Rydberg physics for quantum computing in arrays of neutral atom qubits

Ultracold neutral atoms have recently emerged as a scalable quantum computing platform. Their long coherence times and parallel coherent control portend the realization of high-fidelity quantum operations on large arrays of qubits. Interactions between neutral atoms in Rydberg states provide a means to 2-qubit and multi-qubit gates. Understanding the energy level structure of Rydberg atoms and their interactions are a necessary prerequisite to designing gate schemes. To this end we discuss Rydberg interactions for quantum computing with trapped single atoms, including simulations of the full Hilbert space relevant to 2-qubit gates.