The quantum properties of photons -- allowing low-loss long-distance transmission, multiplexing large amounts of quantum information into a single channel, and operations in standard, room-temperature settings -- yield great promise for scalable quantum computing (QC). However, low interaction is their great weakness for quantum information processing (QIP), as quantum circuits require photon-photon interactions. To date, two-photon interactions have only been facilitated either probabilistically with low efficiency or between individual photons via intermediaries with errors much too large for practical QIP. PANDA has an ambitious core goal of building the foundation for a photonic quantum computer: an array of neutral rubidium atoms with subwavelength spacing carefully designed to harness collective effects to implement lossless, deterministic photon-photon interactions. Combined with novel high-efficiency single-photon handling, we will construct a powerful platform for strong, efficient, controllable non-linear operations with many QIP applications. These include deterministic two-photon quantum gates with unprecedented efficiency and repeat rates. We will especially apply our platform to continuous-variable (CV) QIP, particularly Measurement-Based QC, which fully utilizes quantum light field advantages, but has been hindered by the lack of deterministic non-Gaussian photon state generation and is not addressed in the Quantum Flagship. Using our platform for deterministic photon subtraction will address this and, with a CV theory roadmap we will develop, pave the way for photonic QC. Our two-photon gates will also be applicable to Discrete-Variable QIP, placing PANDA in a complementary position to many possible portfolio projects. PANDA incorporates world-class experimentalists and theorists from leading research groups and SMEs with the expertise required to develop core technology that will both yield marketable IPR and fulfill our ambitious objectives.