The authors demonstrate a method to create controlled many-body quantum matter using a 51-atom quantum simulator. They combine deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. This setup realizes a programmable Ising-type quantum spin model with tunable interactions and system sizes up to 51 qubits. The study observes phase transitions into spatially ordered states that break various discrete symmetries, verifies the high-fidelity preparation of these states, and investigates the dynamics across the phase transition in large atom arrays. Specifically, they observe robust many-body dynamics corresponding to persistent oscillations of the order after a rapid quantum quench, which results from a sudden transition across the phase boundary. The method provides a way to explore many-body phenomena on a programmable quantum simulator and could enable the realization of new quantum algorithms. The experimental setup and techniques used to achieve these results are detailed, including the trapping and Rydberg laser setups, interaction strength measurements, and methods for correcting for finite detection fidelity. The authors also discuss the implications of their findings for the study of quantum dynamics and the potential for further applications in quantum information processing.The authors demonstrate a method to create controlled many-body quantum matter using a 51-atom quantum simulator. They combine deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. This setup realizes a programmable Ising-type quantum spin model with tunable interactions and system sizes up to 51 qubits. The study observes phase transitions into spatially ordered states that break various discrete symmetries, verifies the high-fidelity preparation of these states, and investigates the dynamics across the phase transition in large atom arrays. Specifically, they observe robust many-body dynamics corresponding to persistent oscillations of the order after a rapid quantum quench, which results from a sudden transition across the phase boundary. The method provides a way to explore many-body phenomena on a programmable quantum simulator and could enable the realization of new quantum algorithms. The experimental setup and techniques used to achieve these results are detailed, including the trapping and Rydberg laser setups, interaction strength measurements, and methods for correcting for finite detection fidelity. The authors also discuss the implications of their findings for the study of quantum dynamics and the potential for further applications in quantum information processing.