Quantum computers, which take advantage of the strange quantum properties of superposition and entanglement, can theoretically solve certain problems exponentially faster than classical computers. Current systems, however, are orders of magnitude smaller than what would be needed for the most interesting applications, and all leading platforms have challenges with increasing their sizes. With their perfect replicability, ability to store quantum information for times much longer than any other quantum system demonstrated thus far, and high-fidelity operations, trapped atomic ions have many advantages compared with other quantum information systems. However, increasing the number of ions in a single trap beyond a few hundred is a formidable, if not impossible, feat. We thus develop a modular system that links multiple ion traps using the photons emitted from the ions and distributed entanglement, or as Einstein described it, “spooky action at a distance.” Here, we discuss the architecture of our system and the physics that describes its behavior, and present results for one of the key components of the system–the generation of a pure single photon entangled with an ion with high fidelity. Our current two-ion trap modular quantum computer serves as a proof-of-principle for the scaling of ion trap systems using photonic links and as a demonstration of a small quantum network.