Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on classical approaches. Here we demonstrate a method for creating controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states. We realize a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits. Within this model, we observe phase transitions into spatially ordered states that break various discrete symmetries, verify the high-fidelity preparation of these states and investigate the dynamics across the phase transition in large arrays of atoms. In particular, we observe robust many-body dynamics corresponding to persistent oscillations of the order after a rapid quantum quench that results from a sudden transition across the phase boundary. Our method provides a way of exploring many-body phenomena on a programmable quantum simulator and could enable realizations of new quantum algorithms.

At the most fundamental level, the interaction between light and matter is manifested by the emission and absorption of single photons by single quantum emitters. Controlling light-matter interaction is the basis for diverse applications ranging from light technology to quantum-information processing. Many of these applications are nowadays based on photonic nanostructures strongly benefitting from their scalability and integrability. The confinement of light in such nanostructures imposes an inherent link between the local polarization and propagation direction of light. This leads to chiral light-matter interaction, i.e., the emission and absorption of photons depend on the propagation direction and local polarization of light as well as the polarization of the emitter transition. The burgeoning research field of chiral quantum optics offers fundamentally new functionalities and applications both for single emitters and ensembles thereof. For instance, a chiral light-matter interface enables the realization of integrated non-reciprocal single-photon devices and deterministic spin-photon interfaces. Moreover, engineering directional photonic reservoirs opens new avenues for constructing complex quantum circuits and networks, which may be applied to simulate a new class of quantum many-body systems.

We report the implementation of universal two-and three-qubit entangling gates on neutral atom qubits encoded in long-lived hyperfine ground states. The gates are mediated by excitation to strongly interacting Rydberg states, and are implemented in parallel on several clusters of atoms in a one-dimensional array of optical tweezers. Specifically, we realize the controlled-phase gate, enacted by a novel, fast protocol involving only global coupling of two qubits to Rydberg states. We benchmark this operation by preparing Bell states with fidelity F ≥ 95.0(2)%, and extract gate fidelity ≥ 97.4(3)%, averaged across five atom pairs. In addition, we report a proof-of-principle implementation of the three-qubit Toffoli gate, in which two control atoms simultaneously constrain the behavior of one target atom. These experiments demonstrate key ingredients for high-fidelity quantum information processing in a scalable neutral atom platform.