The deterministic generation and evolution of highly entangled quantum many-body states presents one of the biggest frontiers in current research. It is essential to quantum computing architectures, quantum chemistry, quantum-enhanced precision measurements, and it allows for quantum simulations of condensed matter models. In recent years, this spectacular premise has triggered enormous interest in academic research, government agencies, technology industry, and the public. Entanglement encodes the detailed structure of the quantum states that underlie physical systems, with fundamental connections to the physics we observe. In recent years, a number of platforms have emerged that are striving to achieve such systems on a scale exceeding classical computations, including superconducting circuits, trapped ions, optical tweezer arrays, and solid-state defects. In this context neutral atoms, which had traditionally rather been used for ensemble-based measurements, garnered much attraction through the revolutionary advances of quantum gas microscopy. However, a key challenge in those approaches remains the efficient creation of highly entangled states. Owing to their geometry, entanglement in those platforms is typically generated through two-body operations among neighbouring qubits. This makes these platforms particularly suitable to create entangled states with local correlations. For some quantum algorithms, efficient scalings have been found theoretically that are faster than for a classical processor. Yet, many computation tasks are related to graph problems graph problems with high connectivity, where local two-qubit operations become inefficient. A much more efficient entanglement generation could be achieved with non-local operations. In such a system, entanglement can spread super ballistically, and new target states can be reached. Recent theoretical considerations have found much more favourable scalings with system size for a number of quantum algorithms. The possibilities and the performance can be boosted even further by going from two- to multi-qubit operations. Despite those exciting opportunities, however, experimental implementations of such a system remain elusive, due to technical challenges. With OptimAL, I intend to build a research program that addresses these challenges, to push the frontier in exploring few to many-body quantum states. With a revolutionary new platform, I will reach beyond the paradigm of local operations, and instead explore the opportunities of entanglement generation through non-local multi-qubit operations. Recent advances in the fabrication of optical cavities, as well as in the microscopic control of individual atoms allow me now to bring together the relevant techniques for this crucial step. I will explore how many-body phenomena emerge within a highly entangled system whose size exceeds the available computational power of classical processors. The experiments described in this proposal will have far-reaching impact on quantum information processing, quantum many-body physics and computational sciences. Several platforms have demonstrated quantum many-body dynamics with single-qubit control, however, the experimental implementation of quantum optimization algorithms in quantum systems is still in its infancy. Apart from early experimental attempts on annealing in superconducting systems, whose quantum aspects have been debated, some optimization algorithms have been recently demonstrated on few qubit systems with trapped ions and superconducting circuits. However, a key challenge in those implementations is the lack of efficient non-local entangling operations: many optimization tasks are graph problems with high connectivity, where local two-qubit operations become inefficient. A promising approach to create non-local, multi-qubit entanglement is to use light as a mediator for interactions among neutral atoms. This technique is well-established in the context of atomic ensembles that are coupled to the light field of an optical cavity. To date, those couplings have mostly been studied collectively for atomic ensembles, whereas microscopic control, has remained limited to two particles. Until today, the realization of a platform with programmable connectivity for quantum optimization tasks has remained elusive. The platform is highly innovative, as atom-light interactions have not yet been harnessed for quantum many-body dynamics with single-atom control. Our approach complements existing quantum computing platforms, which focus on nearest-neighbour interactions and two-qubit interactions. As a consequence, the enormous flexibility provided by our setup is expected to lead to significant advances in quantum information processing, as it allows us to implement quantum optimization algorithms that are currently out of reach for state-of the-art platforms.