A programmable quantum simulator based on two-dimensional arrays of neutral atoms with tunable interactions has been demonstrated. The system uses deterministically prepared arrays of neutral atoms, with strong interactions controlled via coherent atomic excitation into Rydberg states. This approach enables the realization of a quantum spin model with tunable interactions for system sizes ranging from 64 to 256 qubits. The system was benchmarked by creating and characterizing high-fidelity antiferromagnetically ordered states, and the universal properties of an Ising quantum phase transition in (2+1) dimensions were demonstrated. Several new quantum phases arising from the interplay between interactions and coherent laser excitation were created and studied, with the phase diagram experimentally mapped and the role of quantum fluctuations investigated. The quantum simulator was implemented using arrays of up to 256 neutral atoms, with tunable interactions. The system was used to explore quantum dynamics in one- and two-dimensional systems, to create high-fidelity and large-scale entanglement, and to perform parallel quantum logic operations. The system also demonstrated the potential for optical atomic clocks and other quantum technologies. The experiments were carried out on the second generation of an experimental platform, using a spatial light modulator to form a large, two-dimensional array of optical tweezers. The array was loaded with individual 87Rb atoms from a magneto-optical trap, and rearranged into programmable, defect-free patterns using a second set of moving optical tweezers. Qubits were encoded in the electronic ground state and the highly-excited n = 70 Rydberg state of each atom. The system was used to study quantum phase transitions, including the (2+1)D Ising quantum phase transition, and to explore the phase diagram of the square lattice, revealing new quantum phases such as the checkerboard, striated, and star phases. The system was also used to study quantum fluctuations in the striated phase, revealing the nature of the phase and its dependence on the quench phase. The results demonstrated the potential of programmable quantum simulators with tunable, long-range interactions for studying large quantum many-body systems that are challenging to access with state-of-the-art computational tools. The experiments also demonstrated the potential for quantum information processing, including the study of non-equilibrium entanglement dynamics, topological quantum states of matter, lattice gauge theories, and broader classes of spin models. The results highlight the importance of quantum coherence and the potential for hardware-efficient quantum algorithms and protocols for quantum error correction and fault-tolerant control. The experiments also demonstrated the potential for efficient implementation of novel algorithms for quantum optimization and sampling.A programmable quantum simulator based on two-dimensional arrays of neutral atoms with tunable interactions has been demonstrated. The system uses deterministically prepared arrays of neutral atoms, with strong interactions controlled via coherent atomic excitation into Rydberg states. This approach enables the realization of a quantum spin model with tunable interactions for system sizes ranging from 64 to 256 qubits. The system was benchmarked by creating and characterizing high-fidelity antiferromagnetically ordered states, and the universal properties of an Ising quantum phase transition in (2+1) dimensions were demonstrated. Several new quantum phases arising from the interplay between interactions and coherent laser excitation were created and studied, with the phase diagram experimentally mapped and the role of quantum fluctuations investigated. The quantum simulator was implemented using arrays of up to 256 neutral atoms, with tunable interactions. The system was used to explore quantum dynamics in one- and two-dimensional systems, to create high-fidelity and large-scale entanglement, and to perform parallel quantum logic operations. The system also demonstrated the potential for optical atomic clocks and other quantum technologies. The experiments were carried out on the second generation of an experimental platform, using a spatial light modulator to form a large, two-dimensional array of optical tweezers. The array was loaded with individual 87Rb atoms from a magneto-optical trap, and rearranged into programmable, defect-free patterns using a second set of moving optical tweezers. Qubits were encoded in the electronic ground state and the highly-excited n = 70 Rydberg state of each atom. The system was used to study quantum phase transitions, including the (2+1)D Ising quantum phase transition, and to explore the phase diagram of the square lattice, revealing new quantum phases such as the checkerboard, striated, and star phases. The system was also used to study quantum fluctuations in the striated phase, revealing the nature of the phase and its dependence on the quench phase. The results demonstrated the potential of programmable quantum simulators with tunable, long-range interactions for studying large quantum many-body systems that are challenging to access with state-of-the-art computational tools. The experiments also demonstrated the potential for quantum information processing, including the study of non-equilibrium entanglement dynamics, topological quantum states of matter, lattice gauge theories, and broader classes of spin models. The results highlight the importance of quantum coherence and the potential for hardware-efficient quantum algorithms and protocols for quantum error correction and fault-tolerant control. The experiments also demonstrated the potential for efficient implementation of novel algorithms for quantum optimization and sampling.