Colloquium: Quantum networks with trapped ions

Quantum computation and communication exploit the quantum properties of superposition and entanglement in order to perform tasks that may be impossible using classical means. In this Colloquium recent experimental and theoretical progress in the generation of entangled quantum networks based on the use of optical photons as carriers of information between fixed trapped atomic ion quantum memories are reviewed. Taken together, these quantum platforms offer a promising vision for the realization of a large-scale quantum network that could impact the future of communication and computation.