effective Hamiltonians can be engineered and probed in Rydberg arrays, highlighting representative phenomena such as quantum phase transitions, frustrated spin-liquid-like states, symmetry-protected topological phases, and nonequilibrium dynamics. We further discuss recent progress in machine learning-based approaches, including phase identification from experimental snapshots, neural network quantum states, Hamiltonian learning, and quantum reservoir computing. A central theme is the emergence of closed-loop classical-quantum hybrid workflows, in which quantum simulation, measurement, and classical inference are integrated through iterative feedback. These developments position Rydberg atom arrays not only as programmable simulators but also as data-driven platforms for the scalable exploration, characterization, and design of complex quantum materials.