Abstract: The realization of large-scale controlled quantum systems is an exciting frontier in modern physical science. Such systems can provide insights into fundamental properties of quantum matter, enable the realization of exotic quantum phases, and ultimately offer a platform for quantum information processing that could surpass any classical approach.

Recently, reconfigurable arrays of neutral atoms with programmable Rydberg interactions have become promising systems for studying such quantum many-body phenomena, because of their isolation from the environment and high degree of control. Using this approach, we demonstrate high-fidelity manipulation of individual atoms and entangled atomic states. Furthermore, we realize a programmable Ising-type quantum spin model with tunable interactions and system sizes up to 51 qubits. Within this model, we observe transitions into ordered states that break various discrete symmetries and study the critical dynamics across quantum phase transitions. Prospects for scaling this approach beyond hundreds of qubits and the implementation of quantum algorithms will be discussed.