Benchmarking highly-entangled states on a large-scale analog quantum simulator

Quantum devices have reached a competitive stage where classical computers struggle to accurately represent the highly-entangled quantum states targeted in experiments. Here, we utilize a high-fidelity, Rydberg quantum simulator to perform fidelity benchmarking in the high entanglement regime where exact classical simulation becomes impractical. Our approach involves a learning-based extrapolation protocol for benchmarking a 60-atom system, along with the introduction of a new, highly-efficient approximate classical algorithm. Additionally, we develop an efficient estimator for mixed-state entanglement, demonstrating the competitiveness of our quantum simulator with state-of-the-art digital quantum devices. We also evaluate the cost of approximate classical simulation, which enables us to quantify the boundary between quantum and classical systems. Our results provide a new paradigm for evaluating the performance of both analog and digital quantum devices in the beyond-classically-exact regime.